plugins/optimization/qaoa.py

"""
High-Fidelity Quantum Approximate Optimization Algorithm (QAOA) Simulation using Google Cirq.

QAOA is a hybrid quantum-classical algorithm designed for solving combinatorial optimization problems.
This implementation demonstrates QAOA for solving the MaxCut problem on small graphs.
"""
import cirq
import numpy as np
import networkx as nx
import sympy
import random
from cirq.contrib.svg import circuit_to_svg

def create_maxcut_cost_operator(qubits, graph):
    """
    Creates the cost Hamiltonian for the MaxCut problem.
    
    Args:
        qubits: Dictionary mapping node indices to qubits
        graph: NetworkX graph representing the problem
        
    Returns:
        A cirq.Circuit implementing the cost Hamiltonian evolution
    """
    circuit = cirq.Circuit()
    
    # The cost Hamiltonian for MaxCut is sum_(i,j)∈E (1 - Z_i Z_j)/2
    # For circuit implementation, we use ZZ rotations
    for i, j in graph.edges():
        circuit.append(cirq.ZZ(qubits[i], qubits[j])**sympy.Symbol('gamma'))
    
    return circuit

def create_mixer_operator(qubits):
    """
    Creates the mixer Hamiltonian for QAOA.
    
    Args:
        qubits: List of qubits
        
    Returns:
        A cirq.Circuit implementing the mixer Hamiltonian evolution
    """
    circuit = cirq.Circuit()
    
    # The mixer Hamiltonian is sum_i X_i
    # For circuit implementation, we use X rotations
    for qubit in qubits.values():
        circuit.append(cirq.X(qubit)**sympy.Symbol('beta'))
    
    return circuit

def create_qaoa_circuit(qubits, graph, p=1):
    """
    Creates a QAOA circuit for the MaxCut problem.
    
    Args:
        qubits: Dictionary mapping node indices to qubits
        graph: NetworkX graph representing the problem
        p: Number of QAOA layers
        
    Returns:
        A cirq.Circuit implementing QAOA
    """
    circuit = cirq.Circuit()
    
    # Initialize in superposition
    circuit.append(cirq.H.on_each(*qubits.values()))
    
    # Apply p layers of QAOA
    for layer in range(p):
        # Apply cost Hamiltonian with parameter gamma_layer
        gamma = sympy.Symbol(f'gamma_{layer}')
        for i, j in graph.edges():
            circuit.append(cirq.ZZ(qubits[i], qubits[j])**gamma)
        
        # Apply mixer Hamiltonian with parameter beta_layer
        beta = sympy.Symbol(f'beta_{layer}')
        for qubit in qubits.values():
            circuit.append(cirq.X(qubit)**beta)
    
    return circuit

def add_noise(circuit, noise_prob):
    """
    Adds realistic quantum noise to the circuit.
    
    Args:
        circuit: A Cirq circuit
        noise_prob: Probability of depolarizing noise
        
    Returns:
        A circuit with added noise operations
    """
    if noise_prob <= 0:
        return circuit
        
    noisy_ops = []
    for op in circuit.all_operations():
        noisy_ops.append(op)
        for q in op.qubits:
            noisy_ops.append(cirq.DepolarizingChannel(noise_prob).on(q))
    return cirq.Circuit(noisy_ops)

def evaluate_maxcut(bitstring, graph):
    """
    Evaluates the MaxCut value for a given bitstring.
    
    Args:
        bitstring: String of '0's and '1's representing the cut
        graph: NetworkX graph
        
    Returns:
        The value of the cut (number of edges between partitions)
    """
    cut_value = 0
    for i, j in graph.edges():
        # Edge contributes to the cut if the endpoints are in different partitions
        if bitstring[i] != bitstring[j]:
            cut_value += 1
    return cut_value

def run_qaoa(n_nodes=4, edge_probability=0.5, p_layers=1, noise_prob=0.0, num_samples=100):
    """
    Runs the QAOA algorithm for the MaxCut problem.
    
    Args:
        n_nodes: Number of nodes in the graph
        edge_probability: Probability of edge creation in random graph
        p_layers: Number of QAOA layers (depth)
        noise_prob: Probability of depolarizing noise
        num_samples: Number of circuit samples to take
        
    Returns:
        Dictionary with QAOA results and visualization
    """
    log = []
    log.append("=== Quantum Approximate Optimization Algorithm (QAOA) Simulation ===")
    
    # Create a random graph
    graph = nx.gnp_random_graph(n_nodes, edge_probability, seed=42)
    log.append(f"Created random graph with {n_nodes} nodes and {graph.number_of_edges()} edges")
    log.append(f"Edges: {list(graph.edges())}")
    
    # Create qubits
    qubits = {i: cirq.NamedQubit(f'q{i}') for i in range(n_nodes)}
    
    # Create QAOA circuit
    circuit = create_qaoa_circuit(qubits, graph, p=p_layers)
    log.append(f"Created QAOA circuit with p={p_layers} layers")
    
