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7.62k
QPC004_C3
A3A70AB7DC992
1
WA
1801 ms
160 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: x = QuantumRegister(n) # Register for x y = QuantumRegister(n + 1) # Register for y (n + 1 qubits) qc = QuantumCircuit(x, y) # We will use a series of controlled additions to implement the oracle for x_value in range(0, L): # Calculate ax mod L ax_mod_L = (a * x_value) % L # Convert x_value to binary and apply controlled addition for i in range(n): if (x_value >> i) & 1: # If the i-th bit of x_value is 1 # We need to add ax_mod_L to y # We will add ax_mod_L to y using controlled operations for j in range(n + 1): if (ax_mod_L >> j) & 1: # If the j-th bit of ax_mod_L is 1 # Apply a controlled NOT gate to add the j-th bit of ax_mod_L to y qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A8675F16998A9
1
RE
1644 ms
157 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(x): if (a >> i) & 1: # Check if the i-th bit of 'a' is 1 for j in range(ny): oracle.append(CXGate(), [x + j, i]) # Controlled-X from y to x # Add the y register to the result (modular addition is handled implicitly by Qiskit) for i in range(y): oracle.append(CXGate(), [x + y + i, x + i]) # Controlled-X from output to x # Apply the modular reduction (mod L) if L < 2^n if L < 2**n: # Implement modular reduction using subtraction and conditional flips for i in range(n - 1, -1, -1): if (L >> i) & 1: # Check if the i-th bit of L is 1 for j in range(i): oracle.append(CXGate(), [x + y + j, x + y + i]) # Controlled-X from lower bits to i-th bit return qc '''
QPC004_C3
A99EBFB8A8CD1
1
WA
1928 ms
161 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers for x and y x, y = QuantumRegister(n), QuantumRegister(n + 1) # Create quantum circuit qc = QuantumCircuit(x, y) # We need to implement: |x⟩|y⟩ → |x⟩|(y + ax) mod L⟩ # For each bit position i in x register for i in range(n): # Control on x[i] being 1 # If x[i] is 1, add (2^i * a) mod L to y controlled_value = (pow(2, i) * a) % L # Implement controlled modular addition # Use standard quantum addition circuits with modulo L # This typically involves quantum adders and modular reduction for j in range(n): if (controlled_value >> j) & 1: qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A99EBFB8A8CD1
2
UME
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import QFT def modular_addition(qc, x, y, a, L, n): """ Implements y -> (y + ax) mod L """ for i in range(n): for j in range(n + 1): if (a >> i) & 1: qc.ccx(x[i], y[j], y[(j + (1 << i)) % (n + 1)]) # Modulo L enforcement qc.append(QFT(n+1, do_swaps=False).inverse(), y) qc.x(y[n]) qc.append(QFT(n+1, do_swaps=False), y) return qc def solve(n: int, a: int, L: int) -> QuantumCircuit: x = QuantumRegister(n, name='x') y = QuantumRegister(n + 1, name='y') qc = QuantumCircuit(x, y) # Implement modular addition oracle modular_addition(qc, x, y, a, L, n) return qc '''
QPC004_C3
A99EBFB8A8CD1
3
WA
1942 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: x = QuantumRegister(n, 'x') y = QuantumRegister(n + 1, 'y') qc = QuantumCircuit(x, y) # Apply controlled addition for each qubit in x for i in range(n): # Controlled addition of a * 2^i to y for j in range(n + 1): if (a * (1 << i)) & (1 << j): qc.cx(x[i], y[j]) # Apply modulo L operation # Since L <= 2^n, we can use a comparison and subtraction approach # This is a simplified approach and may need refinement for specific cases # For a full implementation, additional qubits and gates would be needed return qc '''
QPC004_C3
A99EBFB8A8CD1
4
WA
1620 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers for x and y x = QuantumRegister(n, 'x') y = QuantumRegister(n, 'y') # Create quantum circuit qc = QuantumCircuit(x, y) # We need to perform (y + ax) mod L # We can implement this using controlled additions # For each qubit i in x register for i in range(n): # If the i-th bit of x is 1, we add a*2^i to y (controlled addition) value = (a * (1 << i)) % L # Calculate the value to add (mod L) # Break down value into binary for controlled additions for j in range(n): if value & (1 << j): qc.cx(x[i], y[j]) # The modulo L operation is handled implicitly since: # 1. L <= 2^n (from constraints) # 2. We're already doing (a * 2^i) mod L in our addition return qc '''
QPC004_C3
A99EBFB8A8CD1
5
WA
1665 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers for x and y x = QuantumRegister(n, 'x') y = QuantumRegister(n + 1, 'y') # Note: n+1 qubits for y as per problem # Create quantum circuit qc = QuantumCircuit(x, y) # For each bit i in x for i in range(n): # For each bit j in y for j in range(n + 1): # Apply controlled addition based on the pattern: # If bit i in x is 1, we add corresponding value to y if (a * (1 << i)) & (1 << j): qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A99EBFB8A8CD1
6
WA
1988 ms
161 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers for x and y x = QuantumRegister(n, 'x') y = QuantumRegister(n + 1, 'y') # Create quantum circuit qc = QuantumCircuit(x, y) # Apply controlled addition for each qubit in x for i in range(n): # Controlled addition of a * 2^i to y for j in range(n + 1): if (a * (1 << i)) & (1 << j): if j > 0: # Only apply when j > 0 as per example qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A99EBFB8A8CD1
7
WA
1801 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers for x and y x = QuantumRegister(n, 'x') y = QuantumRegister(n + 1, 'y') # n+1 qubits for y register # Create quantum circuit qc = QuantumCircuit(x, y) # Apply controlled addition for each qubit in x for i in range(n): for j in range(n + 1): # Following exactly the condition from the example if (a * (1 << i)) & (1 << j): qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A99EBFB8A8CD1
8
WA
1732 ms
160 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: # Initialize registers x = QuantumRegister(n, 'x') y = QuantumRegister(n, 'y') # Note: Problem shows n qubits for y qc = QuantumCircuit(x, y) # Controlled addition of ax mod L to y # The key is to apply controlled-X gates based on the binary representation # of (a * x) mod L # For each control qubit in x for i in range(n): # For each target qubit in y for j in range(n): # The condition from example: if this bit position should flip if (a * (1 << i)) & (1 << j): # Apply controlled-NOT from x[i] to y[j] qc.cx(x[i], y[j]) return qc '''
QPC004_C3
A99EBFB8A8CD1
9
WA
1753 ms
163 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: """ Creates a quantum circuit that performs modular multiplication: |x⟩|y⟩ → |x⟩|y ⊕ (ax mod L)⟩ Args: n (int): Number of qubits in each register a (int): Multiplication factor L (int): Modulus Returns: QuantumCircuit: Circuit implementing the modular multiplication """ # Initialize registers x = QuantumRegister(n, 'x') y = QuantumRegister(n, 'y') qc = QuantumCircuit(x, y) # For each possible value of x for x_val in range(1 << n): # Calculate (a * x_val) mod L result = (a * x_val) % L # For each target qubit in y for j in range(n): # If this bit should be flipped for this x_val if result & (1 << j): # Create control pattern for this x_val for i in range(n): # Apply X or CX gates based on x_val bits if x_val & (1 << i): qc.cx(x[i], y[j]) else: # If control bit should be 0, add X gates before and after qc.x(x[i]) qc.cx(x[i], y[j]) qc.x(x[i]) return qc '''
QPC004_C3
A99EBFB8A8CD1
10
WA
1626 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: """ Creates a quantum circuit that performs modular multiplication: |x⟩|y⟩ → |x⟩|y ⊕ (ax mod L)⟩ Args: n (int): Number of qubits in each register a (int): Multiplication factor L (int): Modulus Returns: QuantumCircuit: Circuit implementing the modular multiplication """ # Initialize registers x = QuantumRegister(n, 'x') y = QuantumRegister(n, 'y') qc = QuantumCircuit(x, y) # Create table of all possible values and their modular products for x_val in range(1 << n): result = (a * x_val) % L # For each bit in result for j in range(n): if result & (1 << j): # Create control pattern controls = [] neg_controls = [] # Determine which qubits should be controlled on 0 vs 1 for i in range(n): if x_val & (1 << i): controls.append(i) else: neg_controls.append(i) # Apply X gates before controlled operation for i in neg_controls: qc.x(x[i]) # Apply multi-controlled X gate if len(controls + neg_controls) > 0: for control in controls + neg_controls: qc.cx(x[control], y[j]) # Restore X gates after controlled operation for i in neg_controls: qc.x(x[i]) return qc '''
QPC004_C3
AC58B559AAF5B
1
WA
1594 ms
161 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): for j in range(n+1): if (a >> i) & 1: qc.cx(x[i], y[j]) # CNOTゲートでx[i]に基づいてy[j]に操作を行う return qc '''
QPC004_C3
ADE5FF0F4C260
1
RE
1575 ms
