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https://github.com/Tojarieh97/VQE
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Tojarieh97
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%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from linear_entangelment_and_full_entangelment_ansatz_circuits import *
def get_ansatz_state(thetas, ansatz_entangelment, input_state):
if ansatz_entangelment=="full":
return get_full_entangelment_ansatz(QUBITS_NUM, thetas, input_state)
if ansatz_entangelment=="linear":
return get_linear_entangelment_ansatz(QUBITS_NUM, thetas, input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(reduced_pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian, ansatz_entangelment):
initial_eigenvector = np.identity(N)[0]
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
ansatz_state = get_ansatz_state(thetas, ansatz_entangelment, initial_eigenvector)
L = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(L)
return L
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian, ansatz_entangelment):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=PARAMS_NUM)
optimizer_result = minimize(cost_function,
x0=initial_thetas,
args=(hamiltonian, ansatz_entangelment),
method="POWELL",
options={"maxiter":NUM_ITERATIONS,
"return_all": True,
"disp": True})
optimal_thetas = optimizer_result.x
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian, ansatz_entangelment):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian, ansatz_entangelment)
print(optimal_thetas)
initial_eigenvector = np.identity(N)[0]
optimal_ansatz_state = get_ansatz_state(optimal_thetas, ansatz_entangelment, initial_eigenvector)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian):
eigen_values = LA.eigvals(hamiltonian.to_matrix())
print(sorted(eigen_values))
return min(sorted(eigen_values))
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("\nApproximated Eigenvalue:")
print(approximated_eigenvalue)
print("\nApproximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin=3)
approximated_energies = []
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies[-NUM_ITERATIONS])
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.grid()
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, I, H, Y
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 3
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit.opflow import X, Z, I
transverse_ising_3_qubits = 0.0 * (I^I^I) \
+ 0.012764169333459807 * (X^I^I) \
+ 0.7691573729160869 * (I^X^I) \
+ 0.398094746026449 * (Z^Z^I) \
+ 0.15250261906586637 * (I^I^X) \
+ 0.2094051920882264 * (Z^I^Z) \
+ 0.5131291860752999 * (I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 2
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
transverse_ising_2_qubits = 0.13755727363376802 * (I^X) \
+ 0.43305656297810435 * (X^I) \
+ 0.8538597608997253 * (Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
from qiskit.opflow import X, Z, I
H2_molecule_Hamiltonian_2_qubits = -0.5053051899926562*(I^I) + \
-0.3277380754984016*(Z^I) + \
0.15567463610622564*(Z^Z) + \
-0.3277380754984016*(I^Z)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits, "linear")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits, "full")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from linear_entangelment_and_full_entangelment_ansatz_circuits import *
def get_ansatz_state(thetas, ansatz_entangelment, input_state):
if ansatz_entangelment=="full":
return get_full_entangelment_ansatz(QUBITS_NUM, thetas, input_state)
if ansatz_entangelment=="linear":
return get_linear_entangelment_ansatz(QUBITS_NUM, thetas, input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(reduced_pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in tqdm(zip(pauli_coeffs, pauli_strings)):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian, ansatz_entangelment):
initial_eigenvector = np.identity(N)[0]
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
ansatz_state = get_ansatz_state(thetas, ansatz_entangelment, initial_eigenvector)
L = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(L)
return L
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian, ansatz_entangelment):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=PARAMS_NUM)
optimizer_result = minimize(cost_function,
x0=initial_thetas,
args=(hamiltonian, ansatz_entangelment),
method="TNC",
options={"maxiter":NUM_ITERATIONS,
"disp": True})
optimal_thetas = optimizer_result.x
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian, ansatz_entangelment):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian, ansatz_entangelment)
print(optimal_thetas)
initial_eigenvector = np.identity(N)[0]
optimal_ansatz_state = get_ansatz_state(optimal_thetas, ansatz_entangelment, initial_eigenvector)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian):
eigen_values = LA.eigvals(hamiltonian.to_matrix())
print(sorted(eigen_values))
return min(sorted(eigen_values))
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("\nApproximated Eigenvalue:")
print(approximated_eigenvalue)
print("\nApproximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin=3)
initialize_approximated_energy_to_list_of_all_approximated_energies()
approximated_energies = []
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies[-NUM_ITERATIONS:])
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.grid()
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, I, H, Y
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 3
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 1000
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit.opflow import X, Z, I
transverse_ising_3_qubits = 0.0 * (I^I^I) \
+ 0.012764169333459807 * (X^I^I) \
+ 0.7691573729160869 * (I^X^I) \
+ 0.398094746026449 * (Z^Z^I) \
+ 0.15250261906586637 * (I^I^X) \
+ 0.2094051920882264 * (Z^I^Z) \
+ 0.5131291860752999 * (I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 2
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 1000
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
transverse_ising_2_qubits = 0.13755727363376802 * (I^X) \
+ 0.43305656297810435 * (X^I) \
+ 0.8538597608997253 * (Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits, "linear")
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits, "full")
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
from qiskit.opflow import X, Z, I
H2_molecule_Hamiltonian_2_qubits = -0.5053051899926562*(I^I) + \
-0.3277380754984016*(Z^I) + \
0.15567463610622564*(Z^Z) + \
-0.3277380754984016*(I^Z)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits, "linear")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits, "full")
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
from qiskit.circuit.library.standard_gates import RXGate, RZGate, CXGate, CZGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
def get_thetas_circuit(thetas, D2):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
for d in range(D2):
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
qc.append(CZGate(), [qr[0], qr[1]])
qc.append(CZGate(), [qr[1], qr[2]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
return qc
def get_phis_circuit(phis, D1, input_state):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
qc.initialize(input_state)
for d in range(D1):
qc.append(RXGate(phis[0]), [qr[2]])
qc.append(RXGate(phis[1]), [qr[3]])
qc.append(RZGate(phis[2]), [qr[2]])
qc.append(RZGate(phis[3]), [qr[3]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
return qc
def get_full_variational_quantum_circuit(thetas, phis, D1, D2, input_state):
thetas_quantum_circuit = get_thetas_circuit(thetas, D2)
phis_quantum_circuit = get_phis_circuit(phis, D1, input_state)
variational_quantum_circuit = phis_quantum_circuit.compose(thetas_quantum_circuit)
return variational_quantum_circuit
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import numpy as np
def get_first_k_eigenvectors_from_n_computational_basis(k, n):
n_computational_basis = np.identity(n)
return n_computational_basis[:k]
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 2**QUBITS_NUM
K = 4
w = 0.5
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 6
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 6
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(reduced_pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
k_ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[K-1])
approximated_energey = get_expectation_value(k_ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energey)
L_w = w*approximated_energey
for j in range(K-1):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
L_w += get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=PARAMS_NUM)
optimizer_result = minimize(cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="BFGS",
options={"maxiter":NUM_ITERATIONS,
"disp": True})
optimal_thetas = optimizer_result.x
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
print("### The optimal parameters found by the optimizer ###")
print(optimal_thetas)
optimal_circuit_params = prepare_circuit_params(optimal_thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
optimal_ansatz_state = get_ansatz_state(optimal_circuit_params, computational_eigenvectors[K-1])
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian):
eigen_values = LA.eigvals(hamiltonian.to_matrix())
print(sorted(eigen_values))
return min(sorted(eigen_values))
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("\nApproximated Eigenvalue:")
print(approximated_eigenvalue)
print("\nApproximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin=3)
approximated_energies = []
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies[-NUM_ITERATIONS:])
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.grid()
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, I, H, Y
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 3
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit.opflow import X, Z, I
transverse_ising_3_qubits = 0.0 * (I^I^I) \
+ 0.012764169333459807 * (X^I^I) \
+ 0.7691573729160869 * (I^X^I) \
+ 0.398094746026449 * (Z^Z^I) \
+ 0.15250261906586637 * (I^I^X) \
+ 0.2094051920882264 * (Z^I^Z) \
+ 0.5131291860752999 * (I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 2
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
transverse_ising_2_qubits = 0.13755727363376802 * (I^X) \
+ 0.43305656297810435 * (X^I) \
+ 0.8538597608997253 * (Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
from qiskit.opflow import X, Z, I
H2_molecule_Hamiltonian_2_qubits = -0.5053051899926562*(I^I) + \
-0.3277380754984016*(Z^I) + \
0.15567463610622564*(Z^Z) + \
-0.3277380754984016*(I^Z)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 2**QUBITS_NUM
K = 4
w = 0.5
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 6
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 6
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(reduced_pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in tqdm(zip(pauli_coeffs, pauli_strings)):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
k_ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[K-1])
approximated_energey = get_expectation_value(k_ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energey)
L_w = w*approximated_energey
for j in range(K-1):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
L_w += get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=PARAMS_NUM)
optimizer_result = minimize(cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="COBYLA",
options={"maxiter":NUM_ITERATIONS,
"disp": True})
optimal_thetas = optimizer_result.x
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
print("### The optimal parameters found by the optimizer ###")
print(optimal_thetas)
optimal_circuit_params = prepare_circuit_params(optimal_thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
optimal_ansatz_state = get_ansatz_state(optimal_circuit_params, computational_eigenvectors[K-1])
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian):
eigen_values = LA.eigvals(hamiltonian.to_matrix())
print(sorted(eigen_values))
return min(sorted(eigen_values))
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_minimum_exact_eigenvalue_of_hamiltonian(hamiltonian)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("\nApproximated Eigenvalue:")
print(approximated_eigenvalue)
print("\nApproximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin=3)
approximated_energies = []
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies[-NUM_ITERATIONS])
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.grid()
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, I, H, Y
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 3
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
from qiskit.opflow import X, Z, I
transverse_ising_3_qubits = 0.0 * (I^I^I) \
+ 0.012764169333459807 * (X^I^I) \
+ 0.7691573729160869 * (I^X^I) \
+ 0.398094746026449 * (Z^Z^I) \
+ 0.15250261906586637 * (I^I^X) \
+ 0.2094051920882264 * (Z^I^Z) \
+ 0.5131291860752999 * (I^Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_3_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_3_qubits, TI_approximated_eigenvalue)
QUBITS_NUM = 2
N = 2**QUBITS_NUM
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
CIRCUIT_DEPTH = 3
PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)
transverse_ising_2_qubits = 0.13755727363376802 * (I^X) \
+ 0.43305656297810435 * (X^I) \
+ 0.8538597608997253 * (Z^Z)
%%time
TI_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_2_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_2_qubits, TI_approximated_eigenvalue)
from qiskit.opflow import X, Z, I
H2_molecule_Hamiltonian_2_qubits = -0.5053051899926562*(I^I) + \
-0.3277380754984016*(Z^I) + \
0.15567463610622564*(Z^Z) + \
-0.3277380754984016*(I^Z)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_2_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_2_qubits, H2_approximated_eigenvalue)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 50
w = 0.5
approximated_energies = []
from qiskit import IBMQ
provider = IBMQ.enable_account('4cd532424f249f20233857b3b211eb28dfc0e790386bd2ea14d3e0d03c867dfcfec4c2c968e4693f1c9caf7b3f6fad3f6a6393065fb45719692fd1a5177536cb')
real_backend = provider.get_backend('ibmq_belem')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 6
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 6
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, real_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = real_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
k_ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[K-1])
approximated_energey = get_expectation_value(k_ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energey)
L_w = w*approximated_energey
for j in range(K-1):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
L_w += get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=12)
optimizer_result = minimize(cost_function,x0=initial_thetas,args=(hamiltonian),method="BFGS",options={"maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
print(optimal_thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
optimal_ansatz_state = get_ansatz_state(optimal_thetas, computational_eigenvectors[K-1])
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, k):
eigen_values = LA.eig(hamiltonian.to_matrix())[0]
print(sorted(eigen_values, reverse=True))
return sorted(eigen_values,reverse=True)[k-1]
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, K)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("Approximated K Eigenvalues:")
print(approximated_eigenvalue)
print("Approximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies)
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, Y, I, H, S
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