    # Generate random circuit parameters (in a real QAOA, these would be optimized)
    params = {}
    for layer in range(p_layers):
        # Typical ranges for parameters
        params[f'gamma_{layer}'] = random.uniform(0, 2 * np.pi)
        params[f'beta_{layer}'] = random.uniform(0, np.pi)
    
    log.append("Generated random parameters for demonstration:")
    for param, value in params.items():
        log.append(f"  {param} = {value:.4f}")
    
    # Resolve the circuit with the parameters
    resolved_circuit = cirq.resolve_parameters(circuit, params)
    
    # Add noise if specified
    if noise_prob > 0:
        resolved_circuit = add_noise(resolved_circuit, noise_prob)
        log.append(f"Added noise with probability {noise_prob}")
    
    # Add measurements
    measure_circuit = cirq.Circuit()
    measure_circuit.append(cirq.measure(*qubits.values(), key='cut'))
    
    # Combine circuits
    full_circuit = resolved_circuit + measure_circuit
    
    # Run the circuit
    simulator = cirq.Simulator()
    result = simulator.run(full_circuit, repetitions=num_samples)
    
    # Process the measurement results
    cut_counts = {}
    cut_values = {}
    
    for sample in result.measurements['cut']:
        bitstring = ''.join([str(bit) for bit in sample])
        if bitstring not in cut_counts:
            cut_counts[bitstring] = 0
            cut_values[bitstring] = evaluate_maxcut(bitstring, graph)
        cut_counts[bitstring] += 1
    
    # Find the best cut
    best_bitstring = max(cut_values, key=cut_values.get)
    best_cut_value = cut_values[best_bitstring]
    best_count = cut_counts[best_bitstring]
    
    log.append(f"\nSampling Results (from {num_samples} samples):")
    for bitstring, count in sorted(cut_counts.items(), key=lambda x: cut_values[x[0]], reverse=True)[:5]:
        log.append(f"  Cut {bitstring}: value = {cut_values[bitstring]}, frequency = {count}/{num_samples} ({count/num_samples:.2%})")
    
    log.append(f"\nBest cut found: {best_bitstring}")
    log.append(f"Cut value: {best_cut_value}")
    log.append(f"Frequency: {best_count}/{num_samples} ({best_count/num_samples:.2%})")
    
    # Brute force the optimal solution for comparison
    optimal_cut = 0
    optimal_bitstring = None
    for i in range(2**n_nodes):
        bitstring = format(i, f'0{n_nodes}b')
        cut_value = evaluate_maxcut(bitstring, graph)
        if cut_value > optimal_cut:
            optimal_cut = cut_value
            optimal_bitstring = bitstring
    
    log.append(f"\nOptimal cut (brute force): {optimal_bitstring}")
    log.append(f"Optimal cut value: {optimal_cut}")
    
    # Calculate approximation ratio
    approx_ratio = best_cut_value / optimal_cut if optimal_cut > 0 else 1.0
    log.append(f"Approximation ratio: {approx_ratio:.4f}")
    
    # Generate circuit SVG for visualization
    circuit_svg = circuit_to_svg(circuit)
    
    # Generate simple text representation of the graph and cut
    partition_visualization = "Graph partitioning based on best cut:\n"
    partition_0 = []
    partition_1 = []
    for i in range(n_nodes):
        if best_bitstring[i] == '0':
            partition_0.append(i)
        else:
            partition_1.append(i)
    
    partition_visualization += f"  Partition 0: {partition_0}\n"
    partition_visualization += f"  Partition 1: {partition_1}\n\n"
    
    partition_visualization += "Edge cuts:\n"
    for i, j in graph.edges():
        if best_bitstring[i] != best_bitstring[j]:
            partition_visualization += f"  ({i}, {j}) - Cut\n"
        else:
            partition_visualization += f"  ({i}, {j}) - Not cut\n"
    
    log.append(f"\n{partition_visualization}")
    
    # Return results
    return {
        "n_nodes": n_nodes,
        "n_edges": graph.number_of_edges(),
        "p_layers": p_layers,
        "noise_prob": noise_prob,
        "num_samples": num_samples,
        "best_cut": best_bitstring,
        "best_cut_value": best_cut_value,
        "best_frequency": best_count/num_samples,
        "optimal_cut": optimal_bitstring,
        "optimal_cut_value": optimal_cut,
        "approximation_ratio": float(approx_ratio),
        "params": params,
        "circuit_svg": circuit_svg,
        "graph_edges": list(graph.edges()),
        "partition_0": partition_0,
        "partition_1": partition_1,
        "log": "\n".join(log)
    }

if __name__ == '__main__':
    # Run QAOA examples
    qaoa_simple = run_qaoa(4, 0.5, p_layers=1)
    qaoa_larger = run_qaoa(6, 0.4, p_layers=2)
    qaoa_noisy = run_qaoa(5, 0.6, p_layers=1, noise_prob=0.01)