159 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import RYGate import numpy as np import math def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc def add(n: int, a: int) -> QuantumCircuit: k = QuantumRegister(n) qc = QuantumCircuit(k) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.p(theta, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def controlled_add(n: int, a: int, control_count: int) -> QuantumCircuit: k, c = QuantumRegister(n), QuantumRegister(control_count) qc = QuantumCircuit(k, c) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.mcp(theta, c, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def oracle_less(bitcount: int, n: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) qc = QuantumCircuit(regin, regout) if n >= 2**bitcount: qc.x(regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: controls = [] for idx in range(bitcount): if mask[idx] == "*": continue controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.x(regin[idx]) if len(controls) != 0: qc.mcx(controls, regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def controlled_oracle_less(bitcount: int, n: int, control_count: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) control = QuantumRegister(control_count) qc = QuantumCircuit(regin, regout, control) if n >= 2**bitcount: qc.mcx(control, regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: regin_controls = [] for idx in range(bitcount): if mask[idx] == "*": continue regin_controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.mcx(control, regin[idx]) if len(regin_controls) != 0: qc.mcx([*regin_controls, *control], regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def cmodadd(n: int, a: int, L: int) -> QuantumCircuit: """in(n+1), control, anc1, anc2, anc3""" regin = QuantumRegister(n + 1) control = QuantumRegister(1) qc = QuantumCircuit(regin, control) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.cx(control, anc_range1) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L - a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.mcx([*control, anc_range1, anc_range2], anc_range3) qc.compose(controlled_add(n + 1, a, 1), [*regin, *control], inplace=True) qc.compose( controlled_add(n + 1, -L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.mcx([anc_range1, anc_range2, *control], anc_range3) qc.cx(control, anc_range2) qc.cx(control, regin[-1]) qc.mcx([regin[-1], *anc_range2, *control], anc_range3) qc.cx(control, regin[-1]) qc.compose( controlled_add(n + 1, L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.compose( controlled_oracle_less(n + 1, 2 ** (n + 1) + 1 - L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.compose(controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range3,*control], inplace=True) qc.cx(control, anc_range2) qc.compose(controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2,*control], inplace=True) qc.compose(controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range1,*control], inplace=True) qc.compose(controlled_oracle_less(n + 1, a, 1), [*regin, *anc_range1,*control], inplace=True) qc.cx(control, anc_range1) return qc def modfma(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) for idx in range(n): add = pow(a, 2**idx, L) qc.compose(cmodadd(n, add, L), [*y, x[idx], *ancs], inplace=True) return qc '''
QPC004_C3
ADE5FF0F4C260
2
RE
1598 ms
159 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import RYGate import numpy as np import math def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc def add(n: int, a: int) -> QuantumCircuit: k = QuantumRegister(n) qc = QuantumCircuit(k) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.p(theta, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def controlled_add(n: int, a: int, control_count: int) -> QuantumCircuit: k, c = QuantumRegister(n), QuantumRegister(control_count) qc = QuantumCircuit(k, c) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.mcp(theta, c, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def oracle_less(bitcount: int, n: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) qc = QuantumCircuit(regin, regout) if n >= 2**bitcount: qc.x(regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: controls = [] for idx in range(bitcount): if mask[idx] == "*": continue controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.x(regin[idx]) if len(controls) != 0: qc.mcx(controls, regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def controlled_oracle_less(bitcount: int, n: int, control_count: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) control = QuantumRegister(control_count) qc = QuantumCircuit(regin, regout, control) if n >= 2**bitcount: qc.mcx(control, regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: regin_controls = [] for idx in range(bitcount): if mask[idx] == "*": continue regin_controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.mcx(control, regin[idx]) if len(regin_controls) != 0: qc.mcx([*regin_controls, *control], regout) for idx in range(bitcount): if flipped[idx]: qc.mcx(control, regin[idx]) return qc def modadd(n: int, a: int, L: int) -> QuantumCircuit: regin = QuantumRegister(n + 1) qc = QuantumCircuit(regin) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.x(anc_range1) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L - a), [*regin, *anc_range1], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.compose(add(n + 1, a), inplace=True) qc.compose(controlled_add(n + 1, -L, 1), [*regin, *anc_range3], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.x(anc_range2) qc.x(regin[-1]) qc.ccx(regin[-1], anc_range2, anc_range3) qc.x(regin[-1]) qc.compose(controlled_add(n + 1, L, 1), [*regin, *anc_range3], inplace=True) qc.compose( oracle_less(n + 1, 2 ** (n + 1) + 1 - L), [*regin, *anc_range3], inplace=True ) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range3], inplace=True) qc.x(anc_range2) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range1], inplace=True) qc.compose(oracle_less(n + 1, a), [*regin, *anc_range1], inplace=True) qc.x(anc_range1) return qc def cmodadd(n: int, a: int, L: int) -> QuantumCircuit: """in(n+1), control, anc1, anc2, anc3""" regin = QuantumRegister(n + 1) control = QuantumRegister(1) qc = QuantumCircuit(regin, control) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.cx(control, anc_range1) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L - a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.mcx([*control, anc_range1, anc_range2], anc_range3) qc.compose(controlled_add(n + 1, a, 1), [*regin, *control], inplace=True) qc.compose( controlled_add(n + 1, -L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.mcx([anc_range1, anc_range2, *control], anc_range3) qc.cx(control, anc_range2) qc.cx(control, regin[-1]) qc.mcx([regin[-1], *anc_range2, *control], anc_range3) qc.cx(control, regin[-1]) qc.compose( controlled_add(n + 1, L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.compose( controlled_oracle_less(n + 1, 2 ** (n + 1) + 1 - L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.cx(control, anc_range2) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.cx(control, anc_range1) return qc def modfma(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) for idx in range(n): add = pow(a, 2**idx, L) qc.compose(cmodadd(n, add, L), [*y, x[idx], *ancs], inplace=True) return qc '''
QPC004_C3
ADE5FF0F4C260
3
RE
1527 ms
160 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import RYGate import numpy as np import math def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc def add(n: int, a: int) -> QuantumCircuit: k = QuantumRegister(n) qc = QuantumCircuit(k) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.p(theta, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def controlled_add(n: int, a: int, control_count: int) -> QuantumCircuit: k, c = QuantumRegister(n), QuantumRegister(control_count) qc = QuantumCircuit(k, c) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.mcp(theta, c, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def oracle_less(bitcount: int, n: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) qc = QuantumCircuit(regin, regout) if n >= 2**bitcount: qc.x(regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: controls = [] for idx in range(bitcount): if mask[idx] == "*": continue controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.x(regin[idx]) if len(controls) != 0: qc.mcx(controls, regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def controlled_oracle_less(bitcount: int, n: int, control_count: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) control = QuantumRegister(control_count) qc = QuantumCircuit(regin, regout, control) if n >= 2**bitcount: qc.mcx(control, regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: regin_controls = [] for idx in range(bitcount): if mask[idx] == "*": continue regin_controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.mcx(control, regin[idx]) if len(regin_controls) != 0: qc.mcx([*regin_controls, *control], regout) for idx in range(bitcount): if flipped[idx]: qc.mcx(control, regin[idx]) return qc def modadd(n: int, a: int, L: int) -> QuantumCircuit: regin = QuantumRegister(n + 1) qc = QuantumCircuit(regin) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.x(anc_range1) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L - a), [*regin, *anc_range1], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.compose(add(n + 1, a), inplace=True) qc.compose(controlled_add(n + 1, -L, 1), [*regin, *anc_range3], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.x(anc_range2) qc.x(regin[-1]) qc.ccx(regin[-1], anc_range2, anc_range3) qc.x(regin[-1]) qc.compose(controlled_add(n + 1, L, 1), [*regin, *anc_range3], inplace=True) qc.compose( oracle_less(n + 1, 2 ** (n + 1) + 1 - L), [*regin, *anc_range3], inplace=True ) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range3], inplace=True) qc.x(anc_range2) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range1], inplace=True) qc.compose(oracle_less(n + 1, a), [*regin, *anc_range1], inplace=True) qc.x(anc_range1) return qc def cmodadd(n: int, a: int, L: int) -> QuantumCircuit: """in(n+1), control, anc1, anc2, anc3""" regin = QuantumRegister(n + 1) control = QuantumRegister(1) qc = QuantumCircuit(regin, control) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.cx(control, anc_range1) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L - a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.mcx([*control, anc_range1, anc_range2], anc_range3) qc.compose(controlled_add(n + 1, a, 1), [*regin, *control], inplace=True) qc.compose( controlled_add(n + 1, -L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.mcx([anc_range1, anc_range2, *control], anc_range3) qc.cx(control, anc_range2) qc.cx(control, regin[-1]) qc.mcx([regin[-1], *anc_range2, *control], anc_range3) qc.cx(control, regin[-1]) qc.compose( controlled_add(n + 1, L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.compose( controlled_oracle_less(n + 1, 2 ** (n + 1) + 1 - L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.cx(control, anc_range2) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.cx(control, anc_range1) return qc def modfma(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) for idx in range(n): add = a * (2**idx) % L qc.compose(cmodadd(n, add, L), [*y, x[idx], *ancs], inplace=True) return qc '''