LiH_approximated_energies = [-7.086471480342895, -7.100658534270067, -7.099715987203259, -7.104706322802394, -7.0881767422400515, -7.094941901238781, -7.101189782415803, -7.091782649949064, -7.095129380762572, -7.089782186084561, -7.103641494347653, -7.08770304365008, -7.097466178879243, -6.927386893001271, -6.918605722866235, -6.929889900623873, -6.929547677497744, -6.9144751585444, -6.92705204011207, -6.928594209576469, -6.918356322098606, -6.922146575259048, -6.928167910638778, -6.920735015129623, -6.934524032800371, -6.9240609972824645, -7.054992091903585, -7.056718682779798, -7.047680065570422, -7.057958949601671, -7.049809365284406, -7.04886498241836, -7.061382947330433, -7.047727314056423, -7.05595544969352, -7.0549833626221155, -7.064687065647647, -7.04480704575676, -7.053986384203245, -7.079305098939433, -7.08780253307097, -7.079683274206787, -7.082864577262481, -7.074313240029014, -7.076075827379148, -7.094328957871822, -7.08496554875689, -7.08017425919163, -7.080091087607597, -7.091782059567345, -7.091247992689509, -7.070866930379006, -7.090286264563848, -7.104283776653907, -7.105507768659804, -7.082013868585181, -7.089272262553638, -7.093947194681023, -7.074106629342778, -7.098394252872861, -7.0959686725785405, -7.07952225336062, -7.095513342542343, -7.09416071736501, -7.096369979461571, -7.099848242069214, -7.084955688773306, -7.100455873892028, -7.093183696883554, -7.0975872306150345, -7.088097397700704, -7.106647897103562, -7.093977686069661, -7.087712543786841, -7.111504280126781, -7.1022363547755125, -7.087493749330183, -7.086287626873361, -7.093369560806178, -7.078161435586905, -7.09441449134148, -7.089607689893512, -7.0932238396900935, -7.111989359310854, -7.104929885548429, -7.091436536609016, -7.08666585935681, -7.082934757346767, -7.101100532138134, -7.088104163062988, -7.096424567809472, -7.099068194469176, -7.092174139685106, -7.093834778605302, -7.102211865551155, -7.093273952141729, -7.098925944110142, -7.094136827312879, -7.096515152172171, -7.106869073487611, -7.105025480517323, -7.08291256775595, -7.090057760157153, -7.101077914837238, -7.098981572929163, -7.103243624466709, -7.081271774215078, -7.113017035519717, -7.081225379146937, -7.116834711504442, -7.095492739824888, -7.092682578748099, -7.101013785481937, -7.1014895178629045, -7.089392729188864, -7.107015846039383, -7.098163688087048, -7.111610506727951, -7.107437432724649, -7.104541043920935, -7.104814557146702, -7.088507490097296, -7.091868681777208, -7.092327160052328, -7.110303366341896, -7.084971369187621, -7.106279269575924, -7.08748298127782, -7.1068551105826145, -7.091008955160712, -7.096443978916333, -7.084657042850862, -7.091138219995237, -7.0998677627359195, -7.0888015973421545, -7.077323969498798, -7.090075437365467, -7.103938600828348, -7.085513121721133, -7.093846377275633, -7.100739101641138, -7.092065649168193, -7.094889058778457, -7.092173541005391, -7.101259881230652, -7.093329510244533, -7.105936945903171, -7.087603313944616, -7.097873442997792, -7.101002397868193, -7.085514640470669, -7.104346225751653, -7.108225666766319, -7.111418621976149, -7.092840805395079, -7.0997679722989115, -7.103255616021782, -7.1174210275723695, -7.102934036335791, -7.094670120993602, -7.0951047953871305, -7.089065125835845, -7.09840645780722, -7.105211057511607, -7.089083299917603, -7.093536455196501, -7.089028853201778, -7.085106562924485, -7.094025566715013, -7.093679961728104, -7.097635614184673, -7.097876397476181, -7.094228767292644, -7.095176655148256, -7.098376263483634, -7.103892028959518, -7.086136465046034, -7.087496098005651, -7.116101776894849, -7.0836112045512705, -7.087318451256026, -7.089288193935741, -7.0990242642314785, -7.095138019651596, -7.098662991437872, -7.094562027567983, -7.099690770432304, -7.10097689047591, -7.103828491824173, -7.095403813862108, -7.092482494208955, -7.0961542900231755, -7.097735395547859, -7.101840243383003, -7.094728079435617, -7.089079166461775, -7.0918303529233695, -7.093445910102374, -7.0824677848419855, -7.088613823891637, -7.094448016211003, -7.102567463647013, -7.093674126629666, -7.107515891897475, -7.091175773435145, -7.099878612823926, -7.108888487835898, -7.0932901938871025, -7.100690499032453, -7.1027627009989205, -7.095985679639996, -7.103159134683138, -7.101594099093457, -7.09708690219646, -7.089839220984511, -7.110835783093937, -7.1106173669768005, -7.105706223928073, -7.101671068636789, -7.093043127308357, -7.107499275434534, -7.098620367705562, -7.101791302589503, -7.093974565602916, -7.100086270996543, -7.103967087697664, -7.096334501266853, -7.093197040678562, -7.090566503804324, -7.10777548347143, -7.0940663715743515, -7.079435919407288, -7.1045995778828575, -7.10782600555929, -7.095063062315657, -7.088283716422724, -7.083549548308807, -7.109182438307642, -7.0973139726115155, -7.091323880662006, -7.089267567957862, -7.093801064885492, -7.096478431968507, -7.096450570087517, -7.0834951672860145, -7.105536970385327, -7.091694022844323, -7.0987246829979735, -7.105823728075208, -7.091466927556181, -7.087866391118642, -7.086779542808011, -7.082284206870279, -7.102748671032144, -7.094013649749645, -7.076280227170458, -7.09268421659322, -7.098730097915838, -7.095792848436216, -7.090464809457003, -7.098254342554415, -7.098030162423567, -7.0935066669889375, -7.086557591264656, -7.102526761243724, -7.098181739651888, -7.10872784155506, -7.097459195380401, -7.095191100812662, -7.102890507504376, -7.0923183296893795, -7.102156393269663, -7.09845792437554, -7.096080365452766, -7.10013103533166, -7.1005268316155945, -7.092915662727403, -7.095654857173873, -7.10922258172602, -7.099831667590216, -7.108845117487635, -7.082825083394153, -7.09107742992335, -7.077237571417883, -7.096191060913464, -7.0969085540182455, -7.114145172610189, -7.108437033980985, -7.105356395396853, -7.102301352541805, -7.103938890772344, -7.101405935547222, -7.1113452563763815, -7.0947122361413415, -7.099371225641347, -7.102428612231857, -7.080811315146189, -7.091175823108694, -7.1006602596540445, -7.085633248686943, -7.101715269263441, -7.0835485945728305, -7.0994928231977195, -7.09758387589104, -7.0795693729863505, -7.093444335523969, -7.102404867274401, -7.09942952825781, -7.092772226440181, -7.104709368820088, -7.098167881166478, -7.090812612388616, -7.104342211111905, -7.095634875814595, -7.092173851473915, -7.096806777226616, -7.104061399180975, -7.103310800731109, -7.083274172204216, -7.097915562847112, -7.077818214117743, -7.083628375959302, -7.093476904190158, -7.089513462892567, -7.090304705450007, -7.093392779706353, -7.10554680082769, -7.088962810558666, -7.091859039419992, -7.095055353625999, -7.095717126988325, -7.083592132581408, -7.100324224161871, -7.0785000809768714, -7.105908001716903, -7.093818438314592, -7.098883881335108, -7.104431926558294, -7.099627499021038, -7.092250021905359, -7.0907944678741535, -7.09293707780021, -7.091586685769627, -7.089190047620321, -7.1018597532027385, -7.100262126701205, -7.09131145193086, -7.09482991668717, -7.088031963725242, -7.09771658959787, -7.089270186131905, -7.096846356920972, -7.09686896582669, -7.092845267851078, -7.11130293906202, -7.091518158249563, -7.094435352643231, -7.097573980280066, -7.097401803322267, -7.09679214923423, -7.096140093891424, -7.105779785807971, -7.101284059739653]
plot_convergence_of_optimization_process(LiH_approximated_energies, exact_eigenvalue=-7.151525481896562,margin=1)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
H2_approximated_energies = [-0.6479084750255486, -0.6276579569919597, -0.6079422008169065, -0.616731159779808, -0.6325842283091055, -0.6393897280901208, -0.6171807581727554, -0.632653791572579, -0.6213172282987715, -0.6295655663398093, -0.6289772030449229, -0.6186181091776035, -0.624022941533276, -0.5082839240612291, -0.48226570208794234, -0.4821361107003052, -0.4954020352078101, -0.4793435904590445, -0.49199670120300654, -0.49416478838441447, -0.502190052373643, -0.49599755978221166, -0.5020643548684793, -0.4889205213711024, -0.5018939914800866, -0.5099878400191491, -0.5856552068715944, -0.54923382599589, -0.5582306982767166, -0.5444314531693122, -0.5567710700669415, -0.5659113697818672, -0.552668511160273, -0.5735134318844516, -0.549852476753314, -0.5503189869962759, -0.5601864836520486, -0.5659896127460298, -0.5446950460298908, -0.615920984439197, -0.5928640404070656, -0.5879106801498322, -0.5935911543775607, -0.6075920247035514, -0.6201194518598445, -0.60623970115924, -0.6162790804378995, -0.6070899791213487, -0.6105620077787796, -0.604279338203177, -0.5953765787888684, -0.6176510100281449, -0.6121876903025966, -0.6221925707825862, -0.6167720694769763, -0.6138135616671906, -0.6141332165079305, -0.6280212409220817, -0.6360069982326235, -0.6007258601159454, -0.6251861183198779, -0.6230618384361196, -0.6294049945914133, -0.6233533946933156, -0.608497712991425, -0.6496414061454564, -0.6486467922145787, -0.6248046230879923, -0.6382435950247505, -0.6396933212611499, -0.6313975747684536, -0.6205882624714589, -0.6408121049037772, -0.6358325058878442, -0.6483418584555031, -0.6371649113759628, -0.6291839190391355, -0.6347573834032361, -0.6407098912056699, -0.6159176260854965, -0.6384554645835627, -0.6164080207309359, -0.625543079338974, -0.6382937503891668, -0.6264097132175528, -0.6420718561520969, -0.6267262725213436, -0.6374963711667498, -0.6193193504433864, -0.6078143278866533, -0.634472486357409, -0.6223512323012782, -0.6351163020561015, -0.634661177023637, -0.6327899211075433, -0.6336448686497769, -0.6193351633432258, -0.6281755978797693, -0.6264777231208046, -0.6414830476329384, -0.6307683399864691, -0.6307085701314388, -0.6206080402310008, -0.6348255969934301, -0.6396136598903551, -0.6119662685652434, -0.6416707355866279, -0.6413693107560723, -0.6177947197203094, -0.6298765228276698, -0.6523529064199631, -0.6449003109571184, -0.653383311719062, -0.6114270075961685, -0.6288547938898695, -0.618693644838608, -0.6474406100562011, -0.6311230491106903, -0.6116401562656182, -0.636431790506111, -0.6291838050229098, -0.6323232015973214, -0.6084567336875317, -0.6260410898582017, -0.6558980736383361, -0.6088478495140429, -0.6362772541154403, -0.6229687283270671, -0.6337477882049586, -0.6146890139542273, -0.6109822191193143, -0.6410668717503976, -0.6050360295204666, -0.6127109227117324, -0.613969481075047, -0.6330316470359499, -0.6336428860578563, -0.6579205656897767, -0.6226609914498723, -0.6308197002529959, 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-0.6349930744741815, -0.6553915345015394, -0.6333982709804692, -0.6323784240845362, -0.597462603561814, -0.6354799343741077, -0.6435513818689228, -0.6288306285283861, -0.6252986455639116, -0.6338258059332423, -0.6354797897494069, -0.6118871374772903]
plot_convergence_of_optimization_process(H2_approximated_energies, exact_eigenvalue=-0.353325104107155, margin=5)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigen_value = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
TI_approximated_energies = [1.8984375, 1.943359375, 1.9619140625, 1.978515625, 1.984375, 1.9873046875, 1.9931640625, 1.9248046875, 1.962890625, 1.9248046875, 1.9150390625, 1.9052734375, 1.9267578125, 1.802734375, 1.81640625, 1.86328125, 1.8623046875, 1.7939453125, 1.8623046875, 1.89453125, 1.880859375, 1.8388671875, 1.8720703125, 1.83984375, 1.8837890625, 1.8359375, 1.701171875, 1.7470703125, 1.69140625, 1.73828125, 1.833984375, 1.69921875, 1.7744140625, 1.7529296875, 1.7353515625, 1.7265625, 1.7666015625, 1.708984375, 1.7421875, 1.79296875, 1.8671875, 1.91015625, 1.8828125, 1.884765625, 1.875, 1.86328125, 1.85546875, 1.8134765625, 1.84375, 1.79296875, 1.865234375, 1.8916015625, 1.908203125, 1.900390625, 1.8837890625, 1.876953125, 1.896484375, 1.9921875, 1.9208984375, 1.94921875, 1.96875, 1.8466796875, 1.92578125, 1.8740234375, 1.9716796875, 1.9130859375, 1.939453125, 1.9599609375, 1.9716796875, 1.9150390625, 1.98828125, 1.865234375, 1.9248046875, 1.890625, 2.0146484375, 1.9560546875, 1.947265625, 1.9619140625, 1.955078125, 1.9208984375, 1.955078125, 1.9384765625, 1.96484375, 1.9150390625, 1.923828125, 1.9580078125, 1.958984375, 2.013671875, 1.935546875, 1.9443359375, 2.0546875, 2.001953125, 1.958984375, 1.98828125, 1.962890625, 2.0205078125, 2.0029296875, 1.93359375, 1.91015625, 1.9765625, 1.9365234375, 1.8984375, 1.9072265625, 1.939453125, 1.9033203125, 2.0556640625, 1.947265625, 1.9267578125, 1.9541015625, 1.962890625, 1.9287109375, 1.9072265625, 1.962890625, 1.966796875, 1.9560546875, 1.970703125, 1.9580078125, 1.9833984375, 2.013671875, 1.966796875, 1.9599609375, 1.943359375, 1.974609375, 1.9619140625, 1.9462890625, 1.974609375, 1.9482421875, 1.943359375, 1.9697265625, 1.9033203125, 1.9794921875, 1.98828125, 1.94140625, 1.9658203125, 2.0078125, 1.9912109375, 1.916015625, 1.916015625, 2.0068359375, 1.9130859375, 1.9267578125, 1.90234375, 1.921875, 1.943359375, 1.9755859375, 1.90234375, 1.95703125, 1.9482421875, 1.97265625, 1.9658203125, 1.990234375, 1.9384765625, 1.935546875, 1.916015625, 1.91796875, 1.99609375, 1.87109375, 1.9599609375, 1.919921875, 1.951171875, 1.9521484375, 1.9716796875, 1.9736328125, 1.9794921875, 1.99609375, 1.9765625, 1.9228515625, 1.9482421875, 1.9462890625, 1.986328125, 1.927734375, 1.9482421875, 2.0771484375, 2.0009765625, 1.9267578125, 1.9638671875, 1.904296875, 1.9365234375, 1.962890625, 1.958984375, 1.96875, 1.9521484375, 1.8935546875, 1.916015625, 1.939453125, 1.98046875, 1.9560546875, 1.9541015625, 1.955078125, 1.9228515625, 1.9951171875, 1.93359375, 1.9736328125, 1.9443359375, 1.96484375, 1.984375, 1.8681640625, 1.923828125, 1.947265625, 1.96484375, 1.94140625, 1.9375, 1.96875, 1.94921875, 1.943359375, 1.8935546875, 1.9638671875, 1.912109375, 2.0, 1.921875, 2.064453125, 1.95703125, 1.9287109375, 1.951171875, 1.982421875, 1.8955078125, 1.9482421875, 1.9970703125, 1.9423828125, 1.9697265625, 1.90625, 1.9306640625, 1.9716796875, 1.92578125, 1.98046875, 1.9521484375, 1.9072265625, 1.962890625, 1.9365234375, 1.9609375, 1.9560546875, 1.9462890625, 2.0166015625, 1.9609375, 1.9287109375, 1.962890625, 1.9677734375, 1.9169921875, 1.876953125, 1.9443359375, 1.984375, 1.9697265625, 1.978515625, 1.958984375, 1.9677734375, 2.0341796875, 1.9697265625, 1.93359375, 1.966796875, 1.9482421875, 1.9345703125, 1.9453125, 1.9912109375, 1.986328125, 1.955078125, 1.927734375, 2.03125, 1.921875, 1.951171875, 1.9990234375, 1.8955078125, 1.9794921875, 2.0078125, 1.9580078125, 1.986328125, 1.9287109375, 1.9853515625, 1.9990234375, 1.9365234375, 2.0048828125, 1.9462890625, 1.9580078125, 1.970703125, 1.951171875, 1.91015625, 1.8662109375, 1.9013671875, 1.9267578125, 1.943359375, 1.9814453125, 1.927734375, 1.99609375, 1.9580078125, 1.904296875, 1.912109375, 1.978515625, 1.9453125, 1.990234375, 1.97265625, 1.9580078125, 1.93359375, 1.9599609375, 1.986328125, 1.970703125, 1.966796875, 1.947265625, 1.875, 1.953125, 1.966796875, 1.931640625, 1.9140625, 1.98828125, 1.919921875, 1.970703125, 1.8916015625, 2.0615234375, 2.015625, 1.8466796875, 1.916015625, 1.96875, 1.9697265625, 2.0029296875, 1.9326171875, 1.939453125, 1.873046875, 1.9345703125, 1.9501953125, 1.927734375, 1.9453125, 2.005859375, 1.96484375, 1.9384765625, 1.9609375, 1.990234375, 1.951171875, 1.951171875, 1.994140625, 2.015625, 1.9462890625, 1.94140625, 2.0439453125, 1.9755859375, 1.9326171875, 2.0224609375, 1.9248046875, 1.990234375, 2.0, 1.9091796875, 1.9267578125, 1.951171875, 1.95703125, 1.9521484375]
plot_convergence_of_optimization_process(TI_approximated_energies, exact_eigenvalue=1.6816520928402046, margin=3)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 50
w = 0.5
approximated_energies = []
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 6
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 6
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
k_ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[K-1])
approximated_energey = get_expectation_value(k_ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energey)
L_w = w*approximated_energey
for j in range(K-1):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
L_w += get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=12)
optimizer_result = minimize(cost_function,x0=initial_thetas,args=(hamiltonian),method="BFGS",options={"maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
print(optimal_thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
optimal_ansatz_state = get_ansatz_state(optimal_thetas, computational_eigenvectors[K-1])
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, k):
eigen_values = LA.eig(hamiltonian.to_matrix())[0]
print(sorted(eigen_values, reverse=True))
return sorted(eigen_values,reverse=True)[k-1]
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, K)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("Approximated K Eigenvalues:")
print(approximated_eigenvalue)
print("Approximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies[-NUM_ITERATIONS:])
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.grid()
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, I, H, Y
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
