""" This module provides quantum-inspired optimization algorithms for enhanced performance. """ try: import numpy as np except Exception: np = None import math from typing import List, Dict, Any, Callable, Optional, Tuple class QuantumInspiredOptimizer: def __init__(self): self.population_size = 50 self.num_qubits = 32 self.max_iterations = 100 self.optimization_history = [] self.best_solution = None self.best_fitness = float('-inf') def optimize(self, objective_function: Callable[[np.ndarray], float], constraints: Optional[List[Dict[str, Any]]] = None) -> Dict[str, Any]: """ Perform quantum-inspired optimization. Args: objective_function: The function to optimize constraints: Optional list of constraint dictionaries Returns: Optimization results """ # Initialize quantum population population = self._initialize_quantum_population() for iteration in range(self.max_iterations): # Measure quantum states classical_solutions = self._measure_quantum_states(population) # Apply constraints if any if constraints: classical_solutions = self._apply_constraints(classical_solutions, constraints) # Evaluate fitness fitness_values = [objective_function(solution) for solution in classical_solutions] # Update best solution if np is not None: current_best_idx = int(np.argmax(fitness_values)) else: current_best_idx = int(max(range(len(fitness_values)), key=lambda i: fitness_values[i])) if fitness_values[current_best_idx] > self.best_fitness: self.best_fitness = fitness_values[current_best_idx] self.best_solution = classical_solutions[current_best_idx] # Apply quantum gates population = self._apply_quantum_gates(population, fitness_values) # Store iteration history self.optimization_history.append({ "iteration": iteration, "best_fitness": self.best_fitness, "population_diversity": self._calculate_diversity(classical_solutions) }) return { "best_solution": self.best_solution, "best_fitness": self.best_fitness, "convergence": self.optimization_history, "final_population": self._measure_quantum_states(population) } def _initialize_quantum_population(self) -> np.ndarray: """ Initialize the quantum population with superposition states. """ if np is not None: # Create population of quantum individuals population = np.zeros((self.population_size, self.num_qubits, 2), dtype=np.complex128) # Initialize in superposition state population[:, :, 0] = 1/np.sqrt(2) # amplitude for |0⟩ population[:, :, 1] = 1/np.sqrt(2) # amplitude for |1⟩ else: # Fallback simple population representation (probabilities) population = [[ [1/math.sqrt(2), 1/math.sqrt(2)] for _ in range(self.num_qubits)] for _ in range(self.population_size)] return population def _measure_quantum_states(self, population: np.ndarray) -> np.ndarray: """ Perform measurement on quantum states to get classical solutions. """ if np is not None: classical_solutions = np.zeros((self.population_size, self.num_qubits)) for i in range(self.population_size): # Calculate probabilities probabilities = np.abs(population[i, :, 1])**2 # Perform measurement classical_solutions[i] = np.random.random(self.num_qubits) < probabilities return classical_solutions else: import random classical_solutions = [] for i in range(self.population_size): probs = [abs(complex(pair[1]))**2 for pair in population[i]] classical_solutions.append([1 if random.random() < p else 0 for p in probs]) return classical_solutions def _apply_quantum_gates(self, population: np.ndarray, fitness_values: List[float]) -> np.ndarray: """ Apply quantum gates to update the quantum states. """ # Normalize fitness values if np is not None: fitness_normalized = np.array(fitness_values) fitness_normalized = (fitness_normalized - np.min(fitness_normalized)) / \ (np.max(fitness_normalized) - np.min(fitness_normalized) + 1e-10) # Quantum rotation gate theta = np.pi * fitness_normalized[:, np.newaxis] / 2 # Apply rotation for i in range(self.population_size): rotation_matrix = np.array([ [np.cos(theta[i]), -np.sin(theta[i])], [np.sin(theta[i]), np.cos(theta[i])] ]) population[i] = np.einsum('ij,kj->ki', rotation_matrix, population[i]) else: # fitness_normalized already computed by caller theta = None theta = [math.pi * f / 2 for f in fitness_normalized] # Simple perturbation fallback for i in range(self.population_size): for q in range(self.num_qubits): amp0, amp1 = population[i][q] # rotate amplitudes slightly based on theta t = theta[i] new0 = amp0*math.cos(t) - amp1*math.sin(t) new1 = amp0*math.sin(t) + amp1*math.cos(t) population[i][q] = [new0, new1] return population def _apply_constraints(self, solutions: np.ndarray, constraints: List[Dict[str, Any]]) -> np.ndarray: """ Apply constraints to classical solutions. """ constrained_solutions = solutions.copy() for constraint in constraints: constraint_type = constraint.get("type", "") if constraint_type == "bound": lower = constraint.get("lower", 0) upper = constraint.get("upper", 1) constrained_solutions = np.clip(constrained_solutions, lower, upper) elif constraint_type == "sum": target_sum = constraint.get("target", 1) current_sums = np.sum(constrained_solutions, axis=1) for i in range(len(constrained_solutions)): if current_sums[i] != 0: # Avoid division by zero constrained_solutions[i] *= target_sum / current_sums[i] return constrained_solutions def _calculate_diversity(self, population: np.ndarray) -> float: """ Calculate diversity of the population. """ return np.mean([ np.mean(np.abs(p1 - p2)) for i, p1 in enumerate(population) for p2 in population[i+1:] ]) def get_optimization_history(self) -> List[Dict[str, Any]]: """ Get the history of optimization progress. """ return self.optimization_history def reset(self): """ Reset the optimizer state. """ self.optimization_history = [] self.best_solution = None self.best_fitness = float('-inf') def get_quantum_state(self) -> Dict[str, Any]: """ Get the current quantum state information. """ if not self.optimization_history: return {"status": "not_initialized"} return { "iterations_completed": len(self.optimization_history), "current_best_fitness": self.best_fitness, "convergence_trend": [h["best_fitness"] for h in self.optimization_history], "diversity_trend": [h["population_diversity"] for h in self.optimization_history] }