QPC004_C3
ADE5FF0F4C260
4
AC
2773 ms
167 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import RYGate import numpy as np import math def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc def add(n: int, a: int) -> QuantumCircuit: k = QuantumRegister(n) qc = QuantumCircuit(k) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.p(theta, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def controlled_add(n: int, a: int, control_count: int) -> QuantumCircuit: k, c = QuantumRegister(n), QuantumRegister(control_count) qc = QuantumCircuit(k, c) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.mcp(theta, c, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def oracle_less(bitcount: int, n: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) qc = QuantumCircuit(regin, regout) if n >= 2**bitcount: qc.x(regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: controls = [] for idx in range(bitcount): if mask[idx] == "*": continue controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.x(regin[idx]) if len(controls) != 0: qc.mcx(controls, regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def controlled_oracle_less(bitcount: int, n: int, control_count: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) control = QuantumRegister(control_count) qc = QuantumCircuit(regin, regout, control) if n >= 2**bitcount: qc.mcx(control, regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: regin_controls = [] for idx in range(bitcount): if mask[idx] == "*": continue regin_controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.mcx(control, regin[idx]) if len(regin_controls) != 0: qc.mcx([*regin_controls, *control], regout) for idx in range(bitcount): if flipped[idx]: qc.mcx(control, regin[idx]) return qc def modadd(n: int, a: int, L: int) -> QuantumCircuit: regin = QuantumRegister(n + 1) qc = QuantumCircuit(regin) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.x(anc_range1) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L - a), [*regin, *anc_range1], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.compose(add(n + 1, a), inplace=True) qc.compose(controlled_add(n + 1, -L, 1), [*regin, *anc_range3], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.x(anc_range2) qc.x(regin[-1]) qc.ccx(regin[-1], anc_range2, anc_range3) qc.x(regin[-1]) qc.compose(controlled_add(n + 1, L, 1), [*regin, *anc_range3], inplace=True) qc.compose( oracle_less(n + 1, 2 ** (n + 1) + 1 - L), [*regin, *anc_range3], inplace=True ) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range3], inplace=True) qc.x(anc_range2) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range1], inplace=True) qc.compose(oracle_less(n + 1, a), [*regin, *anc_range1], inplace=True) qc.x(anc_range1) return qc def cmodadd(n: int, a: int, L: int) -> QuantumCircuit: """in(n+1), control, anc1, anc2, anc3""" regin = QuantumRegister(n + 1) control = QuantumRegister(1) qc = QuantumCircuit(regin, control) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.cx(control, anc_range1) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L - a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.mcx([*control, anc_range1, anc_range2], anc_range3) qc.compose(controlled_add(n + 1, a, 1), [*regin, *control], inplace=True) qc.compose( controlled_add(n + 1, -L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.mcx([anc_range1, anc_range2, *control], anc_range3) qc.cx(control, anc_range2) qc.cx(control, regin[-1]) qc.mcx([regin[-1], *anc_range2, *control], anc_range3) qc.cx(control, regin[-1]) qc.compose( controlled_add(n + 1, L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.compose( controlled_oracle_less(n + 1, 2 ** (n + 1) + 1 - L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.cx(control, anc_range2) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.cx(control, anc_range1) return qc def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) for idx in range(n): add = a * (2**idx) % L qc.compose(cmodadd(n, add, L), [*y, x[idx], *ancs], inplace=True) return qc '''
QPC004_C3
ADF02875A7997
1
TLE
3000 ms
173 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n+1,2**n-L+a), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(add(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(add(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) return qc def add(n,a): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc '''
QPC004_C3
ADF02875A7997
2
TLE
3000 ms
172 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n+1,2**n-L+a), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(add(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(add(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) return qc def add(n,a): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc '''
QPC004_C3
ADF02875A7997
3
AC
3000 ms
172 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n+1,2**n-L+a), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(add(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(iqft(n),qubits = list(range(n)), inplace=True) return qc def add(n,a): qc = QuantumCircuit(n) qc.compose(qft(n), inplace=True) qc.compose(shift(n,a), inplace=True) qc.compose(iqft(n), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def iqft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A39B0C341BDED
1
UME
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import QFT def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Step 1: Apply QFT to input register qft = QFT(n, do_swaps=False) qc.append(qft, x[:]) # Step 2: Phase rotations based on modular multiplication for i in range(n): for j in range(i + 1): # Calculate phase for controlled rotation phase = (2 * (a * 2**(i-j)) % L) / L # Add controlled phase rotation qc.cp(2 * pi * phase, x[j], y[i]) # Step 3: Apply inverse QFT qft_dagger = QFT(n, do_swaps=False).inverse() qc.append(qft_dagger, x[:]) return qc '''
QPC004_C4
A39B0C341BDED
2
WA
1784 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from math import pi def qft(qc: QuantumCircuit, q: QuantumRegister, n: int): """Implement QFT from scratch""" for i in range(n): qc.h(q[i]) for j in range(i+1, n): qc.cp(pi/2**(j-i), q[j], q[i]) def inverse_qft(qc: QuantumCircuit, q: QuantumRegister, n: int): """Implement inverse QFT from scratch""" for i in range(n-1, -1, -1): for j in range(n-1, i, -1): qc.cp(-pi/2**(j-i), q[j], q[i]) qc.h(q[i]) def solve(n: int, a: int, L: int) -> QuantumCircuit: # Create quantum registers x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Step 1: Apply custom QFT to input register qft(qc, x, n) # Step 2: Phase rotations based on modular multiplication for i in range(n): for j in range(i + 1): # Calculate phase for controlled rotation phase = (2 * (a * 2**(i-j)) % L) / L qc.cp(2 * pi * phase, x[j], y[i]) # Step 3: Apply custom inverse QFT inverse_qft(qc, x, n) return qc '''
QPC004_C4
A39B0C341BDED
3
RE
1764 ms
158 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def qft(n: int, inverse=False): """Manually implement the Quantum Fourier Transform (QFT)""" qc = QuantumCircuit(n) for j in range(n): qc.h(j) for k in range(j + 1, n): qc.cp(-np.pi / 2**(k - j), k, j) # Controlled phase gate if inverse: qc = qc.inverse() # Take inverse if needed return qc def modular_addition(n: int, a: int): """Implement modular addition using QFT and controlled phase gates.""" qc = QuantumCircuit(n) # Apply QFT qc.append(qft(n), range(n)) # Apply phase shifts to encode addition for i in range(n): if (a >> i) & 1: # Check if bit i of 'a' is set qc.p(np.pi / 2**(n - i - 1), i) # Apply inverse QFT qc.append(qft(n, inverse=True), range(n)) return qc def solve(n: int, a: int) -> QuantumCircuit: """Controlled constant addition circuit.""" k_reg = QuantumRegister(n, name='k') c_reg = QuantumRegister(1, name='c') # Control qubit qc = QuantumCircuit(k_reg, c_reg) # Controlled modular addition: Apply only if control qubit is 1 controlled_add = modular_addition(n, a).control(1) qc.append(controlled_add, [c_reg[0]] + k_reg[:]) return qc '''
QPC004_C4
A39B0C341BDED
4
RE
1656 ms
157 MiB