LiH_approximated_energies = [-7.5811722185398285, -7.59159646344728, -7.591712498431583, -7.5823144711155255, -7.601228227804495, -7.5736138923664065, -7.599055184917277, -7.595389384370309, -7.586873555877376, -7.586779572764962, -7.587446891289177, -7.58816416037616, -7.606319025241597, -7.5468150612323015, -7.54795274923913, -7.561365217492775, -7.560844694104422, -7.548328551094029, -7.556729381819861, -7.5501822152874825, -7.552787397268313, -7.567509848511693, -7.573107964123815, -7.541648049799553, -7.546799664950377, -7.53654352129788, -7.589160003564084, -7.578598759247515, -7.590933004721402, -7.588143540217285, -7.594244897237276, -7.587510169441045, -7.5868306475144776, -7.587602605379268, -7.59225930178968, -7.5988486139694436, -7.573672664147123, -7.587077981079782, -7.589894569667096, -7.593989957965422, -7.5934638061012665, -7.586978945437706, -7.576471075379983, -7.586002143566326, -7.593009863418946, -7.594930172385808, -7.588512242648442, -7.60293471934649, -7.591877985644651, -7.580969380150128, -7.596119932713606, -7.615516216961582, -7.596055304700592, -7.5996270334260725, -7.586983361838935, -7.596246225349671, -7.590777615173849, -7.5935751302098256, -7.592837174684869, -7.603790076682524, -7.6093363504202145, -7.60522230882189, -7.577824083506902, -7.583940898791256, -7.585838556976443, -7.591352114525316, -7.586985421943245, -7.590516288197774, -7.592645661018166, -7.6022590957403695, -7.591330646171517, -7.594369777609106, -7.588063188591844, -7.590887567834473, -7.58529252287314, -7.590260727471608, -7.592442375670534, -7.588704468391091, -7.589907345471134, -7.594705545462669, -7.6098627506974665, -7.595941589491842, -7.594781927195355, -7.583709436067628, -7.601491453462858, -7.597492855351171, -7.596534669869249, -7.588718115470418, -7.580497184080997, -7.583102004301224, -7.591826652364619, -7.5996868685846355, -7.588597363608952, -7.5813554074546055, -7.583835495117783, -7.59064434908851, -7.58437365137141, -7.590315760666925, -7.597855922766573, -7.590740727486217, -7.596056737044825, -7.5902279046692325, -7.609184282492802, -7.591748265755058, -7.602981872142157, -7.59998915723516, -7.588200490143084, -7.591025078502806, -7.588051902013782, -7.611052590540253, -7.587486622263765, -7.591803731736747, -7.589835728854846, -7.593340824035681, -7.581866774777097, -7.58836662913097, -7.6053870554693805, -7.590489094786991, -7.580771153453858, -7.5905219906055565, -7.602079027418958, -7.59869534734383, -7.592327067764258, -7.586492679563721, -7.5900307096383495, -7.605871180701457, -7.583686251845164, -7.59084383030994, -7.591011259270283, -7.609378670021997, -7.602092819996155, -7.5890139534539784, -7.586869308169689, -7.585646372448603, -7.58076297152655, -7.609251035755286, -7.591515311689081, -7.59257083904225, -7.584083715434293, -7.586450125487619, -7.593598728550749, -7.580488061773295, -7.605496242684976, -7.593414651298946, -7.60217927693839, -7.576912879829302, -7.604154147713128, -7.6084567317964975, -7.578611304029224, -7.591686370715707, -7.596609189738003, -7.5779236456467185, -7.600899390110624, -7.589656688978693, -7.591824476469537, -7.588295121277478, -7.604646934476692, -7.599305159948481, -7.601823274459693, -7.599153286574935, -7.59398640868234, -7.594623264414274, -7.563535780759224, -7.5907374418716795, -7.584497327439853, -7.598880523136912, -7.589930732585632, -7.596773581756135, -7.5820404386071925, -7.591745408563035, -7.595021082718484, -7.591871643380514, -7.5923783623174295, -7.588662444757317, -7.601348684176666, -7.604692130795216, -7.581271720491602, -7.592316763268401, -7.599557460899818, -7.590233868866651, -7.60106633139657, -7.591029502106871, -7.590946526294125, -7.578047392804944, -7.584371216579831, -7.58297181596419, -7.593260068364673, -7.588794164898488, -7.595498777698822, -7.57844959725151, -7.601455854688926, -7.591515635688625, -7.5844746837553405, -7.590480735122996, -7.59115080196329, -7.583228595085926, -7.591838539639781, -7.5880938775924935, -7.591635548561748, -7.591955549690062, -7.598088450438071, -7.582096714835912, -7.588480649207663, -7.575017322673416, -7.591209269166958, -7.582617613707098, -7.596106095701603, -7.562895071846649, -7.581176362485807, -7.578569198893786, -7.591395966192013, -7.589017847713364, -7.576334250015566, -7.587794803768129, -7.616990543910279, -7.5906539038020435, -7.586853063919036, -7.585559440057858, -7.584803368513558, -7.597555640231412, -7.595228097920501, -7.595190095630545, -7.590903350802588, -7.591718676589801, -7.586795506030791, -7.580612481966594, -7.593603416733997, -7.598238714945253, -7.605972868167942, -7.584061079920518, -7.587272086190425, -7.60479190195469, -7.6013951681300655, -7.593690915438579, -7.599320500571691, -7.58002377916205, -7.597620308675762, -7.595205045762717, -7.601282182510587, -7.5764528159136475, -7.58003542137329, -7.577500526862233, -7.585601464645433, -7.594348998755124, -7.594659687853514, -7.584691274533544, -7.579260346160663, -7.589381346695482, -7.581942488616398, -7.585761838931412, -7.5888806656223, -7.5906512594778786, -7.59460061471894, -7.598291131300036, -7.566077017354454, -7.598568920462468, -7.588458586865334, -7.580516851783573, -7.581120795801359, -7.573401531185061, -7.587906649375854, -7.577894400309903, -7.588650004367097, -7.601671473700583, -7.6045987582499, -7.587960747276149, -7.586668925102221, -7.598896396820583, -7.584992838351697, -7.588738488491178, -7.592081956817983, -7.594450290229943, -7.577207933669749, -7.592589318566335, -7.591631016036065, -7.586822528718511, -7.5865236423006515, -7.575498534956321, -7.574278911271381, -7.584707709876169, -7.590472728393561, -7.599499257712318, -7.589231395611416, -7.597168903183947, -7.590381517053034, -7.603836632255566, -7.593864793429861, -7.600191191390682, -7.586817716211005, -7.587970682164855, -7.588438308757338, -7.586491923661776, -7.5849299950060445, -7.5726557026548, -7.605430277807631, -7.583551608530619, -7.590313233780737, -7.582464090187332, -7.587898000394051, -7.57869966024508, -7.59814204971804, -7.58368253706408, -7.583281132917466, -7.596340009605541, -7.580639556870499, -7.594986105182591, -7.597986634078884, -7.605014774124471, -7.595227520703942, -7.6126847535198445, -7.599313575341617, -7.569816760702087, -7.594416054247172, -7.605083757930927, -7.582868819170454, -7.586396258585806, -7.604414920719065, -7.599387572834845, -7.594782011899959, -7.606698086162534, -7.599912812617114, -7.609221282226267, -7.588232008218757, -7.60346462535037, -7.57588689646886, -7.588493577576002, -7.587845316302236, -7.577824438147921, -7.59972110610129, -7.601255963829907, -7.591292742933581, -7.591643875142415, -7.595608436976339, -7.604907684584499, -7.586236901477843, -7.599687143227731, -7.6019079185697205, -7.582693582623832, -7.599300342093287, -7.600243633211197, -7.592954405838291, -7.58819349398165, -7.601064555573852, -7.598241391296196, -7.596549098561609, -7.599227365949463, -7.594832883549281, -7.582626984810636, -7.5759575479403365, -7.587274253615891, -7.592166994254732, -7.599369142236348, -7.592745920229135, -7.574743004640935, -7.6065301484133485, -7.6110277743814025, -7.577220966905672, -7.596052441127596, -7.594975868864067, -7.583058349968933, -7.58912555988364, -7.593591137603428, -7.598784448149547, -7.596526026783077, -7.584847627840902, -7.593575746597375, -7.590229568191782, -7.579561798198312, -7.57274335076671, -7.595408728174156, -7.616555806795029]
plot_convergence_of_optimization_process(LiH_approximated_energies, exact_eigenvalue=-7.7140566916607005,margin=1)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
H2_approximated_energies = [-0.6197535280860968, -0.63113013317311, -0.641885414639814, -0.6482547418356555, -0.65455000829844, -0.6441486895522341, -0.6186687021257633, -0.6337374526097435, -0.63137130321273, -0.6515250743774067, -0.6579678475184173, -0.6398929213318618, -0.6555847628548984, -0.40354990528583756, -0.42633959272606203, -0.39180257499975996, -0.419385140488104, -0.4052452163765543, -0.3968392598264421, -0.41327196278701983, -0.3897682032307278, -0.41190320628798593, -0.4155349659846535, -0.38689315655724943, -0.39488576584884966, -0.4101577563997251, -0.646246089992425, -0.64640556215564, -0.6408025316083132, -0.6481729361748543, -0.6321210801588072, -0.6169734445936428, -0.6531880101925263, -0.6516595101969759, -0.6370106901252102, -0.6410493390206395, -0.6549643568126738, -0.6434282271634354, -0.6374465180654254, -0.6998006222609853, -0.6989411616133739, -0.7113515779782615, -0.6845563444533804, -0.6912851288084605, -0.6823206756219158, -0.6715092561687758, -0.6950950360064898, -0.7048125041323035, -0.6949055673239051, -0.6876195557523046, -0.6871916327390696, -0.6920620441807598, -0.6754031102431696, -0.6405037528920269, -0.6479106194443648, -0.6571243727534537, -0.6585210677012743, -0.6619852684486195, -0.6306692686820092, -0.6426806791628032, -0.6605101341410042, -0.6581734283582826, -0.6602845191858175, -0.6403463546120416, -0.6838573980740288, -0.6367601998705805, -0.6389697979320161, -0.6342448131512901, -0.6275459264150375, -0.6397639594996816, -0.6516652787828084, -0.6568333186072677, -0.6337354077401545, -0.6534843394293214, -0.6561183148929468, -0.6394550125097977, -0.6282040909709646, -0.6566726955439391, -0.6480962237754406, -0.6391249852824691, -0.6302805184048759, -0.6134825837204779, -0.6324807924099654, -0.648200184148801, -0.6411199725353807, -0.6368985204497558, -0.6299450915767432, -0.6077929487594798, -0.650795244723779, -0.6364396855992979, -0.6561074752564185, -0.6411855472811453, -0.6636963692795997, -0.644828181245867, -0.6426381659395819, -0.6395444214753829, -0.6428019435419277, -0.6477507227847618, -0.6245247077953339, -0.6524683695964778, -0.657026854334116, -0.6358256453202371, -0.6549216159614076, -0.6414823984346717, -0.6559324505625062, -0.6184921814281965, -0.6243527663890307, -0.6347039342445667, -0.6423667818441274, -0.6416632437237163, -0.6355679476249553, -0.6101453551739199, -0.6428657380183808, -0.6371993803542474, -0.6190951873626491, -0.6300491872725141, -0.6443076254087124, -0.6346503527906344, -0.6374022072525142, -0.6365415695138426, -0.6215329044766564, -0.6025672090796137, -0.6262126292580317, -0.6121655900183715, -0.6372581587495586, -0.6532601474080465, -0.6502386208320281, -0.6374473928211839, -0.649108661977176, -0.6428978019524852, -0.6377680232901412, -0.62148731332837, -0.6295014947278836, -0.6303577746392046, -0.6311824700622705, -0.6485908334116913, -0.6555308247607579, -0.6387533756242247, -0.6387831688041341, -0.6362224138123854, -0.6321326357150927, -0.622886094438443, -0.6381661184242305, -0.6207598749285432, -0.633337235851305, -0.6433014163336428, -0.6216780295166963, -0.640547648407052, -0.6504721343163778, -0.6289231121104825, -0.6420313548519503, -0.6491871272384829, -0.6303753733515429, -0.6422070448022406, -0.6283882694196357, -0.6379372975401341, -0.6298035124355486, -0.6376118905742243, -0.6112071558166968, -0.6243668348101994, -0.601586210931813, -0.6246804576520302, -0.6225112843707201, -0.6385828114683393, -0.6308445065147489, -0.6459667238092578, -0.6420608286322824, -0.6284852174798609, -0.619517446532688, -0.6502311414153916, -0.6209974249236357, -0.6500441487817326, -0.6270160102758754, -0.6321138163295283, -0.6318213468032534, -0.6308663247351938, -0.6351155382454959, -0.6206589579897115, -0.6230425476232493, -0.6457261606370266, -0.638217697666363, -0.5967596291858532, -0.6308080357393553, -0.645343139596654, -0.6361652737273936, -0.6216439843718955, -0.6381345598638063, -0.6436054044017382, -0.6402634016890136, -0.6286637688911421, -0.6176910501936059, -0.6426835317643965, -0.6392144191408344, -0.6379698862857323, -0.6294007310483538, -0.6536384710745602, -0.6358065891830973, -0.6281936714944539, -0.6198882142883465, -0.6667152509756108, -0.6478727132696764, -0.639743219643381, -0.6594605134740277, -0.6208263182667817, -0.6484844194562659, -0.6560350644220397, -0.6400305393668726, -0.6082390327656634, -0.6177097860668552, -0.6444776983490096, -0.6405638061358565, -0.6531983360761086, -0.6384666560316292, -0.6026381248979216, -0.6205265201994276, -0.6580811400893553, -0.6242879958522837, -0.6256237085721144, -0.6370627576610521, -0.6193780381228698, -0.6110480817069229, -0.6348741804124418, -0.6469297212858536, -0.6284047197112129, -0.6425857646008404, -0.6227145680975487, -0.6543951355139729, -0.6135377860147931, -0.6151008019528299, -0.6332371262963544, -0.6213803615123089, -0.6197342220002152, -0.6553553047211762, -0.6542865700842904, -0.6447201703460987, -0.607866355025946, -0.6300084394962439, -0.6411144050158086, -0.6178965245521646, -0.616191998658104, -0.6348708952923955, -0.623907264080751, -0.641086457337346, -0.6444154604034792, -0.621800174387, -0.6244882763185394, -0.6376556734303133, -0.6375013731590747, -0.6275068048204745, -0.6623644844595649, -0.630649046531283, -0.6548727406536676, -0.6362997093395338, -0.6061815282744116, -0.6546951895602897, -0.6309023807683508, -0.6508388161226021, -0.6385027712100855, -0.6190137561886869, -0.6696046214509908, -0.6562145856438492, -0.6186112558608597, -0.6473301190677272, -0.6462712478136641, -0.673403768067784, -0.6530082059325099, -0.6543125213926978, -0.6378511211667697, -0.6345475633154861, -0.6368035646034413, -0.6420046649037825, -0.6415451595381126, -0.6447601324975634, -0.6308090659348322, -0.6442243984560325, -0.6337552468237352, -0.6652098463681152, -0.6450651275200792, -0.6415608484514996, -0.6297426007842335, -0.628971981721844, -0.6290368436378584, -0.6296828008139378, -0.6326057245473052, -0.6287268748618635, -0.6523495046628819, -0.654514736278266, -0.6503390006896462, -0.6267667849085593, -0.6518861485724909, -0.6213049629142335, -0.6152511068093129, -0.6444920885486036, -0.6538763157213386, -0.6169162063050543, -0.6374557936296323, -0.639117369570508, -0.636462951162852, -0.6517593736006154, -0.6076877031233741, -0.6403602223149248, -0.6298396251235469, -0.6637221198146037, -0.64886754893841, -0.6345453470146507, -0.6382894853660541, -0.6177025318805094, -0.652638852060324, -0.622038295932382, -0.6415029691455418, -0.6482039684567894, -0.6444058652688481, -0.6431931740464266, -0.6348402433271942, -0.6526661449410499, -0.6274506541843567, -0.6588510196703152, -0.6552920830042773, -0.6460730559750325, -0.6595908999970469, -0.6246926245873604, -0.6332020529350273, -0.6548958894755552, -0.6261489147202579]
plot_convergence_of_optimization_process(H2_approximated_energies, exact_eigenvalue=-1.2445845498133272, margin=5)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigen_value = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
TI_approximated_energies = [1.8984375, 1.943359375, 1.9619140625, 1.978515625, 1.984375, 1.9873046875, 1.9931640625, 1.9248046875, 1.962890625, 1.9248046875, 1.9150390625, 1.9052734375, 1.9267578125, 1.802734375, 1.81640625, 1.86328125, 1.8623046875, 1.7939453125, 1.8623046875, 1.89453125, 1.880859375, 1.8388671875, 1.8720703125, 1.83984375, 1.8837890625, 1.8359375, 1.701171875, 1.7470703125, 1.69140625, 1.73828125, 1.833984375, 1.69921875, 1.7744140625, 1.7529296875, 1.7353515625, 1.7265625, 1.7666015625, 1.708984375, 1.7421875, 1.79296875, 1.8671875, 1.91015625, 1.8828125, 1.884765625, 1.875, 1.86328125, 1.85546875, 1.8134765625, 1.84375, 1.79296875, 1.865234375, 1.8916015625, 1.908203125, 1.900390625, 1.8837890625, 1.876953125, 1.896484375, 1.9921875, 1.9208984375, 1.94921875, 1.96875, 1.8466796875, 1.92578125, 1.8740234375, 1.9716796875, 1.9130859375, 1.939453125, 1.9599609375, 1.9716796875, 1.9150390625, 1.98828125, 1.865234375, 1.9248046875, 1.890625, 2.0146484375, 1.9560546875, 1.947265625, 1.9619140625, 1.955078125, 1.9208984375, 1.955078125, 1.9384765625, 1.96484375, 1.9150390625, 1.923828125, 1.9580078125, 1.958984375, 2.013671875, 1.935546875, 1.9443359375, 2.0546875, 2.001953125, 1.958984375, 1.98828125, 1.962890625, 2.0205078125, 2.0029296875, 1.93359375, 1.91015625, 1.9765625, 1.9365234375, 1.8984375, 1.9072265625, 1.939453125, 1.9033203125, 2.0556640625, 1.947265625, 1.9267578125, 1.9541015625, 1.962890625, 1.9287109375, 1.9072265625, 1.962890625, 1.966796875, 1.9560546875, 1.970703125, 1.9580078125, 1.9833984375, 2.013671875, 1.966796875, 1.9599609375, 1.943359375, 1.974609375, 1.9619140625, 1.9462890625, 1.974609375, 1.9482421875, 1.943359375, 1.9697265625, 1.9033203125, 1.9794921875, 1.98828125, 1.94140625, 1.9658203125, 2.0078125, 1.9912109375, 1.916015625, 1.916015625, 2.0068359375, 1.9130859375, 1.9267578125, 1.90234375, 1.921875, 1.943359375, 1.9755859375, 1.90234375, 1.95703125, 1.9482421875, 1.97265625, 1.9658203125, 1.990234375, 1.9384765625, 1.935546875, 1.916015625, 1.91796875, 1.99609375, 1.87109375, 1.9599609375, 1.919921875, 1.951171875, 1.9521484375, 1.9716796875, 1.9736328125, 1.9794921875, 1.99609375, 1.9765625, 1.9228515625, 1.9482421875, 1.9462890625, 1.986328125, 1.927734375, 1.9482421875, 2.0771484375, 2.0009765625, 1.9267578125, 1.9638671875, 1.904296875, 1.9365234375, 1.962890625, 1.958984375, 1.96875, 1.9521484375, 1.8935546875, 1.916015625, 1.939453125, 1.98046875, 1.9560546875, 1.9541015625, 1.955078125, 1.9228515625, 1.9951171875, 1.93359375, 1.9736328125, 1.9443359375, 1.96484375, 1.984375, 1.8681640625, 1.923828125, 1.947265625, 1.96484375, 1.94140625, 1.9375, 1.96875, 1.94921875, 1.943359375, 1.8935546875, 1.9638671875, 1.912109375, 2.0, 1.921875, 2.064453125, 1.95703125, 1.9287109375, 1.951171875, 1.982421875, 1.8955078125, 1.9482421875, 1.9970703125, 1.9423828125, 1.9697265625, 1.90625, 1.9306640625, 1.9716796875, 1.92578125, 1.98046875, 1.9521484375, 1.9072265625, 1.962890625, 1.9365234375, 1.9609375, 1.9560546875, 1.9462890625, 2.0166015625, 1.9609375, 1.9287109375, 1.962890625, 1.9677734375, 1.9169921875, 1.876953125, 1.9443359375, 1.984375, 1.9697265625, 1.978515625, 1.958984375, 1.9677734375, 2.0341796875, 1.9697265625, 1.93359375, 1.966796875, 1.9482421875, 1.9345703125, 1.9453125, 1.9912109375, 1.986328125, 1.955078125, 1.927734375, 2.03125, 1.921875, 1.951171875, 1.9990234375, 1.8955078125, 1.9794921875, 2.0078125, 1.9580078125, 1.986328125, 1.9287109375, 1.9853515625, 1.9990234375, 1.9365234375, 2.0048828125, 1.9462890625, 1.9580078125, 1.970703125, 1.951171875, 1.91015625, 1.8662109375, 1.9013671875, 1.9267578125, 1.943359375, 1.9814453125, 1.927734375, 1.99609375, 1.9580078125, 1.904296875, 1.912109375, 1.978515625, 1.9453125, 1.990234375, 1.97265625, 1.9580078125, 1.93359375, 1.9599609375, 1.986328125, 1.970703125, 1.966796875, 1.947265625, 1.875, 1.953125, 1.966796875, 1.931640625, 1.9140625, 1.98828125, 1.919921875, 1.970703125, 1.8916015625, 2.0615234375, 2.015625, 1.8466796875, 1.916015625, 1.96875, 1.9697265625, 2.0029296875, 1.9326171875, 1.939453125, 1.873046875, 1.9345703125, 1.9501953125, 1.927734375, 1.9453125, 2.005859375, 1.96484375, 1.9384765625, 1.9609375, 1.990234375, 1.951171875, 1.951171875, 1.994140625, 2.015625, 1.9462890625, 1.94140625, 2.0439453125, 1.9755859375, 1.9326171875, 2.0224609375, 1.9248046875, 1.990234375, 2.0, 1.9091796875, 1.9267578125, 1.951171875, 1.95703125, 1.9521484375]
