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import numpy as np
from qiskit import Aer
from qiskit import QuantumCircuit
from qiskit.algorithms import QAOA
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization import QuadraticProgram
from qiskit.aqua.operators import Z, X
from qiskit.aqua.algorithms import Grover
from qiskit import execute
# Quantum Optimization: MaxCut Problem
def create_maxcut_problem(num_nodes, edges, weights):
"""
Creates a QuadraticProgram for the MaxCut optimization problem.
:param num_nodes: number of nodes in the graph
:param edges: list of tuples representing edges
:param weights: dictionary of edge weights
:return: QuadraticProgram instance
"""
qp = QuadraticProgram()
# Define binary variables for each node
for i in range(num_nodes):
qp.binary_var(f'x{i}')
# Set the quadratic objective function based on edges and weights
for i, j in edges:
weight = weights.get((i, j), 1) # Default weight is 1 if not specified
qp.minimize(constant=0, linear=[], quadratic={(f'x{i}', f'x{j}'): weight})
return qp
def quantum_optimization(qp):
"""
Performs quantum optimization using QAOA (Quantum Approximate Optimization Algorithm).
:param qp: QuadraticProgram to optimize
:return: Optimal solution and its value
"""
# Set up the quantum instance and QAOA
backend = Aer.get_backend('statevector_simulator')
qaoa = QAOA(quantum_instance=backend, reps=3) # Increase reps for better optimization
# Use the MinimumEigenOptimizer to solve the problem with QAOA
optimizer = MinimumEigenOptimizer(qaoa)
result = optimizer.solve(qp)
return result
def quantum_machine_learning(X_train, y_train, X_test, y_test):
"""
Simulate a quantum-enhanced machine learning model by performing quantum optimization
alongside classical machine learning models.
:param X_train: training data features
:param y_train: training data labels
:param X_test: test data features
:param y_test: test data labels
:return: SVM model score and quantum optimization result
"""
# Classical SVM as a baseline for performance comparison
from sklearn.svm import SVC
clf = SVC(kernel='linear')
clf.fit(X_train, y_train)
score = clf.score(X_test, y_test)
# Perform Quantum Optimization (MaxCut)
maxcut_problem = create_maxcut_problem(4, [(0, 1), (1, 2), (2, 3), (3, 0)], {(0, 1): 1, (1, 2): 1, (2, 3): 1, (3, 0): 1})
quantum_result = quantum_optimization(maxcut_problem)
return score, quantum_result
# Example to create a problem and solve it
if __name__ == '__main__':
# Sample data for testing the quantum optimization integration
X_train = np.random.rand(100, 5)
y_train = np.random.choice([0, 1], size=100)
X_test = np.random.rand(50, 5)
y_test = np.random.choice([0, 1], size=50)
# Simulate Quantum-enhanced Machine Learning (using SVM and Quantum Optimization)
accuracy, quantum_result = quantum_machine_learning(X_train, y_train, X_test, y_test)
print(f"Accuracy of SVM model: {accuracy:.2f}")
print(f"Quantum Optimization Result: {quantum_result}") |