'''python import numpy as np from qiskit import QuantumCircuit, QuantumRegister def manual_qft(n): """Constructs the Quantum Fourier Transform (QFT) without using the Qiskit QFT library.""" qc = QuantumCircuit(n) for j in range(n): qc.h(j) for k in range(j + 1, n): qc.cp(np.pi / 2**(k - j), k, j) return qc def manual_iqft(n): """Constructs the Inverse Quantum Fourier Transform (IQFT) manually.""" return manual_qft(n).inverse() def controlled_modular_addition(n, a): """Implements controlled modular addition using QFT and controlled phase shifts.""" qc = QuantumCircuit(n + 1) # +1 for the control qubit # Apply QFT to the lower n qubits qft_circuit = manual_qft(n) qc.append(qft_circuit, range(n)) # Apply controlled phase shifts based on 'a' for i in range(n): if (a >> i) & 1: # Check if bit i of 'a' is set qc.cp(np.pi / 2**(n - i - 1), n, i) # Controlled phase shift by control qubit # Apply inverse QFT iqft_circuit = manual_iqft(n) qc.append(iqft_circuit, range(n)) return qc def solve(n: int, a: int) -> QuantumCircuit: """Implements the Controlled Constant Addition circuit while following constraints.""" k_reg = QuantumRegister(n, name='k') # Register for 'k' c_reg = QuantumRegister(1, name='c') # Control qubit qc = QuantumCircuit(k_reg, c_reg) # Controlled addition: Applied only if c = 1 controlled_add = controlled_modular_addition(n, a).to_gate(label="C-ADD(a)").control(1) qc.append(controlled_add, [c_reg[0]] + k_reg[:]) return qc '''
QPC004_C4
A39B0C341BDED
5
RE
2016 ms
158 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def controlled_modular_addition(n, a): """Implements controlled modular addition using bitwise operations.""" qc = QuantumCircuit(n + 1) # Extra qubit for control for i in range(n): if (a >> i) & 1: # If the i-th bit of 'a' is 1 qc.cx(n, i) # Controlled-X: If control is 1, flip bit i of 'k' return qc def solve(n: int, a: int) -> QuantumCircuit: """Constructs an optimized controlled modular addition circuit.""" k_reg = QuantumRegister(n, name='k') # Register for k c_reg = QuantumRegister(1, name='c') # Control qubit qc = QuantumCircuit(k_reg, c_reg) # Apply controlled modular addition (bitwise controlled-X operations) controlled_add = controlled_modular_addition(n, a).to_gate(label="C-ADD(a)").control(1) qc.append(controlled_add, [c_reg[0]] + k_reg[:]) return qc '''
QPC004_C4
A49D000568755
1
AC
2455 ms
170 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import RYGate import numpy as np import math def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc def add(n: int, a: int) -> QuantumCircuit: k = QuantumRegister(n) qc = QuantumCircuit(k) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.p(theta, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def controlled_add(n: int, a: int, control_count: int) -> QuantumCircuit: k, c = QuantumRegister(n), QuantumRegister(control_count) qc = QuantumCircuit(k, c) # Write your code here: qc.compose(qft(n), inplace=True) for idx in range(n): theta = 2 * a * math.pi * (2**idx) / (2**n) qc.mcp(theta, c, k[idx]) qc.compose(qft(n).inverse(), inplace=True) return qc def oracle_less(bitcount: int, n: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) qc = QuantumCircuit(regin, regout) if n >= 2**bitcount: qc.x(regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: controls = [] for idx in range(bitcount): if mask[idx] == "*": continue controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.x(regin[idx]) if len(controls) != 0: qc.mcx(controls, regout) for idx in range(bitcount): if flipped[idx]: qc.x(regin[idx]) return qc def controlled_oracle_less(bitcount: int, n: int, control_count: int) -> QuantumCircuit: regin, regout = QuantumRegister(bitcount), QuantumRegister(1) control = QuantumRegister(control_count) qc = QuantumCircuit(regin, regout, control) if n >= 2**bitcount: qc.mcx(control, regout) return qc bitrep = bin(n)[2:].zfill(bitcount)[::-1] masks = [] for idx in range(bitcount): if bitrep[idx] == "1": mask = ("0" + bitrep[idx + 1 :]).rjust(bitcount, "*") masks.append(mask) flipped = [False] * bitcount for mask in masks: regin_controls = [] for idx in range(bitcount): if mask[idx] == "*": continue regin_controls.append(regin[idx]) if (mask[idx] == "0") != (flipped[idx]): flipped[idx] = not flipped[idx] qc.mcx(control, regin[idx]) if len(regin_controls) != 0: qc.mcx([*regin_controls, *control], regout) for idx in range(bitcount): if flipped[idx]: qc.mcx(control, regin[idx]) return qc def modadd(n: int, a: int, L: int) -> QuantumCircuit: regin = QuantumRegister(n + 1) qc = QuantumCircuit(regin) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.x(anc_range1) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L - a), [*regin, *anc_range1], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.compose(add(n + 1, a), inplace=True) qc.compose(controlled_add(n + 1, -L, 1), [*regin, *anc_range3], inplace=True) qc.ccx(anc_range1, anc_range2, anc_range3) qc.x(anc_range2) qc.x(regin[-1]) qc.ccx(regin[-1], anc_range2, anc_range3) qc.x(regin[-1]) qc.compose(controlled_add(n + 1, L, 1), [*regin, *anc_range3], inplace=True) qc.compose( oracle_less(n + 1, 2 ** (n + 1) + 1 - L), [*regin, *anc_range3], inplace=True ) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range3], inplace=True) qc.x(anc_range2) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range2], inplace=True) qc.compose(oracle_less(n + 1, L), [*regin, *anc_range1], inplace=True) qc.compose(oracle_less(n + 1, a), [*regin, *anc_range1], inplace=True) qc.x(anc_range1) return qc def cmodadd(n: int, a: int, L: int) -> QuantumCircuit: """in(n+1), control, anc1, anc2, anc3""" regin = QuantumRegister(n + 1) control = QuantumRegister(1) qc = QuantumCircuit(regin, control) # Write your code here: anc_range1 = QuantumRegister(1) anc_range2 = QuantumRegister(1) anc_range3 = QuantumRegister(1) qc.add_register(anc_range1) qc.add_register(anc_range2) qc.add_register(anc_range3) qc.cx(control, anc_range1) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L - a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.mcx([*control, anc_range1, anc_range2], anc_range3) qc.compose(controlled_add(n + 1, a, 1), [*regin, *control], inplace=True) qc.compose( controlled_add(n + 1, -L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.mcx([anc_range1, anc_range2, *control], anc_range3) qc.cx(control, anc_range2) qc.cx(control, regin[-1]) qc.mcx([regin[-1], *anc_range2, *control], anc_range3) qc.cx(control, regin[-1]) qc.compose( controlled_add(n + 1, L, 2), [*regin, *anc_range3, *control], inplace=True ) qc.compose( controlled_oracle_less(n + 1, 2 ** (n + 1) + 1 - L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range3, *control], inplace=True, ) qc.cx(control, anc_range2) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range2, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, L, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.compose( controlled_oracle_less(n + 1, a, 1), [*regin, *anc_range1, *control], inplace=True, ) qc.cx(control, anc_range1) return qc def cmodfma(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) for idx in range(n): add = a * (2**idx) % L qc.compose(cmodadd(n, add, L), [*y, x[idx], *ancs], inplace=True) return qc def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: ancs = QuantumRegister(3) qc.add_register(ancs) qc.compose(cmodfma(n, a, L), inplace=True) for idx in range(n): qc.swap(x[idx], y[idx]) qc.compose(cmodfma(n, -pow(a, -1, L), L), inplace=True) return qc '''
QPC004_C4
A841677C41D28
1
WA
1933 ms
160 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, a: int, L: int) -> QuantumCircuit: x = QuantumRegister(n) # Register for input x y = QuantumRegister(n + 1) # Register for output ax mod L qc = QuantumCircuit(x, y) # We will implement the multiplication by a and then take mod L # We will use a series of controlled additions to achieve this. # We need to add a * x to the output register for i in range(n): if (a >> i) & 1: # Check if the i-th bit of a is set # We will add x to the output register controlled by the i-th qubit of x for j in range(n + 1): # Controlled addition of x to y qc.cx(x[i], y[j]) # Controlled-X gate to add x to y # Now we need to apply the modulo operation # We will use a series of Toffoli gates to implement the modulo operation # This is a simplified version and may not be the most efficient way to implement mod L # but it will work for small values of n and L. # We will use a classical approach to implement the modulo operation # by checking if the value exceeds L and then subtracting L if necessary. # This is a naive implementation and may need optimization for larger values. # For simplicity, we will assume L is a power of 2, which is true for the given constraints. # We will use the last qubit of y to store the carry for the modulo operation. # Example: if L = 2^n, we can simply ignore the overflow bits. # This is a placeholder for the actual modulo operation. # In practice, you would need to implement a more complex circuit to handle arbitrary L. return qc '''
QPC004_C4
A8FFDD8E2F3A2
1
TLE
3000 ms
178 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.cx(i,n+i) qc.cx(n+i,i) qc.cx(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(add(n+1,2**n-L+a), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(add(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(iqft(n),qubits = list(range(n)), inplace=True) return qc def add(n,a): qc = QuantumCircuit(n) qc.compose(qft(n), inplace=True) qc.compose(shift(n,a), inplace=True) qc.compose(iqft(n), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def iqft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
2
TLE
3000 ms
182 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.cx(i,n+i) qc.cx(n+i,i) qc.cx(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(iqft(n+1),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(shift(n+1,2**n-L+a), inplace=True) qc.compose(iqft(n+1), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(iqft(n),qubits = list(range(n)), inplace=True) return qc def add(n,a): qc = QuantumCircuit(n) qc.compose(qft(n), inplace=True) qc.compose(shift(n,a), inplace=True) qc.compose(iqft(n), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def iqft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