plot_convergence_of_optimization_process(TI_approximated_energies, exact_eigenvalue=-1.7583827504312988, margin=3)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 50
w = 0.5
approximated_energies = []
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 6
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 6
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
k_ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[K-1])
approximated_energey = get_expectation_value(k_ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energey)
L_w = w*approximated_energey
for j in range(K-1):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
L_w += get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=2*np.pi, size=12)
optimizer_result = minimize(cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="COBYLA",
options={"disp": True, "maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_eigenvalue_of_hamiltonian(hamiltonian):
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
print(optimal_thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
optimal_ansatz_state = get_ansatz_state(optimal_thetas, computational_eigenvectors[K-1])
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
return approximated_eigenvalue
from numpy import linalg as LA
def get_approximation_error(exact_eigenvalue, approximated_eigenvalue):
return abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue)
def get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, k):
eigen_values = LA.eig(hamiltonian.to_matrix())[0]
print(sorted(eigen_values, reverse=True))
return sorted(eigen_values,reverse=True)[k-1]
def compare_exact_and_approximated_eigenvalue(hamiltonian, approximated_eigenvalue):
exact_eigenvalue = get_k_exact_eigenvalue_of_hamiltonian(hamiltonian, K)
print("Exact Eigenvalue:")
print(exact_eigenvalue)
print("Approximated K Eigenvalues:")
print(approximated_eigenvalue)
print("Approximation Error")
print(get_approximation_error(exact_eigenvalue, approximated_eigenvalue))
def insert_approximated_energy_to_list_of_all_approximated_energies(energy):
approximated_energies.append(energy)
import matplotlib.pyplot as plt
def plot_convergence_of_optimization_process(approximated_energies, exact_eigenvalue, margin):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0, margin)
plt.plot(approximated_energies)
plt.axhline(y = exact_eigenvalue, color = 'r', linestyle = '-')
plt.xlabel("# of iterations")
plt.ylabel("Energy")
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, Y, I, H, S
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvalue(LiH_molecule_4_qubits, LiH_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
LiH_approximated_energies = [-7.6274591415582105, -7.607576828257072, -7.632200935003245, -7.609855196623901, -7.6059250397280795, -7.854597415729809, -7.628956794318834, -7.6784378048763715, -7.640342773091634, -7.665298199108273, -7.4589086431520615, -7.64400728822478, -7.63919074876535, -7.5712982052834015, -7.644638404908841, -7.646954760531615, -7.755301596699023, -7.631831246253383, -7.631061799605215, -7.616310788526333, -7.611576222526171, -7.620105483420993, -7.6417862171136335, -7.589952292685995, -7.610418644012381, -7.674320046442037, -7.61956694546109, -7.627683802497983, -7.623678295984975, -7.617228428549745, -7.633104604686701, -7.629086274819348, -7.595694407363554, -7.617836676264696, -7.617389773769819, -7.634299221424122, -7.598467942904893, -7.630191480144404, -7.63698619980098, -7.623626950424333, -7.612007795510998, -7.6261074907011634, -7.6148982305668405, -7.623709634670492, -7.61204075447679, -7.6106110013026385, -7.620711346718306, -7.618187492707977, -7.612462844967995, -7.623640830688807]
plot_convergence_of_optimization_process(LiH_approximated_energies, exact_eigenvalue=-7.7140566916607005,margin=1)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_eigenvalue = get_approximated_eigenvalue_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvalue(H2_molecule_Hamiltonian_4_qubits, H2_approximated_eigenvalue)
print(approximated_energies)
approximated_energies = []
H2_approximated_energies = [-1.009976657006965, -0.9238284763706393, -0.9884320852467877, -0.9805917857984984, -1.0167176344158073, -0.803009921527331, -0.4598306468944341, -0.5114890962692614, -0.8589176393087158, -0.9346855734783651, -0.8412382644084648, -0.6224404303456501, -0.653317087612677, -0.7607656559263039, -0.7930275875404521, -0.4281158503125878, -0.5788815212789364, -0.7176165386431208, -0.8701142070097521, -0.8688095826524974, -0.9151572025822381, -0.6635735611840398, -0.6037067550586409, -0.9285839833437391, -0.5058550482270441, -0.9291800596309192, -0.49550483773798376, -0.7464398349372543, -0.9433354608506894, -0.8895971844704103, -0.9048816527272305, -0.8978302385287464, -0.6949574562429168, -0.8304208103551916, -0.4692230966986817, -0.8462497998117152, -0.7185585023635032, -0.8077110062007753, -0.5192275804166049, -0.5640061209546482, -0.8011222125790844, -0.9513753098344495, -0.8402620344123755, -0.6086751350074949, -0.7369530952207817, -0.7603612456563129, -0.7950958666448285, -0.7999579057635281, -0.7706575601258369, -0.7909119439657882]
plot_convergence_of_optimization_process(H2_approximated_energies, exact_eigenvalue=-1.2445845498133272, margin=5)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_eigen_value = get_approximated_eigenvalue_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvalue(transverse_ising_4_qubits, TI_approximated_eigen_value)
print(approximated_energies)
approximated_energies = []
TI_approximated_energies = [1.0877911566875362, 1.3339897771771856, 1.1497195956414945, 1.3463775026022828, 1.1824868775928117, 1.6423958284840114, 1.5842407965410792, 1.6377219801098, 1.5250316270225506, 1.626129653972439, 1.3560460449434424, 1.6695319025733455, 1.6842571288891142, 1.5407570120203158, 1.5187677867233031, 1.4564666271629088, 1.7323725293893963, 1.792109013228278, 1.7481282811675565, 1.8139670143156743, 1.6629383661129478, 1.68337823955209, 1.4848944286809986, 1.4845001982657569, 1.6129182843066505, 1.6625400070359255, 1.6104761870181472, 1.7152744787413363, 1.6678413737920048, 1.6869395320619605, 1.6590487040095492, 1.6723344557176432, 1.627252139576561, 1.6998615622327233, 1.6227578573441954, 1.6709380388303952, 1.747587311276882, 1.7146592410359045, 1.7219455615683754, 1.6503664867345986, 1.7349602602365404, 1.767898541795154, 1.7803996165862503, 1.6955748077929296, 1.7174656756704858, 1.715728620581076, 1.7002352954018423, 1.7436412571902764, 1.6757447332820925, 1.7032804122037015]
plot_convergence_of_optimization_process(TI_approximated_energies, exact_eigenvalue=-1.7583827504312988, margin=3)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
%load_ext autoreload
%autoreload 2
from qiskit.circuit.library.standard_gates import RXGate, RZGate, CXGate, CZGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
def get_thetas_circuit(thetas, D2):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
for d in range(D2):
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
qc.append(CZGate(), [qr[0], qr[1]])
qc.append(CZGate(), [qr[1], qr[2]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
return qc
def get_phis_circuit(phis, D1, input_state):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
qc.initialize(input_state)
for d in range(D1):
qc.append(RXGate(phis[0]), [qr[2]])
qc.append(RXGate(phis[1]), [qr[3]])
qc.append(RZGate(phis[2]), [qr[2]])
qc.append(RZGate(phis[3]), [qr[3]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
return qc
def get_full_variational_quantum_circuit(thetas, phis, D1, D2, input_state):
thetas_quantum_circuit = get_thetas_circuit(thetas, D2)
phis_quantum_circuit = get_phis_circuit(phis, D1, input_state)
variational_quantum_circuit = phis_quantum_circuit.compose(thetas_quantum_circuit)
return variational_quantum_circuit
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import numpy as np
def get_first_k_eigenvectors_from_n_computational_basis(k, n):
n_computational_basis = np.identity(n)
return n_computational_basis[:k]
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 50
w_vector = np.asarray([4,3,2,1])
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 8
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 8
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
L_w = 0
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(LiH_molecule_4_qubits)
for j in tqdm(range(K)):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
approximated_energy = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(
approximated_energies_dict["approximated_eneriges_"+str(j)], approximated_energy)
L_w += w_vector[j]*approximated_energy
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=360, size=12)
optimizer_result = minimize(
cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="BFGS",
options={"maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_k_eigenvalues_of_hamiltonian(hamiltonian):
approximated_k_eigenvalues = []
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
for eigenvalue_index, eigenvector in enumerate(computational_eigenvectors):
optimal_ansatz_state = get_ansatz_state(optimal_thetas, eigenvector)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
approximated_k_eigenvalues.append(approximated_eigenvalue)
return approximated_k_eigenvalues
from numpy import linalg as LA
from statistics import mean
def get_mean_approximation_error(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors = []
for exact_eigenvalue, approximated_eigenvalue in zip(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors.append(abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue))
return mean(approximated_errors)
def get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, k):
eigenvalues = LA.eig(hamiltonian.to_matrix())[0]
return sorted(eigenvalues)[:k]
def compare_exact_and_approximated_eigenvectors(hamiltonian, approximated_k_eigenvalues):
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print("Exact K Eigenvalues:")
print(exact_k_eigenvalues)
print("\nApproximated K Eigenvalues:")
print(approximated_k_eigenvalues)
print("\nMean Approximation error:")
print(get_mean_approximation_error(exact_k_eigenvalues, approximated_k_eigenvalues))
approximated_energies_dict = { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def initialize_approximated_energies_dict():
return { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energies_list, energy):
approximated_energies_list.append(energy)
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
def plot_convergence_of_optimization_process(approximated_energies, hamiltonian, margin=0.02):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0,margin)
base_colors_list = list(mcolors.BASE_COLORS.keys())
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print(exact_k_eigenvalues)
for energy_level, eigenvalue in enumerate(exact_k_eigenvalues):
energy_level_name = "E_{0}".format(str(energy_level))
plt.axhline(y = eigenvalue,
color = base_colors_list[energy_level],
linestyle = 'dotted', label=energy_level_name)
plt.plot(approximated_energies["approximated_eneriges_{0}".format(str(energy_level))],
color = base_colors_list[energy_level],
label="Weighted_SSVQE({0})".format(energy_level_name))
# plt.plot(approximated_energies["approximated_eneriges_0"])
# plt.plot(approximated_energies["approximated_eneriges_1"])
# plt.plot(approximated_energies["approximated_eneriges_2"])
# plt.plot(approximated_energies["approximated_eneriges_3"])
plt.xlabel("# of iterations")
plt.ylabel("Energy")
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, Y, I, H, S
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvectors(LiH_molecule_4_qubits, LiH_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
LiH_approximated_energies = {'approximated_eneriges_0': [-7.562071486292104, -7.551346757429608, -7.552944523914135, -7.560116772775394, -7.565448199837231, -7.562546777411176, -7.556370586953186, -7.5674961396597515, -7.562868323640123, -7.569727297671011, -7.577241001152592, -7.569901653592553, -7.560170928569707, -7.50450294015484, -7.507421280130349, -7.513641444931524, -7.505252370983593, -7.504378338149738, -7.511089721083689, -7.492616949145766, -7.504733592874844, -7.505057286909975, -7.500944996847547, -7.510777395650015, -7.50684214460726, -7.494074441023492, -7.560548573373164, -7.562214184024206, -7.568477882703838, -7.5455461632531655, -7.564340538776625, -7.553988541052734, -7.5451955641745085, -7.5609456305954925, -7.5483501889539975, -7.556677716954072, -7.56005590213002, -7.5631439275507315, -7.553392111383577, -7.556743753345377, -7.561551788828242, -7.555342548733728, -7.556766445089764, -7.553542895341899, -7.559683391361186, -7.560925469458819, -7.563572357485119, 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plot_convergence_of_optimization_process(LiH_approximated_energies, LiH_molecule_4_qubits, margin=0.02)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvectors(H2_molecule_Hamiltonian_4_qubits, H2_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
H2_approximated_energies = {'approximated_eneriges_0': [-7.044869071845908, -7.0522159431144695, -7.045826893427681, -7.040956622016025, -7.033636336738691, -7.03852022989153, -7.043777898111554, -7.0415561599539584, -7.04037809487655, -7.0453193426832215, -7.0373470588788996, -7.044564629495382, -7.044754815788807, -7.271419323963639, -7.26052383991807, -7.247357653224691, -7.261820010307763, -7.252539342679122, -7.2626464129237, -7.245920398831287, -7.247035733098027, -7.265952097434155, -7.24887083122739, -7.2531816673861735, -7.265940705468054, -7.25270662157792, -7.102617995399945, -7.089498116849218, -7.093325799353756, -7.096365339245411, -7.094106057615053, -7.107535385025435, -7.103305126646508, -7.091948777305775, -7.086315491445892, -7.10488835709718, -7.096982206618721, -7.0914861370367435, -7.093538444908571, -7.070529105326432, -7.067462257655455, -7.076956405751454, -7.066279474520601, -7.077988558064548, -7.076544412109634, -7.0658723955821845, -7.070992951297235, 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-7.046542176670868, -7.049764702707561, -7.040220654757975, -7.041801890197001, -7.045555266385649, -7.0430106557869046, -7.04329818292906, -7.049868368497418, -7.034838501816597, -7.038414717010243, -7.0480144131089215, -7.041535357301606, -7.043149083278204, -7.050721236368235, -7.04596017384676], 'approximated_eneriges_1': [-7.582453604466945, -7.582164266793541, -7.579073084596599, -7.585141242550659, -7.584589532241155, -7.5804643115002825, -7.5755634547601, -7.575600434478013, -7.582806656947542, -7.576958351501415, -7.574237985466983, -7.580187288314143, -7.574665472867071, -7.474764240900405, -7.4768714938741345, -7.466319706744727, -7.476154028838411, -7.471320885644612, -7.4590599683088294, -7.465030782155778, -7.475164569508971, -7.466084866348124, -7.477792033180828, -7.472963606706828, -7.4729137232137335, -7.466637719941649, -7.566267374472306, -7.557517351122575, -7.578861463899415, -7.566194514775459, -7.572894947849101, -7.558357851874592, -7.558189255072525, 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plot_convergence_of_optimization_process(H2_approximated_energies, H2_molecule_Hamiltonian_4_qubits, margin=0.01)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvectors(transverse_ising_4_qubits, TI_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
