code.py

import numpy as np
from qiskit import QuantumCircuit, Aer, execute
from scipy.optimize import minimize

# ============================
# Define the problem: MaxCut
# ============================

# Define the adjacency matrix of the graph
adj_matrix = np.array([
    [0, 2, 3, 0], 
    [2, 0, 0, 5], 
    [3, 0, 0, 4], 
    [0, 5, 4, 0]
])

# Number of nodes in the graph
num_nodes = len(adj_matrix)

# Number of shots for the quantum circuit execution
num_shots = 1024

# ============================
# Define the RyRz ansatz
# ============================

def ryrz_ansatz(parameters, num_qubits):
    """
    Creates a quantum circuit using the RyRz ansatz.
    
    Args:
        parameters (list or np.ndarray): List of variational parameters.
        num_qubits (int): Number of qubits in the circuit.
        
    Returns:
        QuantumCircuit: The RyRz ansatz quantum circuit.
    """
    circuit = QuantumCircuit(num_qubits)
    num_params = len(parameters)
    
    if num_params != 2 * num_qubits:
        raise ValueError(
            f"Expected {2 * num_qubits} parameters, but got {num_params}."
        )
    
    # Apply Ry and Rz rotations
    for i in range(num_qubits):
        circuit.ry(parameters[2 * i], i)
        circuit.rz(parameters[2 * i + 1], i)
    
    # Add entangling CNOT gates
    for i in range(num_qubits - 1):
        circuit.cx(i, i + 1)
    
    # Optionally, you could measure here (for debugging/testing)
    return circuit

# ============================
# Define the MaxCut cost function
# ============================

def maxcut_cost(parameters, adj_matrix, num_qubits):
    """
    Computes the cost function for the MaxCut problem.
    
    Args:
        parameters (list or np.ndarray): Variational parameters for the RyRz ansatz.
        adj_matrix (np.ndarray): Adjacency matrix of the graph.
        num_qubits (int): Number of qubits in the circuit.
        
    Returns:
        float: The negative cost function value.
    """
    # Build the quantum circuit
    circuit = ryrz_ansatz(parameters, num_qubits)
    circuit.measure_all()
    
    # Simulate the circuit
    simulator = Aer.get_backend('qasm_simulator')
    result = execute(circuit, simulator, shots=num_shots).result()
    counts = result.get_counts()
    
    # Compute the expectation value (MaxCut cost)
    cost = 0
    for bitstring, count in counts.items():
        cut_value = 0
        # Calculate cut value based on the adjacency matrix
        for i in range(num_qubits):
            for j in range(num_qubits):
                if adj_matrix[i, j] > 0:  # Only consider edges
                    bit_i, bit_j = int(bitstring[i]), int(bitstring[j])
                    if bit_i != bit_j:  # Different bit values contribute to the cut
                        cut_value += adj_matrix[i, j]
        cost += cut_value * (count / num_shots)
    
    return -cost  # Negative because we minimize

# ============================
# Optimize the parameters
# ============================

# Number of parameters (2 per qubit for Ry and Rz rotations)
num_parameters = 2 * num_nodes

# Initialize parameters randomly
initial_parameters = np.random.rand(num_parameters) * 2 * np.pi

# Define the cost function for optimization
def cost_function(params):
    return maxcut_cost(params, adj_matrix, num_nodes)

# Perform optimization using SciPy's minimize
optimizer_method = 'L-BFGS-B'  # You can use other methods like 'COBYLA' or 'Nelder-Mead'
result = minimize(cost_function, initial_parameters, method=optimizer_method)

# ============================
# Output the results
# ============================

# Optimized parameters and cost
optimized_parameters = result.x
minimum_cost = result.fun

print("Optimized Parameters:\n", optimized_parameters)
print("Minimum Cost (negative of MaxCut value):", minimum_cost)

# ============================
# Optional: Interpret results
# ============================

def interpret_results(parameters, num_qubits):
    """
    Interprets the optimized parameters to provide a solution to MaxCut.
    
    Args:
        parameters (list or np.ndarray): Optimized parameters for the RyRz ansatz.
        num_qubits (int): Number of qubits in the circuit.
        
    Returns:
        str: A possible solution to the MaxCut problem.
    """
    # Generate the final circuit
    circuit = ryrz_ansatz(parameters, num_qubits)
    circuit.measure_all()
    
    # Simulate the circuit
    simulator = Aer.get_backend('qasm_simulator')
    result = execute(circuit, simulator, shots=num_shots).result()
    counts = result.get_counts()
    
    # Find the most probable bitstring
    max_bitstring = max(counts, key=counts.get)
    return max_bitstring

# Interpret the results
solution_bitstring = interpret_results(optimized_parameters, num_nodes)
print("Optimal Solution Bitstring:", solution_bitstring)