3
TLE
3000 ms
182 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.cx(i,n+i) qc.cx(n+i,i) qc.cx(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(shift(n+1,2**n-L+a), inplace=True) qc.compose(qft(n+1).inverse(), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(qft(n).inverse(),qubits = list(range(n)), inplace=True) return qc def add(n,a): qc = QuantumCircuit(n) qc.compose(qft(n), inplace=True) qc.compose(shift(n,a), inplace=True) qc.compose(qft(n).inverse(), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def iqft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(-2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
4
TLE
3000 ms
182 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.cx(i,n+i) qc.cx(n+i,i) qc.cx(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(shift(n+1,2**n-L+a), inplace=True) qc.compose(qft(n+1).inverse(), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(qft(n).inverse(),qubits = list(range(n)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
5
TLE
3000 ms
182 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L).control(1),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(shift(n+1,2**n-L+a), inplace=True) qc.compose(qft(n+1).inverse(), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,a), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(qft(n).inverse(),qubits = list(range(n)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
6
WA
2534 ms
165 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): b = (a*2**i)%L qc.compose(shift(n+1,2**n-L+b), inplace=True) qc.compose(qft(n+1).inverse(), inplace=True) qc.compose(pack(n,2**n-L+b,2**n+b), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,b), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): b = ((L-a_inv)*2**i)%L qc.compose(shift(n+1,2**n-L+b), inplace=True) qc.compose(qft(n+1).inverse(), inplace=True) qc.compose(pack(n,2**n-L+b,2**n+b), inplace=True) qc.compose(qft(n+1), inplace=True) qc.compose(shift(n+1,b), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) # Write your code here: qc.compose(qft(n),qubits = list(range(n)), inplace=True) qc.compose(shift(n,-t).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(shift(n,-s).control(1),qubits = [n]+list(range(n)), inplace=True) qc.x(n) qc.compose(qft(n).inverse(),qubits = list(range(n)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C4
A8FFDD8E2F3A2
7
AC
2847 ms
164 MiB
'''python import math from qiskit import QuantumCircuit, QuantumRegister def qft(n: int) -> QuantumCircuit: qc = QuantumCircuit(n) for i in reversed(range(n)): qc.h(i) for j in reversed(range(i)): qc.cp(math.pi / 2 ** (i - j), j, i) for i in range(n // 2): qc.swap(i, n - i - 1) return qc def crot(n: int, a: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) for i in range(n): theta = 2 * math.pi * a * 2**i / 2**n qc.cp(theta, n, i) return qc def cadd(n: int, a: int) -> QuantumCircuit: qc = QuantumCircuit(n + 1) qc.compose(qft(n), qubits=range(n), inplace=True) qc.compose(crot(n, a), qubits=range(n + 1), inplace=True) qc.compose(qft(n).inverse(), qubits=range(n), inplace=True) return qc def ccrot(n: int, a: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) for i in range(n): theta = 2 * math.pi * a * 2**i / 2**n qc.mcp(theta, [n, n + 1], i) return qc def ccadd(n: int, a: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) qc.compose(qft(n), qubits=range(n), inplace=True) qc.compose(ccrot(n, a), qubits=range(n + 2), inplace=True) qc.compose(qft(n).inverse(), qubits=range(n), inplace=True) return qc def cpack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) qc.compose(ccadd(n, 2 ** (n + 1) - t), qubits=range(n + 2), inplace=True) qc.x(n) qc.compose(ccadd(n, -s), qubits=range(n + 2), inplace=True) qc.x(n) return qc def add_ax_mod(n: int, L: int, a: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) for i in range(n): b = (2**i * a) % L targets = [*y, x[i]] qc.compose(cadd(n + 1, 2**n - L), qubits=targets, inplace=True) qc.compose(cadd(n + 1, b), qubits=targets, inplace=True) qc.compose(cpack(n, 2**n - L + b, 2**n + b), qubits=targets, inplace=True) qc.compose(cadd(n + 1, b), qubits=targets, inplace=True) return qc def inv_mod(a: int, L: int) -> int: def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: if b == 0: return a, 1, 0 gcd, x1, y1 = extended_euclidean(b, a % b) x = y1 y = x1 - (a // b) * y1 return gcd, x, y _, x, _ = extended_euclidean(a, L) return x % L def solve(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) qc.compose(add_ax_mod(n, L, a), qubits=range(2 * n + 1), inplace=True) for i in range(n): qc.swap(x[i], y[i]) b = -inv_mod(a, L) % L qc.compose(add_ax_mod(n, L, b), qubits=range(2 * n + 1), inplace=True) return qc '''
QPC004_C5
A047671A4EB2D
1
WA
1684 ms
160 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Step 1: Create superposition on the first n qubits for i in range(n): qc.h(x[i]) # Apply Hadamard gate to each qubit in the first register # Step 2: Compute a^k mod L for each k in the superposition # We will use controlled operations to achieve this for k in range(2**n): # Calculate a^k mod L mod_result = pow(a, k, L) # Convert mod_result to binary and store in the second register for j in range(2 * m + 1): if (mod_result >> j) & 1: qc.x(y[j]) # Apply X gate to set the corresponding bit return qc '''
QPC004_C5
A047671A4EB2D
2
UME
'''python from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library.standard_gates import QFT import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Apply Hadamard gates on the first n qubits for i in range(n): qc.h(x[i]) # Apply controlled phase gates based on the value of k for k in range(2**n): binary_k = format(k, '0'+str(n)+'b') # Convert k to binary string for i in range(n): if binary_k[i] == '0': qc.x(x[i]) phase = (a**k) % L binary_phase = format(phase, '0'+str(2*m+1)+'b') # Convert phase to binary string for i in range(2*m+1): if binary_phase[i] == '1': qc.cp(2*math.pi / (2**m), x, y[i]) for i in range(n): if binary_k[i] == '0': qc.x(x[i]) # Apply inverse QFT on the first n qubits qft_dagger = QFT(n, inverse=True) qc.append(qft_dagger, x) return qc '''
QPC004_C5
A047671A4EB2D
3
AC
2076 ms
164 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: """ Create |0>_n |0>_(2m+1) → (1/√(2^n)) Σ_k |k> |a^k mod L> Registers are in little-endian order. """ x = QuantumRegister(n, 'x') # exponent register y = QuantumRegister(2 * m + 1, 'y') # result register (enough qubits for L) qc = QuantumCircuit(x, y) # 1) Prepare uniform superposition on |x> for i in range(n): qc.h(x[i]) # |0…0> → (1/√2^n) Σ_k |k> # helper: multi-controlled X with an arbitrary number of controls def cX(ctrls, tgt): if len(ctrls) == 0: qc.x(tgt) elif len(ctrls) == 1: qc.cx(ctrls[0], tgt) else: qc.mcx(ctrls, tgt) # built-in multi-controlled X # 2) Encode a^k (mod L) into |y> for every computational basis state |k> N = 1 << n # 2^n y_bits = 2 * m + 1 # number of qubits in y for k in range(N): value = pow(a, k, L) # classical a^k mod L if value == 0: continue # all target bits stay 0 # list of control qubits (all qubits of register x) ctrls = [x[i] for i in range(n)] # temporarily flip controls whose bit in k is 0 (so all controls become |1>) zeros = [i for i in range(n) if ((k >> i) & 1) == 0] for i in zeros: qc.x(x[i]) # for every 1-bit in 'value' flip corresponding qubit in y for bit in range(y_bits): if (value >> bit) & 1: cX(ctrls, y[bit]) # undo the temporary flips for i in zeros: qc.x(x[i]) return qc '''
QPC004_C5
A1138001D8D93
1
RE
1844 ms
158 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,a,L).control(1),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(1), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(1,n+2)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(1,n+2)), inplace=True) qc.compose(shift(n+1,a).control(1), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(qft(n),qubits = list(range(1,n+1)), inplace=True) qc.compose(shift(n,-t).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(shift(n,-s).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(qft(n).inverse(),qubits = list(range(1,n+1)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A1138001D8D93
2
WA
2240 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,a,L).control(1),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(1), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(1,n+2)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(1,n+2)), inplace=True) qc.compose(shift(n+1,a).control(1), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(qft(n),qubits = list(range(1,n+1)), inplace=True) qc.compose(shift(n,-t).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(shift(n,-s).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(qft(n).inverse(),qubits = list(range(1,n+1)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A1138001D8D93
3
WA
4744 ms
196 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,multipliers[i],L).control(1),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(1), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(1,n+2)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(1,n+2)), inplace=True) qc.compose(shift(n+1,a).control(1), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(qft(n),qubits = list(range(1,n+1)), inplace=True) qc.compose(shift(n,-t).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(shift(n,-s).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(qft(n).inverse(),qubits = list(range(1,n+1)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A1138001D8D93