TI_approximated_energies = {'approximated_eneriges_0': [-7.230655824291587, -7.232156231813603, -7.2269118466834925, -7.224435292342758, -7.223090510850815, -7.232883464451508, -7.228534606397912, -7.219354944244936, -7.231064944404686, -7.228080867101087, -7.248782779735623, -7.245837078380108, -7.23217415595806, -7.406936545157612, -7.411831457927899, -7.430134402689202, -7.414265944626451, -7.416851880814031, -7.400408350428862, -7.427462455825711, -7.417112403651977, -7.434810143153512, -7.409863282248075, -7.427346672862717, -7.422754759252152, -7.404965523288016, -7.226943186680726, -7.230561909262265, -7.253943248477311, -7.246903128054697, -7.2376364884345, -7.230628484393112, -7.238475770984712, -7.243651868078656, -7.23567385988149, -7.240189611494555, -7.255884627062503, -7.231752576052941, -7.234520596353585, -7.239603528384539, -7.233885207667162, -7.232288789343925, -7.213622523440033, -7.225235252808737, -7.229912235896686, -7.218807050909878, -7.239032049689976, 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-7.226610598619716, -7.235369410121787], 'approximated_eneriges_1': [-7.550683242962277, -7.538822863135065, -7.55008411662876, -7.55897796865705, -7.5632027489170826, -7.571948592178383, -7.560385446643115, -7.548556313213329, -7.557350382776294, -7.539623454091931, -7.554608404243045, -7.543805800289237, -7.552635230989461, -7.41748866035232, -7.4131605710874435, -7.414964422054285, -7.40205786354657, -7.408940043385269, -7.4192390558757255, -7.401615295588742, -7.411025352351437, -7.421010290318388, -7.401690746795952, -7.40417517482812, -7.4162558000248175, -7.397908971882198, -7.548923057644963, -7.546904128323561, -7.537370942920183, -7.560631342158139, -7.556976340568663, -7.560273628380784, -7.54430452309549, -7.543731717970082, -7.54818633166277, -7.543523800200846, -7.551414499272261, -7.5466198041360935, -7.539667932956796, -7.551645714623743, -7.538862222112098, -7.562295138781764, -7.55332466813669, -7.55641294673202, -7.556218619483761, -7.540866660026964, 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plot_convergence_of_optimization_process(TI_approximated_energies, transverse_ising_4_qubits, )
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https://github.com/Tojarieh97/VQE
|
Tojarieh97
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import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 50
w_vector = np.asarray([4,3,2,1])
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 8
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 8
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
L_w = 0
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(LiH_molecule_4_qubits)
for j in tqdm(range(K)):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
approximated_energy = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(
approximated_energies_dict["approximated_eneriges_"+str(j)], approximated_energy)
L_w += w_vector[j]*approximated_energy
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=360, size=12)
optimizer_result = minimize(
cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="COBYLA",
options={"maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_k_eigenvalues_of_hamiltonian(hamiltonian):
approximated_k_eigenvalues = []
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
for eigenvalue_index, eigenvector in enumerate(computational_eigenvectors):
optimal_ansatz_state = get_ansatz_state(optimal_thetas, eigenvector)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
approximated_k_eigenvalues.append(approximated_eigenvalue)
return approximated_k_eigenvalues
from numpy import linalg as LA
from statistics import mean
def get_mean_approximation_error(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors = []
for exact_eigenvalue, approximated_eigenvalue in zip(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors.append(abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue))
return mean(approximated_errors)
def get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, k):
eigenvalues = LA.eig(hamiltonian.to_matrix())[0]
return sorted(eigenvalues)[:k]
def compare_exact_and_approximated_eigenvectors(hamiltonian, approximated_k_eigenvalues):
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print("Exact K Eigenvalues:")
print(exact_k_eigenvalues)
print("\nApproximated K Eigenvalues:")
print(sorted(approximated_k_eigenvalues))
print("\nMean Approximation error:")
print(get_mean_approximation_error(exact_k_eigenvalues, sorted(approximated_k_eigenvalues)))
approximated_energies_dict = { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def initialize_approximated_energies_dict():
return { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energies_list, energy):
approximated_energies_list.append(energy)
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
def plot_convergence_of_optimization_process(approximated_energies, hamiltonian, margin=0.02):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0,margin)
base_colors_list = list(mcolors.BASE_COLORS.keys())
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print(exact_k_eigenvalues)
for energy_level, eigenvalue in enumerate(exact_k_eigenvalues):
energy_level_name = "E_{0}".format(str(energy_level))
plt.axhline(y = eigenvalue,
color = base_colors_list[energy_level],
linestyle = 'dotted', label=energy_level_name)
plt.plot(approximated_energies["approximated_eneriges_{0}".format(str(energy_level))],
color = base_colors_list[energy_level],
label="Weighted_SSVQE({0})".format(energy_level_name))
# plt.plot(approximated_energies["approximated_eneriges_0"])
# plt.plot(approximated_energies["approximated_eneriges_1"])
# plt.plot(approximated_energies["approximated_eneriges_2"])
# plt.plot(approximated_energies["approximated_eneriges_3"])
plt.xlabel("# of iterations")
plt.ylabel("Energy")
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, Y, I, H, S
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvectors(LiH_molecule_4_qubits, LiH_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
LiH_approximated_energies = {'approximated_eneriges_0': [-7.443763256904104, -7.4002130802981165, -7.402247491880844, -7.470848596022202, -7.45320004578142, -7.2037442823809394, -7.606622032604259, -7.432350599744895, -7.432495103535102, -7.141159809219269, -7.34603922757036, -7.476135398795488, -7.280043003574207, -7.4614181224914295, -7.407924717612185, -7.461586578652535, -7.525445976535891, -7.422114431402694, -7.401649526037618, -7.488021953946464, -7.47896570893905, -7.462685937161847, -7.454120832230556, -7.436292572707697, -7.480688115871342, -7.515063846777348, -7.477177021961932, -7.391244710949009, -7.471217858315684, -7.503242588552382, -7.471439257727218, -7.44505573833778, -7.418285185624123, -7.466695823049642, -7.4771052531993325, -7.4637738318283535, -7.520776558858023, -7.526230791574609, -7.533608947411593, -7.503004948009757, -7.519724331102011, -7.493384913528219, -7.485478644775202, -7.516510223399673, -7.503475090881356, -7.494010354458551, -7.510090310795372, -7.526632388070386, -7.492160858734219, -7.5090846022988345], 'approximated_eneriges_1': [-7.611160770738447, -7.612537039823402, -7.5628667736575075, -7.627321643310454, -7.602218901158253, -7.669321267055824, -7.112869137843162, -7.529831878035033, -7.492031424566759, -7.546144927687019, -7.5380518543846815, -7.619806507952486, -7.536960192278364, -7.430594135829916, -7.558781662996708, -7.620192075334588, -7.500080654402885, -7.5874392595184466, -7.60518715593763, -7.587653509223957, -7.612775269021471, -7.6068484660945295, -7.599678769877363, -7.589714279771383, -7.60619548365883, -7.51735676728312, -7.612125836144872, -7.6014638647121675, -7.5899647846917055, -7.5976032888517775, -7.597212073112908, -7.558188737021209, -7.601200874808052, -7.607713345897209, -7.607499093171809, -7.599792654361252, -7.5596730670773855, -7.573728870000363, -7.546383632358012, -7.583001966857374, -7.5523102781572735, -7.560199542695961, -7.588780755315564, -7.566078651167328, -7.5879779290873905, -7.551861316141719, -7.573269260993632, -7.5817304433034804, -7.579569386092089, -7.570120795581553], 'approximated_eneriges_2': [-7.470829844981112, -7.470523575311227, -7.437547474097366, -7.489185208098881, -7.490140854087586, -7.406399694105737, -7.590301545017305, -7.541698353920802, -7.3691554663088015, -7.5191215141999335, -7.5115133084041545, -7.479635969058671, -7.567154091041735, -7.50831667284109, -7.404328307409327, -7.5010681837274165, -7.4650688490182455, -7.472575860441914, -7.402811603611692, -7.488550998068402, -7.488801074870055, -7.487994212250475, -7.515666333417201, -7.544214178703916, -7.510926968697341, -7.5173523503867195, -7.516193644717367, -7.53534000298624, -7.523519316290358, -7.455126696410415, -7.491381392393936, -7.504298259865865, -7.554652346024801, -7.523103712442472, -7.4955202720183, -7.517862423002627, -7.519654460714506, -7.518381698117194, -7.505702129067322, -7.504489391632537, -7.513392952340638, -7.5270772264781485, -7.519299542624053, -7.516485116618228, -7.50529569871512, -7.523333441799501, -7.499747575849092, -7.512325163721414, -7.52439763900249, -7.516395718429318], 'approximated_eneriges_3': [-7.32849500423405, -7.391564768264744, -7.474600394267608, -7.364808119047038, -7.381820772708144, -7.738911447566172, -7.758703374786833, -7.337171319897428, -7.381997666733045, -7.7142353175373115, -7.553174001897375, -7.381334761150993, -7.432289783474271, -7.368363081328347, -7.3468625031342345, -7.361828638208896, -7.480664471801326, -7.400110228803251, -7.3144431418222435, -7.368928231722106, -7.364078865897079, -7.373915189743662, -7.364944693985124, -7.3659051775080195, -7.361913922683342, -7.393984696256876, -7.358970234887909, -7.374457680841522, -7.380263158291077, -7.334590298526401, -7.362071851140452, -7.386812482151001, -7.350540699194575, -7.371636446671611, -7.367436744048734, -7.364018994060641, -7.366669879511723, -7.352155755509138, -7.36382240372502, -7.361211381137372, -7.395275852423786, -7.356090854960467, -7.385525123953955, -7.369782537122054, -7.388817786814771, -7.378669588844872, -7.38373310976381, -7.353810063874061, -7.387305671775982, -7.39466794423844]}
plot_convergence_of_optimization_process(LiH_approximated_energies, LiH_molecule_4_qubits, margin=0.02)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvectors(H2_molecule_Hamiltonian_4_qubits, H2_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
H2_approximated_energies = {'approximated_eneriges_0': [-7.6847981551656215, -7.69669203350899, -7.695360282155182, -7.678547396735197, -7.682475520277694, -7.6665142799074735, -7.628511929237866, -7.727019079759623, -7.674672621892967, -7.782410750059304, -7.782640995023298, -7.774731391845236, -7.820098880570926, -7.644963955279764, -7.765933104421869, -7.689259899346986, -7.75838188322518, -7.7617232185924685, -7.6749058485455, -7.7606516385721775, -7.628823093333026, -7.778442627599486, -7.745777242153594, -7.753227986202937, -7.784556444100247, -7.756083187584806, -7.714476381527707, -7.780522704585265, -7.776979399600117, -7.782311933837449, -7.7842922352561335, -7.7870034099757515, -7.778992899075237, -7.787348917202359, -7.781744204782898, -7.789211430733308, -7.7871397501264985, -7.784088445887376, -7.793805473659068, -7.79346880686618, -7.786308107923922, -7.7925468325707765, -7.793338173915457, -7.78652494500572, -7.790090500177619, -7.792533180308775, -7.7962537918904715, -7.78963405481515, -7.786085398062213, -7.7891853374630635], 'approximated_eneriges_1': [-7.674684523604055, -7.680764074432957, -7.684992567218362, -7.683800571677806, -7.680390184089667, -7.721622516127985, -7.295633734656554, -7.7311487161990256, -7.678587133102517, -7.662425555106433, -7.669138289334058, -7.6673461427248775, -7.626942993490443, -7.538153577774583, -7.662429920440635, -7.619523577002202, -7.614356108241046, -7.658931116094572, -7.761466767269052, -7.64876243086473, -7.575843530150479, -7.675840508678627, -7.587039305802285, -7.66134535231588, -7.659686693231967, -7.6135464123687475, -7.651463803918251, -7.634151979073155, -7.665419894321144, -7.653707767256248, -7.659251797898335, -7.658200706731602, -7.671972673195233, -7.66434999274741, -7.663813235960182, -7.666611902147287, -7.667328389333765, -7.658213410128788, -7.663109239237157, -7.669688709053952, -7.669483352101843, -7.666970692695458, -7.67011145442623, -7.66774490260206, -7.66767261347493, -7.671932371682364, -7.671697879258323, -7.664936996622855, -7.665002841620933, -7.668432858833779], 'approximated_eneriges_2': [-7.216994389513745, -7.162295345496143, -7.340953879090269, -7.354575085834582, -7.25564377642011, -7.148940094695811, -7.524402673550271, -7.354347811404502, -7.25889495057094, -7.643589020627088, -7.644947961476648, -7.625158816558789, -7.620703327132717, -7.45620769838637, -7.630870366832682, -7.575290709380177, -7.596165182631779, -7.637811242834557, -7.170274298321406, -7.641715648367393, -7.601007658607277, -7.599962246378673, -7.554443833932802, -7.635475447591654, -7.64486017630937, -7.626536753201153, -7.6322795435642625, -7.610659904945782, -7.642214540537407, -7.630361126826373, -7.645346880047898, -7.6443043653096305, -7.616965316828286, -7.644233130202644, -7.64564265540827, -7.648497631150577, -7.647931469579165, -7.645272451577426, -7.650160805708954, -7.64876250969817, -7.646823091092999, -7.645297203651874, -7.641287946379679, -7.648284082427012, -7.6468976982996475, -7.6442778318847076, -7.649731833380351, -7.647619040578347, -7.648140904559129, -7.647936421498813], 'approximated_eneriges_3': [-7.202290172665147, -7.136542775453234, -7.32557094169548, -7.3304047498628275, -7.250215528560754, -7.530121383747615, -7.674756284215522, -7.3437821085023725, -7.25926128948872, -7.043725550448698, -7.048032766005656, -7.062091983030029, -7.015079505078198, -7.130094283026538, -7.023198238540297, -6.894206716999318, -6.948244787472701, -7.045666589563991, -7.516441009890359, -7.043138953607762, -7.164113379397319, -7.083629601908816, -6.994407404756581, -7.024569950050662, -7.042675844714379, -7.071398804304009, -7.030579249445848, -6.970942611477129, -7.0452067433138, -7.009655723846796, -7.0465525569622045, -7.041138823294234, -7.0758293298141, -7.037825997609188, -7.042134113140199, -7.045247103049186, -7.04832718431786, -7.060394271726066, -7.041607839469861, -7.04191968859915, -7.038852427210924, -7.034303963384438, -7.046001232407491, -7.0401609547447235, -7.040921144894931, -7.04670117664207, -7.043097516559149, -7.038106821967233, -7.045959853355035, -7.042930913127023]}
plot_convergence_of_optimization_process(H2_approximated_energies, H2_molecule_Hamiltonian_4_qubits,margin=0.01)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvectors(transverse_ising_4_qubits, TI_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