4
RE
2267 ms
158 MiB
'''python def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) qc.x(n) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,multipliers[i],L).control(1),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(1), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(1,n+2)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(1,n+2)), inplace=True) qc.compose(shift(n+1,a).control(1), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(qft(n),qubits = list(range(1,n+1)), inplace=True) qc.compose(shift(n,-t).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(shift(n,-s).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(qft(n).inverse(),qubits = list(range(1,n+1)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A1138001D8D93
5
TLE
10000 ms
228 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) qc.x(n) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,multipliers[i],L).control(1),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.swap(i,n+i) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(n + 1) qc = QuantumCircuit(x, y) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n,2*n+1)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [i]+list(range(n,2*n+1)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n,2*n+1)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(1), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(1,n+2)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(1,n+2)), inplace=True) qc.compose(shift(n+1,a).control(1), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 2) # Write your code here: qc.compose(qft(n),qubits = list(range(1,n+1)), inplace=True) qc.compose(shift(n,-t).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(shift(n,-s).control(2),qubits = [0,n+1]+list(range(1,n+1)), inplace=True) qc.x(n+1) qc.compose(qft(n).inverse(),qubits = list(range(1,n+1)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A1138001D8D93
6
AC
8552 ms
202 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import math def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(i) qc.x(n) multipliers = doubling_powers(n,a,L) for i in range(n): qc.compose(multiply_mod(m,multipliers[i],L),qubits = [i] + list(range(n,n+2*m+1)),inplace=True) return qc def doubling_powers(n: int, a: int, L: int) -> list[int]: result: list[int] = [] # Write your code here: result.append(a) for i in range(1,n): result.append(result[-1]**2%L) return result def multiply_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(2*n+2) # Write your code here: qc.compose(add_multi_mod(n,a,L),inplace=True) gcd,x,y = extended_euclidean(a,L) a_inv = x % L #print(a_inv) for i in range(n): qc.cswap(0,i+1,n+i+1) qc.compose(add_multi_mod(n,L-a_inv,L),inplace=True) return qc def extended_euclidean(a: int, b: int) -> tuple[int, int, int]: # when b == 0: if b == 0: return a, 1, 0 # recursive step gcd, x1, y1 = extended_euclidean(b, a % b) # update x and y x = y1 y = x1 - (a // b) * y1 return gcd, x, y def add_multi_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(2*n+2) # Write your code here: qc.compose(qft(n+1),qubits = list(range(n+1,2*n+2)), inplace=True) for i in range(n): qc.compose(add_mod(n,(a*2**i)%L,L),qubits = [0,i+1]+list(range(n+1,2*n+2)), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(n+1,2*n+2)), inplace=True) return qc def add_mod(n: int, a: int, L: int) -> QuantumCircuit: qc = QuantumCircuit(n + 3) # Write your code here: qc.compose(shift(n+1,2**n-L+a).control(2), inplace=True) qc.compose(qft(n+1).inverse(),qubits = list(range(2,n+3)), inplace=True) qc.compose(pack(n,2**n-L+a,2**n+a), inplace=True) qc.compose(qft(n+1),qubits = list(range(2,n+3)), inplace=True) qc.compose(shift(n+1,a).control(2), inplace=True) return qc def pack(n: int, s: int, t: int) -> QuantumCircuit: qc = QuantumCircuit(n + 3) # Write your code here: qc.compose(qft(n),qubits = list(range(2,n+2)), inplace=True) qc.compose(shift(n,-t).control(3),qubits = [0,1,n+2]+list(range(2,n+2)), inplace=True) qc.x(n+2) qc.compose(shift(n,-s).control(3),qubits = [0,1,n+2]+list(range(2,n+2)), inplace=True) qc.x(n+2) qc.compose(qft(n).inverse(),qubits = list(range(2,n+2)), inplace=True) return qc def qft(n): qc = QuantumCircuit(n) for i in range(n-1,-1,-1): qc.h(i) for j in range(i-1,-1,-1): qc.cp(2*math.pi/2**(i-j+1),j,i) for k in range(n//2): qc.swap(k,n-1-k) return qc def shift(n,a): qc = QuantumCircuit(n) for i in range(n): qc.p(2*math.pi*a/2**(n-i),i) return qc '''
QPC004_C5
A44322E5E4FC3
1
WA
1719 ms
166 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Step 1: Create uniform superposition on input register for i in range(n): qc.h(x[i]) # Step 2: For each basis state |k⟩, compute a^k mod L for k in range(n): # For each qubit in k's binary representation power = 2**k # If kth qubit is 1, multiply by a^(2^k) mod L controlled_modmult(qc, x[k], y, a**power % L, L, m) return qc def controlled_modmult(qc, control, target_reg, factor, modulus, m): """ Applies controlled modular multiplication: If control=1: |y⟩ → |y * factor mod modulus⟩ """ n_target = len(target_reg) # Convert factor to binary representation bin_factor = format(factor % modulus, f'0{n_target}b') # Apply CNOT gates based on binary representation of factor for i, bit in enumerate(reversed(bin_factor)): if bit == '1': qc.cx(control, target_reg[i]) # Apply modular reduction # This is a simplified version - in practice, you'd need # a more sophisticated quantum modular arithmetic implementation # that handles the modular reduction in a reversible way '''
QPC004_C5
A44322E5E4FC3
2
WA
1679 ms
162 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Step 1: Create uniform superposition on input register for i in range(n): qc.h(x[i]) # Step 2: For each basis state |k⟩, compute a^k mod L for k in range(n): # For each qubit in k's binary representation power = 2**k # If kth qubit is 1, multiply by a^(2^k) mod L controlled_modmult(qc, x[k], y, a**power % L, L, m) return qc def controlled_modmult(qc, control, target_reg, factor, modulus, m): """ Applies controlled modular multiplication: If control=1: |y⟩ → |y * factor mod modulus⟩ """ n_target = len(target_reg) # Convert factor to binary representation bin_factor = format(factor % modulus, f'0{n_target}b') # Apply CNOT gates based on binary representation of factor for i, bit in enumerate(reversed(bin_factor)): if bit == '1': qc.cx(control, target_reg[i]) # Apply modular reduction # This is a simplified version - in practice, you'd need # a more sophisticated quantum modular arithmetic implementation # that handles the modular reduction in a reversible way '''
QPC004_C5
A5A72EC447696
1
RE
1530 ms
157 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: def add_constant(qc, const, reg, controls): if const == 0: return n_reg = len(reg) for i in range(n_reg): if (const & (1 << i)): sub_reg = reg[i:] ctrl_list = controls[:] if len(ctrl_list) > 0: qc.mcx(ctrl_list, sub_reg[0]) else: qc.x(sub_reg[0]) for k in range(1, len(sub_reg)): ctrl_list = controls + sub_reg[0:k] qc.mcx(ctrl_list, sub_reg[k]) def modular_add_constant(qc, const, reg, L, controls): if const == 0: return add_constant(qc, const, reg, controls) temp = (1 << len(reg)) - L add_constant(qc, temp, reg, controls) add_constant(qc, L, reg, controls + [reg[-1]]) qc.h(x) qc.x(y[0]) z_reg = y[0:m] aux_reg = y[m:2*m+1] for j in range(n): c = pow(a, 1 << j, L) if c == 0 or c == 1: continue inv = pow(c, -1, L) neg_inv = L - inv # CMULT c for bit in range(m): ctrl2 = z_reg[bit] e = (c * (1 << bit)) % L modular_add_constant(qc, e, aux_reg, L, [x[j], ctrl2]) # cswap for bit in range(m): qc.cswap(x[j], z_reg[bit], aux_reg[bit]) # CMULT neg_inv for bit in range(m): ctrl2 = z_reg[bit] e = (neg_inv * (1 << bit)) % L modular_add_constant(qc, e, aux_reg, L, [x[j], ctrl2]) return qc '''
QPC004_C5
A5A72EC447696
2
UME
'''python from __future__ import annotations from math import pi from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import QFT # ∣x⟩↦∣x̃⟩ helper # ------------------------------------------------------------------ # elementary arithmetic gadgets # ------------------------------------------------------------------ def qft_add_const(qc: QuantumCircuit, q: list, c: int) -> None: """ |x⟩ → |x+c mod 2^k⟩ (no ancilla, k = len(q)) little-endian QFT adder (Cuccaro, Draper 2000) """ k = len(q) qc.append(QFT(k, do_swaps=False).to_gate(label='QFT'), q) for j in range(k): angle = 2*pi*((c % (1<<k)) >> j) / (1 << (j+1)) if abs(angle) > 1e-12: qc.p(angle, q[j]) qc.append(QFT(k, do_swaps=False).inverse().to_gate(label='QFT†'), q) def add_const_mod(qc: QuantumCircuit, tgt: list, # k value qubits (little-endian) c: int, # classical const (0 ≤ c < L) L: int, # modulus flag: int) -> None: # *one* ancilla qubit inside tgt-register """ |x⟩|0⟩ → |(x+c) mod L⟩|0⟩ *flag* is the MSB of *tgt*: we recycle it as the “overflow” bit. Steps (all reversible): 1. x ← x+c (plain addition) 2. x-L? set flag if x ≥ L (comparator) 3. conditional −L (controlled on flag) 4. uncompute comparator (flag back to |0⟩) """ k = len(tgt)-1 # data bits 0…k-1, flag at k data = tgt[:k] # shorthand fbit = tgt[k] # 1. add c qft_add_const(qc, data, c) # 2. compute “x ≥ L” (compare to L-1 in two’s complement): inv = ((1 << k) - L) # actually add (2^k − L) qft_add_const(qc, data, inv) # x ← x + 2^k - L (mod 2^k) qc.x(data[-1]) # MSB is 0 ↔ overflow (‖ 2’s-complement sign) qc.cx(data[-1], fbit) # copy sign into flag qc.x(data[-1]) # 3. if overflow, add L back