TI_approximated_energies = {'approximated_eneriges_0': [-7.589752024122858, -7.613360553742977, -7.6190283377699295, -7.606452381315795, -7.623841264856606, -7.494521829539001, -7.646521400209204, -7.497441846730476, -7.679252378794595, -7.568306667439035, -7.635326747625471, -7.581974996633829, -7.6029476683468165, -7.629264364655602, -7.622068391999914, -7.639909424564434, -7.658080921293223, -7.6610216888186935, -7.654527411413256, -7.66008477955216, -7.7547150031040335, -7.7564360961248395, -7.7211692300067325, -7.740308604020784, -7.600566578864045, -7.745346804765525, -7.7462796221068615, -7.751641127972047, -7.731226373852388, -7.759764904228919, -7.738323394248081, -7.75008559994191, -7.776677950424584, -7.753426121197687, -7.782341273752688, -7.779205848396213, -7.748582934815819, -7.770913423670053, -7.762781290918378, -7.757243053876988, -7.771747073785976, -7.77460241775567, -7.768169945808579, -7.775293924988296, -7.777833875967182, -7.772874566073456, -7.770639259052609, -7.780183175053531, -7.770198633263086, -7.772715721535181], 'approximated_eneriges_1': [-7.479491405676765, -7.511836148005719, -7.386839072151142, -7.482910503302419, -7.45350504578557, -7.717645422348506, -7.557130209537956, -7.585292224236378, -7.601455267806437, -7.6053728445146245, -7.652940774863644, -7.495571799306382, -7.498805036929139, -7.665075417141012, -7.564424290629817, -7.649242137492966, -7.63973609380236, -7.662321437170673, -7.6197253632972295, -7.619795999950689, -7.77220111836819, -7.7560901206803, -7.733399518265041, -7.731248976846906, -7.5715275315884965, -7.707440626139587, -7.707393893999951, -7.7348112389201, -7.6963929548826515, -7.7303082911355006, -7.716146462527111, -7.726011057644771, -7.754736352832551, -7.7244308215718, -7.755435989771994, -7.740311979126285, -7.75802286075666, -7.74587377621213, -7.7511355458410875, -7.7524697184268225, -7.752276487330399, -7.752209127687969, -7.745506448113101, -7.763323596450217, -7.753689897688524, -7.761008277453863, -7.742591039142208, -7.750704035603405, -7.754889646373152, -7.762317652046046], 'approximated_eneriges_2': [-7.429773687068325, -7.456290835401122, -7.5244382722139695, -7.449488807771006, -7.475902887301357, -7.323710694006624, -7.382629223743793, -7.319565894330178, -7.37324196562631, -7.4655637009696845, -7.292361426064088, -7.305355248566785, -7.349061659711274, -7.423506442892262, -7.487123730123055, -7.419043739762055, -7.4468612412996995, -7.429270866973703, -7.449287078710123, -7.488601777023326, -7.338899993772503, -7.3479680423849905, -7.4752168162071655, -7.499949509399753, -7.438503219564106, -7.490451691757577, -7.478437506558136, -7.500437702418609, -7.500581801475034, -7.499075900701008, -7.502121265617482, -7.491113049098129, -7.518867376724795, -7.626022727858267, -7.528977849213658, -7.51704786926269, -7.341426863319758, -7.492808200100214, -7.491951333497299, -7.513636940451013, -7.517112352002725, -7.519479170352952, -7.532633970484797, -7.531363773844777, -7.533977320554524, -7.527126270896771, -7.527817041278419, -7.526558961818585, -7.533610800208856, -7.53189647381379], 'approximated_eneriges_3': [-7.491338578949814, -7.5365715669859465, -7.532419245094768, -7.536703941979599, -7.547853449746403, -7.624626489025748, -7.534978590313114, -7.508989186601839, -7.445225566309921, -7.443181538165437, -7.482755392167175, -7.491627334989187, -7.448561403824932, -7.450744878426274, -7.3527159389057335, -7.429044714148724, -7.453107440745492, -7.43199903518407, -7.426905138160319, -7.471734210770166, -7.394515983381335, -7.402658524799258, -7.382535100794421, -7.3287228122787855, -7.4052951836113845, -7.3303577854783635, -7.339337904181725, -7.340771690542788, -7.340357772707655, -7.316555819042501, -7.333550487910194, -7.313936474027675, -7.31041466499232, -7.227826572283069, -7.263505884929646, -7.299661733764759, -7.4931242665258, -7.314755252756475, -7.3482236593292924, -7.29989242094733, -7.3017643952015465, -7.296684067035896, -7.284748556671026, -7.276492262521696, -7.272782406124991, -7.295223632281355, -7.3008113357190965, -7.27265620287829, -7.284622446048762, -7.278514057888236]}
plot_convergence_of_optimization_process(TI_approximated_energies, transverse_ising_4_qubits, )
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import nbimporter
from typing import Dict, Tuple, List
import numpy as np
from tqdm import tqdm
QUBITS_NUM = 4
N = 16
K = 4
NUM_SHOTS = 1024
NUM_ITERATIONS = 100
w_vector = np.asarray([4,3,2,1])
from qiskit import Aer
from qiskit.utils import QuantumInstance, algorithm_globals
seed = 50
algorithm_globals.random_seed = seed
simulator_backend = Aer.get_backend('qasm_simulator')
from scipy.optimize import minimize
from utiles import *
input_states = get_first_k_eigenvectors_from_n_computational_basis(K, N)
from ansatz_circuit_item2 import get_full_variational_quantum_circuit
init_circuit_params = {
"thetas": np.random.uniform(low=0, high=2*np.pi, size=8),
"phis": np.random.uniform(low=0, high=2*np.pi, size=4),
"D1": 2,
"D2": 8
}
def prepare_circuit_params(thetas) -> Dict:
return {
"thetas": thetas[4:],
"phis": thetas[:4],
"D1": 2,
"D2": 8
}
def get_ansatz_state(circuit_params, input_state):
circuit_params_with_input_state = {**circuit_params, "input_state": input_state}
return get_full_variational_quantum_circuit(**circuit_params_with_input_state)
def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:
pauli_operators = hamiltonian.to_pauli_op().settings['oplist']
pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))
pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))
return pauli_coeffs, pauli_strings
from qiskit.circuit.library.standard_gates import HGate, SGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
reducing_to_pauli_z_mapping = {
'I': 'I',
'Z': 'Z',
'X': 'Z',
'Y': 'Z'
}
def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:
reduced_pauli_string = ""
for matrix_index in range(QUBITS_NUM):
pauli_matrix = str(pauli_string[matrix_index])
reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]
reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string
return reduced_pauli_string
def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):
quantum_registers = QuantumRegister(QUBITS_NUM, name="qubit")
additional_circuit_layer = QuantumCircuit(quantum_registers)
for quantum_register_index, pauli_matrix in enumerate(pauli_string):
if pauli_matrix == "X":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
if pauli_string == "Y":
additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])
additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])
extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)
return extended_quantum_circuit
def get_probability_distribution(counts: Dict) -> Dict:
proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}
return proba_distribution
def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:
quantum_state_circuit.measure_all()
transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend)
Qobj = assemble(transpiled_quantum_state_circuit)
result = simulator_backend.run(Qobj).result()
counts = result.get_counts(quantum_state_circuit)
return get_probability_distribution(counts)
def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:
return dict(sorted(proba_distribution.items()))
def reset_power_of_minus_1(power_of_minus_1):
power_of_minus_1 = 0
return power_of_minus_1
def convert_pauli_string_into_str(pauli_string) -> str:
return str(pauli_string)
def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):
pauli_string_expectation_value = 0
power_of_minus_1 = 0
pauli_string_str = convert_pauli_string_into_str(pauli_string)
extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)
probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)
reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)
sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)
for qubits_string, proba in sorted_probas_distribuition.items():
for string_index in range(QUBITS_NUM):
if(str(qubits_string[string_index])=="1" and str(pauli_string[string_index])=="Z"):
power_of_minus_1 += 1
pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba
power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)
return pauli_string_expectation_value
def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):
total_expection_value = 0
for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):
total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(
pauli_string, ansatz_circuit)
return total_expection_value
from qiskit import assemble, transpile
def cost_function(thetas, hamiltonian):
L_w = 0
circuit_params = prepare_circuit_params(thetas)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(LiH_molecule_4_qubits)
for j in tqdm(range(K)):
ansatz_state = get_ansatz_state(circuit_params, computational_eigenvectors[j])
approximated_energy = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)
insert_approximated_energy_to_list_of_all_approximated_energies(
approximated_energies_dict["approximated_eneriges_"+str(j)], approximated_energy)
L_w += w_vector[j]*approximated_energy
return L_w
def get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian):
initial_thetas = np.random.uniform(low=0, high=360, size=12)
optimizer_result = minimize(
cost_function,
x0=initial_thetas,
args=(hamiltonian),
method="COBYLA",
options={"maxiter":NUM_ITERATIONS})
optimal_thetas = prepare_circuit_params(optimizer_result.x)
return optimal_thetas
def get_approximated_k_eigenvalues_of_hamiltonian(hamiltonian):
approximated_k_eigenvalues = []
optimal_thetas = get_optimal_thetas_of_ansatz_circuit_for_hamiltonian(hamiltonian)
computational_eigenvectors = get_first_k_eigenvectors_from_n_computational_basis(K, N)
pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(hamiltonian)
for eigenvalue_index, eigenvector in enumerate(computational_eigenvectors):
optimal_ansatz_state = get_ansatz_state(optimal_thetas, eigenvector)
approximated_eigenvalue = get_expectation_value(optimal_ansatz_state, pauli_coeffs, pauli_strings)
approximated_k_eigenvalues.append(approximated_eigenvalue)
return approximated_k_eigenvalues
from numpy import linalg as LA
from statistics import mean
def get_mean_approximation_error(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors = []
for exact_eigenvalue, approximated_eigenvalue in zip(exact_k_eigenvalues, approximated_k_eigenvalues):
approximated_errors.append(abs(abs(exact_eigenvalue)-abs(approximated_eigenvalue))/abs(exact_eigenvalue))
return mean(approximated_errors)
def get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, k):
eigenvalues = LA.eig(hamiltonian.to_matrix())[0]
return sorted(eigenvalues)[:k]
def compare_exact_and_approximated_eigenvectors(hamiltonian, approximated_k_eigenvalues):
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print("Exact K Eigenvalues:")
print(exact_k_eigenvalues)
print("\nApproximated K Eigenvalues:")
print(sorted(approximated_k_eigenvalues))
print("\nMean Approximation error:")
print(get_mean_approximation_error(exact_k_eigenvalues, sorted(approximated_k_eigenvalues)))
approximated_energies_dict = { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def initialize_approximated_energies_dict():
return { "approximated_eneriges_0": [],
"approximated_eneriges_1":[],
"approximated_eneriges_2": [],
"approximated_eneriges_3": []}
def insert_approximated_energy_to_list_of_all_approximated_energies(approximated_energies_list, energy):
approximated_energies_list.append(energy)
import matplotlib.pyplot as plt
import matplotlib.colors as mcolors
def plot_convergence_of_optimization_process(approximated_energies, hamiltonian, margin=0.02):
plt.title("convergence of optimization process to the exact eigenvalue")
plt.margins(0,margin)
base_colors_list = list(mcolors.BASE_COLORS.keys())
exact_k_eigenvalues = get_exact_k_eigenvalues_of_hamiltonian(hamiltonian, K)
print(exact_k_eigenvalues)
for energy_level, eigenvalue in enumerate(exact_k_eigenvalues):
energy_level_name = "E_{0}".format(str(energy_level))
plt.axhline(y = eigenvalue,
color = base_colors_list[energy_level],
linestyle = 'dotted', label=energy_level_name)
plt.plot(approximated_energies["approximated_eneriges_{0}".format(str(energy_level))],
color = base_colors_list[energy_level],
label="Weighted_SSVQE({0})".format(energy_level_name))
plt.xlabel("# of iterations")
plt.ylabel("Energy")
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
def plot_fidelity():
plt.plot(LiH_approximated_energies)
plt.xlabel("# of iterations")
plt.ylabel("Energy")
from qiskit.opflow import X, Z, Y, I, H, S
LiH_molecule_4_qubits = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
%%time
LiH_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(LiH_molecule_4_qubits)
compare_exact_and_approximated_eigenvectors(LiH_molecule_4_qubits, LiH_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
LiH_approximated_energies = {'approximated_eneriges_0': [-7.443763256904104, -7.4002130802981165, -7.402247491880844, -7.470848596022202, -7.45320004578142, -7.2037442823809394, -7.606622032604259, -7.432350599744895, -7.432495103535102, -7.141159809219269, -7.34603922757036, -7.476135398795488, -7.280043003574207, -7.4614181224914295, -7.407924717612185, -7.461586578652535, -7.525445976535891, -7.422114431402694, -7.401649526037618, -7.488021953946464, -7.47896570893905, -7.462685937161847, -7.454120832230556, -7.436292572707697, -7.480688115871342, -7.515063846777348, -7.477177021961932, -7.391244710949009, -7.471217858315684, -7.503242588552382, -7.471439257727218, -7.44505573833778, -7.418285185624123, -7.466695823049642, -7.4771052531993325, -7.4637738318283535, -7.520776558858023, -7.526230791574609, -7.533608947411593, -7.503004948009757, -7.519724331102011, -7.493384913528219, -7.485478644775202, -7.516510223399673, -7.503475090881356, -7.494010354458551, -7.510090310795372, -7.526632388070386, -7.492160858734219, -7.5090846022988345], 'approximated_eneriges_1': [-7.611160770738447, -7.612537039823402, -7.5628667736575075, -7.627321643310454, -7.602218901158253, -7.669321267055824, -7.112869137843162, -7.529831878035033, -7.492031424566759, -7.546144927687019, -7.5380518543846815, -7.619806507952486, -7.536960192278364, -7.430594135829916, -7.558781662996708, -7.620192075334588, -7.500080654402885, -7.5874392595184466, -7.60518715593763, -7.587653509223957, -7.612775269021471, -7.6068484660945295, -7.599678769877363, -7.589714279771383, -7.60619548365883, -7.51735676728312, -7.612125836144872, -7.6014638647121675, -7.5899647846917055, -7.5976032888517775, -7.597212073112908, -7.558188737021209, -7.601200874808052, -7.607713345897209, -7.607499093171809, -7.599792654361252, -7.5596730670773855, -7.573728870000363, -7.546383632358012, -7.583001966857374, -7.5523102781572735, -7.560199542695961, -7.588780755315564, -7.566078651167328, -7.5879779290873905, -7.551861316141719, -7.573269260993632, -7.5817304433034804, -7.579569386092089, -7.570120795581553], 'approximated_eneriges_2': [-7.470829844981112, -7.470523575311227, -7.437547474097366, -7.489185208098881, -7.490140854087586, -7.406399694105737, -7.590301545017305, -7.541698353920802, -7.3691554663088015, -7.5191215141999335, -7.5115133084041545, -7.479635969058671, -7.567154091041735, -7.50831667284109, -7.404328307409327, -7.5010681837274165, -7.4650688490182455, -7.472575860441914, -7.402811603611692, -7.488550998068402, -7.488801074870055, -7.487994212250475, -7.515666333417201, -7.544214178703916, -7.510926968697341, -7.5173523503867195, -7.516193644717367, -7.53534000298624, -7.523519316290358, -7.455126696410415, -7.491381392393936, -7.504298259865865, -7.554652346024801, -7.523103712442472, -7.4955202720183, -7.517862423002627, -7.519654460714506, -7.518381698117194, -7.505702129067322, -7.504489391632537, -7.513392952340638, -7.5270772264781485, -7.519299542624053, -7.516485116618228, -7.50529569871512, -7.523333441799501, -7.499747575849092, -7.512325163721414, -7.52439763900249, -7.516395718429318], 'approximated_eneriges_3': [-7.32849500423405, -7.391564768264744, -7.474600394267608, -7.364808119047038, -7.381820772708144, -7.738911447566172, -7.758703374786833, -7.337171319897428, -7.381997666733045, -7.7142353175373115, -7.553174001897375, -7.381334761150993, -7.432289783474271, -7.368363081328347, -7.3468625031342345, -7.361828638208896, -7.480664471801326, -7.400110228803251, -7.3144431418222435, -7.368928231722106, -7.364078865897079, -7.373915189743662, -7.364944693985124, -7.3659051775080195, -7.361913922683342, -7.393984696256876, -7.358970234887909, -7.374457680841522, -7.380263158291077, -7.334590298526401, -7.362071851140452, -7.386812482151001, -7.350540699194575, -7.371636446671611, -7.367436744048734, -7.364018994060641, -7.366669879511723, -7.352155755509138, -7.36382240372502, -7.361211381137372, -7.395275852423786, -7.356090854960467, -7.385525123953955, -7.369782537122054, -7.388817786814771, -7.378669588844872, -7.38373310976381, -7.353810063874061, -7.387305671775982, -7.39466794423844]}
plot_convergence_of_optimization_process(LiH_approximated_energies, LiH_molecule_4_qubits, margin=0.02)
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
%%time
H2_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(H2_molecule_Hamiltonian_4_qubits)
compare_exact_and_approximated_eigenvectors(H2_molecule_Hamiltonian_4_qubits, H2_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
H2_approximated_energies = {'approximated_eneriges_0': [-7.231052657869664, -7.078319612689266, -7.215401871826676, -7.230221135636873, -7.262455020005291, -7.267031049860837, -7.501572363017872, -7.4813356803216, -7.4947234955867215, -7.467291869278843], 'approximated_eneriges_1': [-7.563886100199448, -7.658659320088765, -7.578874516640113, -7.5780818494863516, -7.560965458088562, -7.637089945397857, -7.663568893024004, -7.5617725937859115, -7.705323888763656, -7.702392677865555], 'approximated_eneriges_2': [-7.579265030661066, -7.5773451380441585, -7.599916344085796, -7.618297129617218, -7.60986111046384, -7.491511476610149, -7.270122634763994, -7.295684673991992, -7.268791877445621, -7.325654461172013], 'approximated_eneriges_3': [-7.592367719916387, -7.681333606694948, -7.696180773666084, -7.713150310751485, -7.710985775433959, -7.709751408629662, -7.676158468825629, -7.621108302975905, -7.706198964984833, -7.67241616951112]}
plot_convergence_of_optimization_process(H2_approximated_energies, H2_molecule_Hamiltonian_4_qubits, margin=0.01)
transverse_ising_4_qubits = 0.0 * (I^I^I^I) \
+ 0.8398088405253477 * (X^I^I^I) \
+ 0.7989496312070936 * (I^X^I^I) \
+ 0.38189710487113193 * (Z^Z^I^I) \
+ 0.057753122422666725 * (I^I^X^I) \
+ 0.5633292636970458 * (Z^I^Z^I) \
+ 0.3152740621483513 * (I^Z^Z^I) \
+ 0.07209487981989715 * (I^I^I^X) \
+ 0.17892334004292654 * (Z^I^I^Z) \
+ 0.2273896497668042 * (I^Z^I^Z) \
+ 0.09762902934216211 * (I^I^Z^Z)
%%time
TI_approximated_k_eigenvalues = get_approximated_k_eigenvalues_of_hamiltonian(transverse_ising_4_qubits)
compare_exact_and_approximated_eigenvectors(transverse_ising_4_qubits, TI_approximated_k_eigenvalues)
print(approximated_energies_dict)
approximated_energies_dict = initialize_approximated_energies_dict()
TI_approximated_energies = {'approximated_eneriges_0': [-7.527374926796388, -7.490948460217839, -7.471351892950928, -7.490702422799052, -7.515817970419744, -7.31595982882803, -7.099053535351137, -7.366127033312333, -7.558208686809385, -7.245080154006243], 'approximated_eneriges_1': [-7.435160167575143, -7.3454563436422955, -7.467036090723377, -7.46674892502807, -7.512177681355114, -7.551799781215262, -7.56977798445727, -7.337817913611366, -7.542405722352239, -7.604048469384494], 'approximated_eneriges_2': [-7.45094378726649, -7.494835406044515, -7.546427492721137, -7.5519911271001785, -7.621700741850081, -7.480593237888603, -7.63756007071119, -7.485733803067446, -7.551661441110606, -7.532503440725798], 'approximated_eneriges_3': [-7.420383731278358, -7.269163097081034, -7.378626010242662, -7.344163256333969, -7.384431167351, -7.606108205702219, -7.7098709634708, -7.590454974935595, -7.404154849273452, -7.621812392089753]}
plot_convergence_of_optimization_process(TI_approximated_energies, transverse_ising_4_qubits, )
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.opflow import X, Z, I
H2_molecule_hamiltonian = -0.5053051899926562*(I^I) + \
-0.3277380754984016*(Z^I) + \
0.15567463610622564*(Z^Z) + \
-0.3277380754984016*(I^Z)
print("========== H2 Molecule Hamiltonian for Two Qubits ==========\n")
print(H2_molecule_hamiltonian.to_matrix())
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.opflow import X, Z, I, Y
H2_molecule_Hamiltonian_4_qubits = -0.8105479805373279 * (I^I^I^I) \
+ 0.1721839326191554 * (I^I^I^Z) \
- 0.22575349222402372 * (I^I^Z^I) \
+ 0.17218393261915543 * (I^Z^I^I) \
- 0.2257534922240237 * (Z^I^I^I) \
+ 0.12091263261776627 * (I^I^Z^Z) \
+ 0.16892753870087907 * (I^Z^I^Z) \
+ 0.045232799946057826 * (Y^Y^Y^Y) \
+ 0.045232799946057826 * (X^X^Y^Y) \
+ 0.045232799946057826 * (Y^Y^X^X) \
+ 0.045232799946057826 * (X^X^X^X) \
+ 0.1661454325638241 * (Z^I^I^Z) \
+ 0.1661454325638241 * (I^Z^Z^I) \
+ 0.17464343068300453 * (Z^I^Z^I) \
+ 0.12091263261776627 * (Z^Z^I^I)
print("========== H2 Molecule Hamiltonian for Four Qubits ==========\n")
print(H2_molecule_Hamiltonian_4_qubits.to_matrix())
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.opflow import X, Z, I, Y
LiH_molecule_hamiltonian = -7.49894690201071*(I^I^I^I) + \
-0.0029329964409502266*(X^X^Y^Y) + \
0.0029329964409502266*(X^Y^Y^X) + \
0.01291078027311749*(X^Z^X^I) + \
-0.0013743761078958677*(X^Z^X^Z) + \
0.011536413200774975*(X^I^X^I) + \
0.0029329964409502266*(Y^X^X^Y) + \
-0.0029329964409502266*(Y^Y^X^X) + \
0.01291078027311749*(Y^Z^Y^I) + \
-0.0013743761078958677*(Y^Z^Y^Z) + \
0.011536413200774975*(Y^I^Y^I) + \
0.16199475388004184*(Z^I^I^I) + \
0.011536413200774975*(Z^X^Z^X) + \
0.011536413200774975*(Z^Y^Z^Y) + \
0.12444770133137588*(Z^Z^I^I) + \
0.054130445793298836*(Z^I^Z^I) + \
0.05706344223424907*(Z^I^I^Z) + \
0.012910780273117487*(I^X^Z^X) + \
-0.0013743761078958677*(I^X^I^X) + \
0.012910780273117487*(I^Y^Z^Y) + \
-0.0013743761078958677*(I^Y^I^Y) + \
0.16199475388004186*(I^Z^I^I) + \
0.05706344223424907*(I^Z^Z^I) + \
0.054130445793298836*(I^Z^I^Z) + \
-0.013243698330265966*(I^I^Z^I) + \
0.08479609543670981*(I^I^Z^Z) + \
-0.013243698330265952*(I^I^I^Z)
print("========== LiH Molecule Hamiltonian for Four Qubits ==========\n")
print(LiH_molecule_hamiltonian.to_matrix())
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
import numpy as np
from qiskit.opflow import X, Z, I
a_1 = np.random.random_sample()
a_2 = np.random.random_sample()
J_21 = np.random.random_sample()
transverse_ising_2_qubits = a_1*(I^X) + a_2*(X^I) + J_21*(Z^Z)
print("========== Transverse Ising Model Hamiltonian for Two Qubits ==========\n")
print(transverse_ising_2_qubits)
print()
print(transverse_ising_2_qubits.to_matrix())
print()
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.opflow import X, Z, I, Y
import numpy as np
QUBITS_NUM = 3
def create_pauli_string_with_pauli_op_on_index_i(pauli_op, i, qubits_num):
if i == 1:
pauli_string = pauli_op
for qubit in range(qubits_num - 1):
pauli_string = pauli_string ^ I
return pauli_string
pauli_string = I
for qubit in range(2, qubits_num + 1):
if qubit == i:
pauli_string = pauli_string ^ pauli_op
else:
pauli_string = pauli_string ^ I
return pauli_string
def create_pauli_string_with_pauli_ops_on_index_i_and_j(pauli_op_second, i, pauli_op_first, j, qubits_num):
if j == 1:
pauli_string = pauli_op_first
for qubit in range(2, qubits_num + 1):
if qubit == i:
pauli_string = pauli_string ^ pauli_op_second
else:
pauli_string = pauli_string ^ I
return pauli_string
pauli_string = I
for qubit in range(2, qubits_num + 1):
if qubit == j:
pauli_string = pauli_string ^ pauli_op_first
elif qubit == i:
pauli_string = pauli_string ^ pauli_op_second
else:
pauli_string = pauli_string ^ I
return pauli_string
def get_Ising_model_hamiltonian():
hamiltonian = I
for qubit in range(QUBITS_NUM - 1):
hamiltonian = hamiltonian^I
hamiltonian = 0 * hamiltonian
for i in range(1, QUBITS_NUM + 1):
a_i = np.random.random_sample()
x_i = create_pauli_string_with_pauli_op_on_index_i(X, i, QUBITS_NUM)
hamiltonian = hamiltonian + a_i * x_i
for j in range(1, i):
J_ij = np.random.random_sample()
z_ij = create_pauli_string_with_pauli_ops_on_index_i_and_j(Z, i, Z, j, QUBITS_NUM)
hamiltonian = hamiltonian + J_ij * z_ij
return hamiltonian
transverse_ising_3_qubits = get_Ising_model_hamiltonian()
print(transverse_ising_3_qubits)
from qiskit.opflow import X, Z, I
H2_molecule_hamiltonian = 0.0 * (I^I^I)
+ 0.012764169333459807 * (X^I^I)
+ 0.7691573729160869 * (I^X^I)
+ 0.398094746026449 * (Z^Z^I)
+ 0.15250261906586637 * (I^I^X)
+ 0.2094051920882264 * (Z^I^Z)
+ 0.5131291860752999 * (I^Z^Z)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.opflow import X, Z, I, Y
import numpy as np
QUBITS_NUM = 4
def create_pauli_string_with_pauli_op_on_index_i(pauli_op, i, qubits_num):
if i == 1:
pauli_string = pauli_op
for qubit in range(qubits_num - 1):
pauli_string = pauli_string ^ I
return pauli_string
pauli_string = I
for qubit in range(2, qubits_num + 1):
if qubit == i:
pauli_string = pauli_string ^ pauli_op
else:
pauli_string = pauli_string ^ I
return pauli_string
def create_pauli_string_with_pauli_ops_on_index_i_and_j(pauli_op_second, i, pauli_op_first, j, qubits_num):
if j == 1:
pauli_string = pauli_op_first
for qubit in range(2, qubits_num + 1):
if qubit == i:
pauli_string = pauli_string ^ pauli_op_second
else:
pauli_string = pauli_string ^ I
return pauli_string
pauli_string = I
for qubit in range(2, qubits_num + 1):
if qubit == j:
pauli_string = pauli_string ^ pauli_op_first
elif qubit == i:
pauli_string = pauli_string ^ pauli_op_second
else:
pauli_string = pauli_string ^ I
return pauli_string
def get_Ising_model_hamiltonian():
hamiltonian = I
for qubit in range(QUBITS_NUM - 1):
hamiltonian = hamiltonian^I
hamiltonian = 0 * hamiltonian
for i in range(1, QUBITS_NUM + 1):
a_i = np.random.random_sample()
x_i = create_pauli_string_with_pauli_op_on_index_i(X, i, QUBITS_NUM)
hamiltonian = hamiltonian + a_i * x_i
for j in range(1, i):
J_ij = np.random.random_sample()
z_ij = create_pauli_string_with_pauli_ops_on_index_i_and_j(Z, i, Z, j, QUBITS_NUM)
hamiltonian = hamiltonian + J_ij * z_ij
return hamiltonian
transverse_ising_4_qubits = get_Ising_model_hamiltonian()
print(transverse_ising_4_qubits)
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from openfermion.chem import MolecularData
from openfermion.transforms import get_fermion_operator, jordan_wigner
from openfermion.linalg import get_ground_state, get_sparse_operator
import numpy
import scipy
import scipy.linalg
# Load saved file for H2.
diatomic_bond_length = 1.2
geometry = [('H', (0., 0., 0.)), ('H', (0., 0., diatomic_bond_length))]
basis = 'sto-3g'
multiplicity = 1
# Set Hamiltonian parameters.
active_space_start = 1
active_space_stop = 3
# Generate and populate instance of MolecularData.
molecule = MolecularData(geometry, basis, multiplicity, description="1.2")
molecule.load()
# Get the Hamiltonian in an active space.
molecular_hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=range(1),
active_indices=range(1, 2))
# Map operator to fermions and qubits.
fermion_hamiltonian = get_fermion_operator(molecular_hamiltonian)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
qubit_hamiltonian.compress()
print('The Jordan-Wigner Hamiltonian in canonical basis follows:\n{}'.format(qubit_hamiltonian))
# Get sparse operator and ground state energy.
sparse_hamiltonian = get_sparse_operator(qubit_hamiltonian)
energy, state = get_ground_state(sparse_hamiltonian)
print('Ground state energy before rotation is {} Hartree.\n'.format(energy))
# Randomly rotate.
n_orbitals = molecular_hamiltonian.n_qubits // 2
n_variables = int(n_orbitals * (n_orbitals - 1) / 2)
numpy.random.seed(1)
random_angles = numpy.pi * (1. - 2. * numpy.random.rand(n_variables))
kappa = numpy.zeros((n_orbitals, n_orbitals))
index = 0
for p in range(n_orbitals):
for q in range(p + 1, n_orbitals):
kappa[p, q] = random_angles[index]
kappa[q, p] = -numpy.conjugate(random_angles[index])
index += 1
# Build the unitary rotation matrix.
difference_matrix = kappa + kappa.transpose()
rotation_matrix = scipy.linalg.expm(kappa)
# Apply the unitary.
molecular_hamiltonian.rotate_basis(rotation_matrix)
# Get qubit Hamiltonian in rotated basis.
qubit_hamiltonian = jordan_wigner(molecular_hamiltonian)
qubit_hamiltonian.compress()
print('The Jordan-Wigner Hamiltonian in rotated basis follows:\n{}'.format(qubit_hamiltonian))
# Get sparse Hamiltonian and energy in rotated basis.
sparse_hamiltonian = get_sparse_operator(qubit_hamiltonian)
energy, state = get_ground_state(sparse_hamiltonian)
print('Ground state energy after rotation is {} Hartree.'.format(energy))
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from openfermion.chem import MolecularData
from openfermion.transforms import get_fermion_operator, jordan_wigner
from openfermion.linalg import get_ground_state, get_sparse_operator
import numpy
import scipy
import scipy.linalg
# Load saved file for LiH.
diatomic_bond_length = 1.45
geometry = [('Li', (0., 0., 0.)), ('H', (0., 0., diatomic_bond_length))]
basis = 'sto-3g'
multiplicity = 1
# Set Hamiltonian parameters.
active_space_start = 1
active_space_stop = 3
# Generate and populate instance of MolecularData.
molecule = MolecularData(geometry, basis, multiplicity, description="1.45")
molecule.load()
# Get the Hamiltonian in an active space.
molecular_hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=range(active_space_start),
active_indices=range(active_space_start, active_space_stop))
# Map operator to fermions and qubits.
fermion_hamiltonian = get_fermion_operator(molecular_hamiltonian)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
qubit_hamiltonian.compress()
print('The Jordan-Wigner Hamiltonian in canonical basis follows:\n{}'.format(qubit_hamiltonian))
# Get sparse operator and ground state energy.
sparse_hamiltonian = get_sparse_operator(qubit_hamiltonian)
energy, state = get_ground_state(sparse_hamiltonian)
print('Ground state energy before rotation is {} Hartree.\n'.format(energy))
# Randomly rotate.
n_orbitals = molecular_hamiltonian.n_qubits // 2
n_variables = int(n_orbitals * (n_orbitals - 1) / 2)
numpy.random.seed(1)
random_angles = numpy.pi * (1. - 2. * numpy.random.rand(n_variables))
kappa = numpy.zeros((n_orbitals, n_orbitals))
index = 0
for p in range(n_orbitals):
for q in range(p + 1, n_orbitals):
kappa[p, q] = random_angles[index]
kappa[q, p] = -numpy.conjugate(random_angles[index])
index += 1
# Build the unitary rotation matrix.
difference_matrix = kappa + kappa.transpose()
rotation_matrix = scipy.linalg.expm(kappa)
# Apply the unitary.
molecular_hamiltonian.rotate_basis(rotation_matrix)
# Get qubit Hamiltonian in rotated basis.
qubit_hamiltonian = jordan_wigner(molecular_hamiltonian)
qubit_hamiltonian.compress()
print('The Jordan-Wigner Hamiltonian in rotated basis follows:\n{}'.format(qubit_hamiltonian))
# Get sparse Hamiltonian and energy in rotated basis.
sparse_hamiltonian = get_sparse_operator(qubit_hamiltonian)
energy, state = get_ground_state(sparse_hamiltonian)
print('Ground state energy after rotation is {} Hartree.'.format(energy))
|
https://github.com/Tojarieh97/VQE
|
Tojarieh97
|
from qiskit.circuit.library.standard_gates import RXGate, RZGate, CXGate, CZGate
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
def get_thetas_circuit(thetas, D2):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
for d in range(D2):
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
qc.append(CZGate(), [qr[0], qr[1]])
qc.append(CZGate(), [qr[1], qr[2]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
qc.append(RXGate(thetas[0]), [qr[0]])
qc.append(RXGate(thetas[1]), [qr[1]])
qc.append(RXGate(thetas[2]), [qr[2]])
qc.append(RXGate(thetas[3]), [qr[3]])
qc.append(RZGate(thetas[4]), [qr[0]])
qc.append(RZGate(thetas[5]), [qr[1]])
qc.append(RZGate(thetas[6]), [qr[2]])
qc.append(RZGate(thetas[7]), [qr[3]])
return qc
def get_phis_circuit(phis, D1):
qr = QuantumRegister(4, name="qubit")
qc = QuantumCircuit(qr)
for d in range(D1):
qc.append(RXGate(phis[0]), [qr[2]])
qc.append(RXGate(phis[1]), [qr[3]])
qc.append(RZGate(phis[2]), [qr[2]])
qc.append(RZGate(phis[3]), [qr[3]])
qc.append(CZGate(), [qr[2], qr[3]])
qc.barrier(qr)
return qc
def get_full_variational_quantum_circuit(thetas, phis, D1, D2):
thetas_quantum_circuit = get_thetas_circuit(thetas, D2)
phis_quantum_circuit = get_phis_circuit(phis, D1)
variational_quantum_circuit = phis_quantum_circuit.compose(thetas_quantum_circuit)
return variational_quantum_circuit
import numpy as np
thetas = np.random.uniform(low=0, high=2*np.pi, size=8)
phis = np.random.uniform(low=0, high=2*np.pi, size=4)
D1 = 2
D2 = 6
qc1 = get_thetas_circuit(thetas,D2)
print(qc1.draw())
qc2 = get_phis_circuit(phis,D1)
print(qc2.draw())
print(get_full_variational_quantum_circuit(thetas, phis, D1, D2))
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit.circuit import Parameter
from qiskit import pulse
from qiskit.test.mock.backends.almaden import *
phase = Parameter('phase')
with pulse.build(FakeAlmaden()) as phase_test_sched:
pulse.shift_phase(phase, pulse.drive_channel(0))
phase_test_sched.instructions # ()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit.circuit import Parameter
from qiskit import pulse
from qiskit.test.mock.backends.almaden import *
phase = Parameter('phase')
with pulse.build(FakeAlmaden()) as phase_test_sched:
pulse.shift_phase(phase, pulse.drive_channel(0))
phase_test_sched.instructions # ()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit.circuit import Parameter
from qiskit import pulse
from qiskit.test.mock.backends.almaden import *
phase = Parameter('phase')
with pulse.build(FakeAlmaden()) as phase_test_sched:
pulse.shift_phase(phase, pulse.drive_channel(0))
phase_test_sched.instructions # ()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
# https://github.com/Z-726/Bugs-from-Users/edit/main/Program/1999.py
import numpy as np
from qiskit import *
from qiskit.transpiler import transpile
from qiskit.tools.qi.qi import random_unitary_matrix
from qiskit.mapper import two_qubit_kak
from qiskit.mapper import CouplingMap
from qiskit.extensions.standard import SwapGate
from qiskit.converters import circuit_to_dag
def build_qv_circuit(seed, n, depth):
"""Create a quantum program containing model circuits.