qft_add_const(qc, data, (L if c else 0)) # tidy up phase qc.cx(fbit, data[-1]) qc.x(data[-1]) qc.cx(data[-1], fbit) qft_add_const(qc, data, (1 << k) - L) # undo comparator residue # 4. uncompute flag qft_add_const(qc, data, (1 << k) - c) # restore original basis qc.cx(data[-1], fbit) # flag back to |0〉 qft_add_const(qc, data, c) # data contains (x+c) mod L def controlled_mul_const_mod(qc: QuantumCircuit, ctl, tgt: list, const: int, L: int) -> None: """If ctl==1 multiply |y⟩ by fixed *const* modulo L (textbook “double-and-add”). Uses the upper m ancilla qubits already available inside *tgt*. """ k = (len(tgt) - 1) // 2 # k = m acc = tgt[:k] # low m qubits – current value work = tgt[k:2*k] # upper m qubits – scratch (starts/ends |0⟩) flag = tgt[-1] # one shared ancilla # copy acc into work so that we can accumulate there for j in range(k): qc.cx(acc[j], work[j]) for j in range(k): # multiply via “shift-add” bit_const = (const >> j) & 1 if bit_const: # add (2^j mod L) * y controlled on ctl & acc[j] cc = QuantumCircuit(1, name=f'×{const}·2^{j}') add_const_mod(qc, work + [flag], (const << j) % L, L, flag) for t in [*work, flag]: qc.cx(ctl, t).c_if(acc[j], 1) # dual control: ctl & acc[j] # swap result into low register, clean ancilla for j in range(k): qc.cx(work[j], acc[j]) qc.cx(acc[j], work[j]) qc.cx(work[j], acc[j]) # ------------------------------------------------------------------ # complete solution # ------------------------------------------------------------------ def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: """ Prepares (1/√2^n) Σ_k |k⟩ |a^k mod L⟩ with *real* modular arithmetic. Register layout (little-endian): x : n exponent qubits y : m value qubits – current number (< L ≤ 2^m) m work ancillae – scratch that returns to |0〉 1 overflow flag """ x = QuantumRegister(n, 'x') y = QuantumRegister(2 * m + 1, 'y') qc = QuantumCircuit(x, y) # |k〉 superposition qc.h(x) # initialise y to 1 (multiplicative identity) qc.x(y[0]) # repeated-squaring table a^{2^i} (mod L) powers = [pow(a, 1 << i, L) for i in range(n)] # for each exponent bit apply controlled modular-multiplication for i, const in enumerate(powers): if const != 1: # skip no-op factors controlled_mul_const_mod(qc, x[i], list(y), const, L) return qc '''
QPC004_C5
A5A72EC447696
3
UME
'''python from math import pi from qiskit import QuantumCircuit, QuantumRegister from qiskit.circuit.library import QFT # ∣x⟩↦∣x̃⟩ helper # ------------------------------------------------------------------ # elementary arithmetic gadgets # ------------------------------------------------------------------ def qft_add_const(qc: QuantumCircuit, q: list, c: int) -> None: """ |x⟩ → |x+c mod 2^k⟩ (no ancilla, k = len(q)) little-endian QFT adder (Cuccaro, Draper 2000) """ k = len(q) qc.append(QFT(k, do_swaps=False).to_gate(label='QFT'), q) for j in range(k): angle = 2*pi*((c % (1<<k)) >> j) / (1 << (j+1)) if abs(angle) > 1e-12: qc.p(angle, q[j]) qc.append(QFT(k, do_swaps=False).inverse().to_gate(label='QFT†'), q) def add_const_mod(qc: QuantumCircuit, tgt: list, # k value qubits (little-endian) c: int, # classical const (0 ≤ c < L) L: int, # modulus flag: int) -> None: # *one* ancilla qubit inside tgt-register """ |x⟩|0⟩ → |(x+c) mod L⟩|0⟩ *flag* is the MSB of *tgt*: we recycle it as the “overflow” bit. Steps (all reversible): 1. x ← x+c (plain addition) 2. x-L? set flag if x ≥ L (comparator) 3. conditional −L (controlled on flag) 4. uncompute comparator (flag back to |0⟩) """ k = len(tgt)-1 # data bits 0…k-1, flag at k data = tgt[:k] # shorthand fbit = tgt[k] # 1. add c qft_add_const(qc, data, c) # 2. compute “x ≥ L” (compare to L-1 in two’s complement): inv = ((1 << k) - L) # actually add (2^k − L) qft_add_const(qc, data, inv) # x ← x + 2^k - L (mod 2^k) qc.x(data[-1]) # MSB is 0 ↔ overflow (‖ 2’s-complement sign) qc.cx(data[-1], fbit) # copy sign into flag qc.x(data[-1]) # 3. if overflow, add L back qft_add_const(qc, data, (L if c else 0)) # tidy up phase qc.cx(fbit, data[-1]) qc.x(data[-1]) qc.cx(data[-1], fbit) qft_add_const(qc, data, (1 << k) - L) # undo comparator residue # 4. uncompute flag qft_add_const(qc, data, (1 << k) - c) # restore original basis qc.cx(data[-1], fbit) # flag back to |0〉 qft_add_const(qc, data, c) # data contains (x+c) mod L def controlled_mul_const_mod(qc: QuantumCircuit, ctl, tgt: list, const: int, L: int) -> None: """If ctl==1 multiply |y⟩ by fixed *const* modulo L (textbook “double-and-add”). Uses the upper m ancilla qubits already available inside *tgt*. """ k = (len(tgt) - 1) // 2 # k = m acc = tgt[:k] # low m qubits – current value work = tgt[k:2*k] # upper m qubits – scratch (starts/ends |0⟩) flag = tgt[-1] # one shared ancilla # copy acc into work so that we can accumulate there for j in range(k): qc.cx(acc[j], work[j]) for j in range(k): # multiply via “shift-add” bit_const = (const >> j) & 1 if bit_const: # add (2^j mod L) * y controlled on ctl & acc[j] cc = QuantumCircuit(1, name=f'×{const}·2^{j}') add_const_mod(qc, work + [flag], (const << j) % L, L, flag) for t in [*work, flag]: qc.cx(ctl, t).c_if(acc[j], 1) # dual control: ctl & acc[j] # swap result into low register, clean ancilla for j in range(k): qc.cx(work[j], acc[j]) qc.cx(acc[j], work[j]) qc.cx(work[j], acc[j]) # ------------------------------------------------------------------ # complete solution # ------------------------------------------------------------------ def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: """ Prepares (1/√2^n) Σ_k |k⟩ |a^k mod L⟩ with *real* modular arithmetic. Register layout (little-endian): x : n exponent qubits y : m value qubits – current number (< L ≤ 2^m) m work ancillae – scratch that returns to |0〉 1 overflow flag """ x = QuantumRegister(n, 'x') y = QuantumRegister(2 * m + 1, 'y') qc = QuantumCircuit(x, y) # |k〉 superposition qc.h(x) # initialise y to 1 (multiplicative identity) qc.x(y[0]) # repeated-squaring table a^{2^i} (mod L) powers = [pow(a, 1 << i, L) for i in range(n)] # for each exponent bit apply controlled modular-multiplication for i, const in enumerate(powers): if const != 1: # skip no-op factors controlled_mul_const_mod(qc, x[i], list(y), const, L) return qc '''
QPC004_C5
A5A72EC447696
4
RE
1844 ms
158 MiB
'''python from math import pi from qiskit import QuantumCircuit, QuantumRegister # ────────────────────────────────────────────────────────────── # 1. In-place QFT / inverse QFT (little-endian, no final swaps) # ────────────────────────────────────────────────────────────── def qft(qc: QuantumCircuit, qubits) -> None: """Quantum Fourier Transform on *qubits* (little-endian, in-place).""" n = len(qubits) for j in range(n): qc.h(qubits[j]) for k in range(j + 1, n): qc.cp(pi / (1 << (k - j)), qubits[k], qubits[j]) def iqft(qc: QuantumCircuit, qubits) -> None: """Inverse QFT matching qft().""" n = len(qubits) for j in reversed(range(n)): for k in reversed(range(j + 1, n)): qc.cp(-pi / (1 << (k - j)), qubits[k], qubits[j]) qc.h(qubits[j]) # ────────────────────────────────────────────────────────────── # 2. QFT-based in-register constant adder (little-endian) # ────────────────────────────────────────────────────────────── def qft_add_const(qc: QuantumCircuit, q, c: int) -> None: """|x⟩ → |x+c mod 2^k⟩ on little-endian register *q* (k = len(q)).""" k = len(q) qft(qc, q) for j in range(k): angle = 2 * pi * ((c % (1 << k)) >> j) / (1 << (j + 1)) if abs(angle) > 1e-12: qc.p(angle, q[j]) iqft(qc, q) # ────────────────────────────────────────────────────────────── # 3. Add-constant-mod-L gadget (Cuccaro comparator trick) # ────────────────────────────────────────────────────────────── def add_const_mod(qc: QuantumCircuit, tgt: list, c: int, L: int, flag): """ Reversible: |x⟩|0⟩ ↦ |(x+c) mod L⟩|0⟩. *tgt* : k+1 qubits (k data, 1 overflow flag = tgt[-1] = *flag*) *c* : classical integer < L *L* : modulus (≤ 2^k) """ k = len(tgt) - 1 data = tgt[:k] # 1. x ← x + c (mod 2^k) qft_add_const(qc, data, c) # 2. compute overflow : if x ≥ L copy sign bit into flag qft_add_const(qc, data, (1 << k) - L) # add 2^k − L qc.x(data[-1]) qc.cx(data[-1], flag) qc.x(data[-1]) # 3. conditional −L (only if overflow flag = 1) qc.ctrl(1) qft_add_const(qc, data, L) # add L back (controlled) qc.ctrl(0) # 4. uncompute comparator & restore basis qft_add_const(qc, data, L - c) # net effect: +(1<<k)−L−c qc.cx(data[-1], flag) qft_add_const(qc, data, c) # final value (x+c) mod L # ────────────────────────────────────────────────────────────── # 4. Controlled “× const (mod L)” via double-and-add # ────────────────────────────────────────────────────────────── def controlled_mul_const_mod(qc: QuantumCircuit, ctl, tgt: list, const: int, L: int) -> None: """If *ctl*==1 multiply |y⟩ by *const* modulo L in-place.""" m = (len(tgt) - 1) // 2 acc = tgt[:m] # value register work = tgt[m:2 * m] # scratch (starts/ends |0⟩) flag = tgt[-1] # copy acc → work (so we can accumulate result in *work*) for j in range(m): qc.cx(acc[j], work[j]) # “shift–add” multiply for j in range(m): if (const >> j) & 1: # add (2^j · acc) controlled on ctl & acc[j] qc.ccx(ctl, acc[j], flag) # create combined control in *flag* add_const_mod(qc, work + [flag], (const << j) % L, L, flag) qc.ccx(ctl, acc[j], flag) # uncompute flag # swap result into acc, clear work for j in range(m): qc.cx(work[j], acc[j]) qc.cx(acc[j], work[j]) qc.cx(work[j], acc[j]) # ────────────────────────────────────────────────────────────── # 5. Complete solver # ────────────────────────────────────────────────────────────── def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: """ Prepare |A⟩ = 2^{-n/2} Σ_k |k⟩ |a^k mod L⟩ with genuine modular arithmetic. Layout (little-endian): x : n – exponent y : m – value m – work 1 – overflow flag """ x = QuantumRegister(n, 'x') y = QuantumRegister(2 * m + 1, 'y') qc = QuantumCircuit(x, y) # uniform superposition over |k⟩ qc.h(x) # initial value register ← 1 qc.x(y[0]) # repeated-squaring table a^{2^i} (mod L) powers = [pow(a, 1 << i, L) for i in range(n)] # modular exponentiation by controlled multiplications for i, const in enumerate(powers): if const != 1: controlled_mul_const_mod(qc, x[i], list(y), const, L) return qc '''
QPC004_C5
A9FDBB0D03A25
1
AC
6922 ms
192 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import numpy as np import math def make_control(g, bit): return g if bit == 0 else g.control(bit) class QArith: @staticmethod def qft(n): qc = QuantumCircuit(n) thetas = [] for k in range(0, 1 + n): thetas.append(2 * math.pi / (2**k)) for idx in range(0, n): qc.h(n - 1 - idx) for jdx in range(idx + 1, n): thetaidx = jdx - idx + 1 qc.cp(thetas[thetaidx], n - 1 - jdx, n - 1 - idx) for idx in range(0, n // 2): qc.swap(idx, n - idx - 1) return qc @staticmethod def add_const(n: int, add: int, control_bits: int = 0) -> QuantumCircuit: from qiskit.circuit.library.standard_gates import PhaseGate k, control = QuantumRegister(n), QuantumRegister(control_bits) qc = QuantumCircuit(k, control) q = QArith.qft(n) qc.compose(q, inplace=True) for idx in range(n): theta = 2 * add * math.pi * (2**idx) / (2**n) p = make_control(PhaseGate(theta), control_bits) qc.append(p, [*control, k[idx]]) qc.compose(q.inverse(), inplace=True) return qc @staticmethod def modadd_const(n: int, a: int, mod: int, control_bits: int = 0) -> QuantumCircuit: regin, control = QuantumRegister(n + 1), QuantumRegister(control_bits) qc = QuantumCircuit(regin, control) def _separate_rot(n: int, s: int, t: int, control_bits: int = 0) -> QuantumCircuit: from qiskit.circuit.library import XGate regin, control = QuantumRegister(n + 1), QuantumRegister(control_bits) qc = QuantumCircuit(regin, control) mcx = make_control(XGate(), control_bits) qc.append(mcx, [*control, regin[-1]]) qc.compose(QArith.add_const(n, -s, 1 + control_bits), inplace=True) qc.append(mcx, [*control, regin[-1]]) qc.compose( QArith.add_const(n, 2 ** (n + 1) - t, 1 + control_bits), inplace=True, ) return qc qc.compose( QArith.add_const(n + 1, 2**n - mod + a, control_bits), inplace=True, ) qc.compose(_separate_rot(n, 2**n - mod + a, 2**n + a, control_bits), inplace=True) qc.compose(QArith.add_const(n + 1, a, control_bits), inplace=True) return qc @staticmethod def modmult_const(n: int, a: int, mod: int, control_bits: int = 0) -> QuantumCircuit: """|x>|y> -> |x>|y+ax>""" x, y, control = QuantumRegister(n), QuantumRegister(n + 1), QuantumRegister(control_bits) qc = QuantumCircuit(x, y, control) for idx in range(n): add = a * (2**idx) % mod qc.compose(QArith.modadd_const(n, add, mod, 1 + control_bits), [*y, *control, x[idx]], inplace=True) return qc @staticmethod def modmult_const_inplace(n: int, a: int, mod: int, control_bits: int = 0) -> QuantumCircuit: """|x>|0> -> |ax>|0>""" from qiskit.circuit.library import SwapGate x, y, control = QuantumRegister(n), QuantumRegister(n + 1), QuantumRegister(control_bits) qc = QuantumCircuit(x, y, control) qc.compose(QArith.modmult_const(n, a, mod, control_bits), inplace=True) cswap = make_control(SwapGate(), control_bits) for idx in range(n): qc.append(cswap, [*control, x[idx], y[idx]]) qc.compose(QArith.modmult_const(n, -pow(a, -1, mod), mod, control_bits), inplace=True) return qc def solve(n: int, m: int, a: int, mod: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) qc.h(x) qc.x(y[0]) for idx in range(n): multpow = QArith.modmult_const_inplace(m, pow(a, 2**idx, mod), mod, 1) qc.compose(multpow, [*y, x[idx]], inplace=True) return qc '''
QPC004_C5
AE61DC7EA731D
1
RE
2268 ms
158 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit: x, y = QuantumRegister(n), QuantumRegister(2 * m + 1) qc = QuantumCircuit(x, y) # Write your code here: for i in range(n): qc.h(x[i]) qc.x(y[0]) d=2**(2*m+1) def U(r): M=np.zeros((d,d),dtype=complex) for i in range(d): j=(i*r)%L if i<L else i M[j,i]=1 return M for j in range(n): r=pow(a,2**j,L) gate=UnitaryGate(U(r),label="U"+str(r)) cgate=gate.control(1) qc.append(cgate,[x[j]]+list(y)) return qc '''
QPC005_A1
A05D5FC6BBAE2
1
AC
1548 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A06E382F5D541
1
AC
1505 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.h(0) qc.z(0) return qc '''
QPC005_A1
A0BE9E26E580F
1
AC
1694 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A0BEEF60F4768
1
AC
1780 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A0F0BFC24656B
1
AC
1476 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A1582663DF007
1
WA
1576 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.x(0) qc.z(0) return qc '''
QPC005_A1
A1582663DF007
2
WA
1599 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.h(0) return qc '''
QPC005_A1
A1582663DF007
3
AC
1431 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.h(0) qc.z(0) return qc '''
QPC005_A1
A1F54CA412CF2
1
AC
1619 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.x(0) qc.h(0) return qc '''
QPC005_A1
A2BA1C068EDF5
1
AC
1648 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A2D03F3B4C72E
1
RE
1525 ms
140 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x() qc.h() return qc '''
QPC005_A1
A2D03F3B4C72E
2
WA
1577 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.z(0) qc.h(0) return qc '''
QPC005_A1
A2D03F3B4C72E
3
AC
1761 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc '''
QPC005_A1
A2EDD68B9135A
1
AC
1726 ms
142 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister import numpy as np def solve(): qc = QuantumCircuit(1) qc.x(range(1)) qc.h(range(1)) return qc '''
QPC005_A1
A32705E0407B6
1
AC
1635 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A35DF60212067
1
AC
1614 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A3AE260FA7444
1
WA
1599 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: return qc '''
QPC005_A1
A3AE260FA7444
2
AC
1598 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A3CD30B16E678
1
AC
1650 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A4331BE1D88F8
1
AC
1660 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A487BE2155FD7
1
AC
1533 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A49922F869F23
1
AC
1776 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc '''
QPC005_A1
A51C3E261CD21
1
AC
1661 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A5274E872E9EA
1
RE
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc = qc.0 qc = qc.minus return qc '''
QPC005_A1
A5274E872E9EA
2
RE
1590 ms
140 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc=qc.x(0) qc=qc.h(0) return qc '''
QPC005_A1
A5274E872E9EA
3
AC
1700 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A5B31B5EB6667
1
AC
1699 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A5E4EA4DA33F5
1
AC
1543 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc '''
QPC005_A1
A5FAB0EA612F5
1
AC
1604 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A6A59B946F777
1
AC
1673 ms
142 MiB
'''python from qiskit import QuantumCircuit, QuantumRegister from math import pi, acos, sqrt, asin from qiskit.circuit.library import XGate, ZGate, PhaseGate def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.x(0) qc.h(0) return qc '''
QPC005_A1
A6C87E094CE61
1
AC
1659 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A6F65BB19E586
1
RE
1658 ms
140 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.cx(0, 1) qc.h(0) qc.cx(0, 1) return qc '''
QPC005_A1
A6F65BB19E586
2
AC
1506 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A72EFDE62ABFF
1
AC
1617 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A791BAB14EE0A
1
WA
1625 ms
143 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) # Xゲート qc.z(0) # Zゲート qc.x(0) # Xゲート return qc print(solve().draw()) '''
QPC005_A1
A791BAB14EE0A
2
RE
1367 ms
141 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.initialize(initial_state, 0) qc.x(0) # Xゲート qc.z(0) # Zゲート qc.x(0) # Xゲート return qc print(solve().draw()) '''
QPC005_A1
A791BAB14EE0A
3
AC
1547 ms
144 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc print(solve().draw()) '''
QPC005_A1
A83DAC814D178
1
AC
1701 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc '''
QPC005_A1
A8DA370228755
1
AC
1652 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A8FF3D621FF36
1
AC
1531 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A917F53FD43EC
1
AC
1672 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A9B3BB9338454
1
AC
1531 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
A9F155ED37DD1
1
AC
1602 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) qc.x(0) qc.h(0) return qc '''
QPC005_A1
AA1062C37AFBE
1
WA
1653 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.x(0) return qc '''
QPC005_A1
AA1062C37AFBE
2
AC
1530 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) qc.z(0) return qc '''
QPC005_A1
AA5A02268FB76
1
WA
1631 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc = QuantumCircuit(1) qc.h(0) return qc '''
QPC005_A1
AA5A02268FB76
2
WA
1648 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.h(0) return qc '''
QPC005_A1
AA5A02268FB76
3
AC
1781 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''
QPC005_A1
AAC007E1F4D88
1
AC
1587 ms
142 MiB
'''python from qiskit import QuantumCircuit def solve() -> QuantumCircuit: qc = QuantumCircuit(1) # Write your code here: qc.x(0) qc.h(0) return qc '''