The model circuits consist of layers of Haar random
elements of SU(4) applied between corresponding pairs
of qubits in a random bipartition.
name = leading name of circuits
n = number of qubits
depth = ideal depth of each model circuit (over SU(4))
"""
np.random.seed(seed)
q = QuantumRegister(n, "q")
c = ClassicalRegister(n, "c")
# Create measurement subcircuit
qc = QuantumCircuit(q,c)
# For each layer
for j in range(depth):
# Generate uniformly random permutation Pj of [0...n-1]
perm = np.random.permutation(n)
# For each pair p in Pj, generate Haar random SU(4)
# Decompose each SU(4) into CNOT + SU(2) and add to Ci
for k in range(int(np.floor(n/2))):
qubits = [int(perm[2*k]), int(perm[2*k+1])]
U = random_unitary_matrix(4)
for gate in two_qubit_kak(U):
i0 = qubits[gate["args"][0]]
if gate["name"] == "cx":
i1 = qubits[gate["args"][1]]
qc.cx(q[i0], q[i1])
elif gate["name"] == "u1":
qc.u1(gate["params"][2], q[i0])
elif gate["name"] == "u2":
qc.u2(gate["params"][1], gate["params"][2],
q[i0])
elif gate["name"] == "u3":
qc.u3(gate["params"][0], gate["params"][1],
gate["params"][2], q[i0])
elif gate["name"] == "id":
pass # do nothing
#qc.measure(q,c)
return qc
circuit = build_qv_circuit(1234, 20, 100)
dag = circuit_to_dag(circuit)
print(dag.num_tensor_factors())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
#https://github.com/Qiskit/qiskit-terra/issues/2009
import numpy as np
from qiskit import *
from qiskit.tools.qi.qi import random_unitary_matrix
from qiskit.mapper import two_qubit_kak
q = QuantumRegister(2, 'q')
qc = QuantumCircuit(q)
num_gates = np.random.randint(30)
# h = 0, x = 1, y = 2, z = 3, cx = 4
for _ in range(num_gates):
item = np.random.randint(5)
if item in [0, 1, 2, 3]:
idx = np.random.randint(size)
if item == 0:
qc.h(q[idx])
elif item == 1:
qc.x(q[idx])
elif item == 2:
qc.y(q[idx])
elif item == 3:
qc.z(q[idx])
else:
idx = np.random.permutation(size)
qc.cx(q[int(idx[0])], q[int(idx[1])])
uni = Aer.get_backend('unitary_simulator')
res = execute(qc, uni).result()
U = res.get_unitary()
two_qubit_kak(U)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
# https://github.com/Qiskit/qiskit-terra/issues/2036
from qiskit import QuantumRegister, QuantumCircuit, ClassicalRegister, transpiler
import numpy as np
q = QuantumRegister(6, name='qn')
c = ClassicalRegister(2, name='cn')
zz = QuantumCircuit(q, c)
zz.h(q[0])
zz.h(q[5])
zz.cx(q[0], q[5])
zz.u1(2 * np.pi, q[5])
zz.cx(q[0], q[5])
zz.h(q[0])
zz.h(q[5])
zz.barrier(q)
zz.measure(q[0], c[0])
zz.measure(q[5], c[1])
print(zz)
new_zz = transpiler.transpile(zz, basis_gates='u1, u2, u3, cx, id',
coupling_map=[[0, 1], [0, 5], [1, 0], [1, 2], [2, 1], [2, 3],
[3, 2], [3, 4], [4, 3], [4, 9], [5, 0], [5, 6],
[5, 10], [6, 5], [6, 7], [7, 6], [7, 8], [7, 12],
[8, 7], [8, 9], [9, 4], [9, 8], [9, 14], [10, 5],
[10, 11], [10, 15], [11, 10], [11, 12], [12, 7],
[12, 11], [12, 13], [13, 12], [13, 14], [14, 9],
[14, 13], [14, 19], [15, 10], [15, 16], [16, 15],
[16, 17], [17, 16], [17, 18], [18, 17], [18, 19],
[19, 14], [19, 18]], initial_layout = {("qn", 0): ("q", 0), ("qn", 1): ("q", 1),
("qn", 2): ("q", 2), ("qn", 3): ("q", 3), ("qn", 4): ("q", 4), ("qn", 5): ("q", 5)})
print(new_zz)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
# https://github.com/Qiskit/qiskit-terra/issues/2373
# Importing needed libraries
from qiskit import *
from qiskit.mapper import Layout
import numpy as np
import matplotlib as mp
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
# Enable use of real device
IBMQ.load_accounts()
backend_exp = IBMQ.get_backend('ibmq_16_melbourne')
for u in range(0,1): # It isn't important, it is because I measured all qubit's T1
u_st = str(u)
file1 = 'T1__raw_qubit_' + u_st + '.txt'
out1 = open( file1, 'w' )
out1.write('# This is the qubit\'s ' + u_st +' T1 raw data \n' )
circuit = []
q = QuantumRegister(2, 'q') #Only changing this and the layout makes it works
c1 = ClassicalRegister(1, 'c')
qc = QuantumCircuit(q)
mz = QuantumCircuit(q,c1)
lay = Layout({ (q,0) : 0, (q,1):1 })
# Exciting the qubit
qc.x(q[0])
qc.barrier(q)
# Measurment on Z-axis
mz.measure(q[0],c1[0])
# Waiting time ( 30*0.12 us each iteration)
for i in range(50):
identity = QuantumCircuit(q,c1)
identity.barrier(q)
for k in range(i*30):
identity.iden(q)
identity.barrier(q)
circuit.append(qc+identity+mz)
# Running the experiment
jobZ = execute(circuit, backend_exp, initial_layout=lay, shots=1024)
out1.write('# N° id_gates Z-Measure Error \n')
Result = jobZ.result() # Taking the results
counts = []
for i in range(50):
counts.append(Result.get_counts(circuit[i]) )
# Preparing the lists to make fits
y = []
x = []
for i in range(50):
py = counts[i]['1']/1024
x.append(i*30*0.12)
y.append( py )
out1.write(str(i*30) + ' '+ str(py) + '\n')
out1.write( '\n')
def expo(x, amp, slope, high):
y = amp*np.exp(-slope*x)+high
return y
x = np.array(x)
y = np.array(y)
err_y = np.array(err_y)
params , paramscov = curve_fit(expo, x, y,p0=[1,0.02,0] )
a =np.sqrt(np.diag(paramscov))
out1.write('The raw T1 is ' + str(1/params[1])+ ' +- ' + str(a[1]/params[1]) + '\n')
out1.close()
plt.figure()
plt.plot(x, expo(x, *params),
label='Raw fitted function')
plt.plot(x , y, 'ro', label= 'data')
plt.xlabel( ' Time [us] ')
plt.ylabel(' Probability of being in the excited state ')
plt.legend()
plt.savefig('plot_q_'+ u_st+ '_raw.png')
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
# https://github.com/Qiskit/qiskit-terra/issues/5839
from qiskit import QuantumCircuit,QuantumRegister, Aer, execute
from qiskit.compiler import transpile
from qiskit.quantum_info.states.measures import state_fidelity
from IPython.core.display import display
# Create circuit
circ = QuantumCircuit(3)
circ.x(0)
circ.cnot(0,1)
circ.snapshot('snap1', snapshot_type='statevector')
circ.snapshot('snap1', snapshot_type='density_matrix')
circ.cnot(0,2)
circ.snapshot('snap2', snapshot_type='statevector')
circ.snapshot('snap2', snapshot_type='density_matrix')
circ.cnot(1,2)
circ.snapshot('snap3', snapshot_type='statevector')
circ.snapshot('snap3', snapshot_type='density_matrix')
circ.measure_all()
transpiled_circ = transpile(circ, coupling_map=[[0,1],[1,0],[1,2],[2,1]],optimization_level=2)
display(circ.draw())
display(transpiled_circ.draw())
results = execute(circ,Aer.get_backend('qasm_simulator')).result()
statevector1 = results.data()['snapshots']['statevector']['snap1'][0]
statevector2 = results.data()['snapshots']['statevector']['snap2'][0]
statevector3 = results.data()['snapshots']['statevector']['snap2'][0]
density_matrix1 = results.data()['snapshots']['density_matrix']['snap1'][0]['value']
density_matrix2 = results.data()['snapshots']['density_matrix']['snap2'][0]['value']
density_matrix3 = results.data()['snapshots']['density_matrix']['snap3'][0]['value']
results = execute(transpiled_circ,Aer.get_backend('qasm_simulator')).result()
statevector_transpiled1 = results.data()['snapshots']['statevector']['snap1'][0]
statevector_transpiled2 = results.data()['snapshots']['statevector']['snap2'][0]
statevector_transpiled3 = results.data()['snapshots']['statevector']['snap3'][0]
density_matrix_transpiled1 = results.data()['snapshots']['density_matrix']['snap1'][0]['value']
density_matrix_transpiled2 = results.data()['snapshots']['density_matrix']['snap2'][0]['value']
density_matrix_transpiled3 = results.data()['snapshots']['density_matrix']['snap3'][0]['value']
print('Fidelity between transpiled and normal statevector snapshots')
print('snap 1',state_fidelity(statevector_transpiled1,statevector1))
print('snap 2',state_fidelity(statevector_transpiled2,statevector2))
print('snap 3',state_fidelity(statevector_transpiled3,statevector3))
print('\nFidelity between transpiled and normal density matrix snapshots')
print('snap 1',state_fidelity(density_matrix_transpiled1,density_matrix1))
print('snap 2',state_fidelity(density_matrix_transpiled2,density_matrix2))
print('snap 3',state_fidelity(density_matrix_transpiled3,density_matrix3))
print('Counts normal: ',results.get_counts(circ))
print('Counts transpiled: ',results.get_counts(transpiled_circ))
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
open Microsoft.Quantum.Intrinsic;
open Microsoft.Quantum.Math;
operation GlobalPhaseI(q:Qubit):Unit is Adj+Ctl{
X(q);
Z(q);
Y(q);
}
namespace Quantum.Kata.SingleQubitGates{
open Microsoft.Quantum.Intrinsic;
open Microsoft.Quantum.Math;
operation GlobalPhaseI(q:Qubit):Unit is Adj+Ctl{
X(q);
Z(q);
Y(q);
}
}
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit.circuit import Parameter
from qiskit import pulse
from qiskit.test.mock.backends.almaden import *
phase = Parameter('phase')
with pulse.build(FakeAlmaden()) as phase_test_sched:
pulse.shift_phase(phase, pulse.drive_channel(0))
phase_test_sched.instructions # ()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit.circuit import Parameter
from qiskit import pulse
from qiskit.test.mock.backends.almaden import *
phase = Parameter('phase')
with pulse.build(FakeAlmaden()) as phase_test_sched:
pulse.shift_phase(phase, pulse.drive_channel(0))
phase_test_sched.instructions # ()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.wrapper import available_backends, get_backend
from qiskit.wrapper import execute as q_execute
q = QuantumRegister(2, name='q')
c = ClassicalRegister(2, name='c')
qc = QuantumCircuit(q,c)
qc.h(q[0])
qc.h(q[1])
qc.cx(q[0], q[1])
qc.measure(q, c)
z = 0.995004165 + 1j * 0.099833417
z = z / abs(z)
u_error = np.array([[1, 0], [0, z]])
noise_params = {'U':
{'gate_time': 1,
'p_depol': 0.001,
'p_pauli': [0, 0, 0.01],
'U_error': u_error
}
}
config = {"noise_params": noise_params}
ret = q_execute(qc, 'local_qasm_simulator_cpp', shots=1024, config=config)
ret = ret.result()
print(ret.get_counts())
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
# The snipplet above ==== is buggy version; the code below ==== is fixed version.
from math import pi,pow
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, BasicAer, execute
def IQFT(circuit, qin, n):
for i in range (int(n/2)):
circuit.swap(qin[i], qin[n -1 -i])
for i in range (n):
circuit.h(qin[i])
for j in range (i +1, n, 1):
circuit.cu1(-pi/ pow(2, j-i), qin[j], qin[i])
n = 3
qin = QuantumRegister(n)
cr = ClassicalRegister(n)
circuit = QuantumCircuit(qin, cr, name="Inverse_Quantum_Fourier_Transform")
circuit.h(qin)
circuit.z(qin[2])
circuit.s(qin[1])
circuit.z(qin[0])
circuit.t(qin[0])
IQFT(circuit, qin, n)
circuit.measure (qin, cr)
backend = BasicAer.get_backend("qasm_simulator")
result = execute(circuit, backend, shots = 500).result()
counts = result.get_counts(circuit)
print(counts)
#============
from math import pi,pow
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, BasicAer, execute
def QFT(n, inverse=False):
"""This function returns a circuit implementing the (inverse) QFT."""
circuit = QuantumCircuit(n, name='IQFT' if inverse else 'QFT')
# here's your old code, building the inverse QFT
for i in range(int(n/2)):
# note that I removed the qin register, since registers are not
# really needed and you can just use the qubit indices
circuit.swap(i, n - 1 - i)
for i in range(n):
circuit.h(i)
for j in range(i + 1, n, 1):
circuit.cu1(-pi / pow(2, j - i), j, i)
# now we invert it to get the regular QFT
if inverse:
circuit = circuit.inverse()
return circuit
n = 3
qin = QuantumRegister(n)
cr = ClassicalRegister(n)
circuit = QuantumCircuit(qin, cr)
circuit.h(qin)
circuit.z(qin[2])
circuit.s(qin[1])
circuit.z(qin[0])
circuit.t(qin[0])
# get the IQFT and add it to your circuit with ``compose``
# if you want the regular QFT, just set inverse=False
iqft = QFT(n, inverse=True)
circuit.compose(iqft, inplace=True)
circuit.measure (qin, cr)
backend = BasicAer.get_backend("qasm_simulator")
result = execute(circuit, backend, shots = 500).result()
counts = result.get_counts(circuit)
print(counts)
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import Aer, QuantumCircuit, transpile
from qiskit.circuit.library import PhaseEstimation
qc= QuantumCircuit(3,3)
# dummy unitary circuit
unitary_circuit = QuantumCircuit(1)
unitary_circuit.h(0)
# QPE
qc.append(PhaseEstimation(2, unitary_circuit), list(range(3)))
qc.measure(list(range(3)), list(range(3)))
backend = Aer.get_backend('qasm_simulator')
qc_transpiled = transpile(qc, backend)
result = backend.run(qc, shots = 8192).result()
|
https://github.com/Z-928/Bugs4Q
|
Z-928
|
from qiskit import *
qc = QuantumCircuit(2)
qc.h(i)
qc.crz (PI/4, 0, 1)
|
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