QuantumSynergyStateReconstruction.py

import numpy as np
import matplotlib.pyplot as plt
from typing import Tuple, List
from dataclasses import dataclass

@dataclass
class QuantumSynergyConfig:
    """Configuration parameters for the quantum synergy algorithm"""
    dimension: int = 200          # Dimensionality of the system
    regularization: float = 0.01  # Regularization parameter μ
    learning_rate: float = 1e-3   # Gradient descent step size
    iterations: int = 100         # Number of optimization iterations
    convergence_threshold: float = 1e-6  # Convergence criterion

class QuantumSynergyStateReconstruction:
    """
    A breakthrough algorithm for reconstructing minimal synergy states in quantum systems
    using advanced optimization techniques and non-linear dynamics.
    
    Mathematical Foundation:
    The algorithm minimizes the energy functional:
    E(x) = x^T W x + μ * ||G(x)||^2
    
    where:
    - x is the state vector
    - W is a symmetric interaction matrix
    - G(x) is a nonlinear transformation
    - μ is a regularization parameter
    """
    
    def __init__(self, config: QuantumSynergyConfig):
        """
        Initialize the quantum synergy reconstruction system.
        
        Args:
            config: Configuration parameters for the algorithm
        """
        self.config = config
        self.dimension = config.dimension
        
        # Initialize interaction matrix W (symmetric)
        M = np.random.randn(self.dimension, self.dimension)
        self.W = 0.5 * (M + M.T)
        
        # Initialize state vector
        self.x = np.random.randn(self.dimension)
        
        # History tracking
        self.energy_history = []
        self.state_history = []
        
    def nonlinear_transform(self, x: np.ndarray) -> np.ndarray:
        """
        Nonlinear transformation G(x) combining trigonometric and polynomial terms.
        
        Args:
            x: Input state vector
            
        Returns:
            Transformed state vector
        """
        return np.sin(x) + x**3 - np.cos(x)
    
    def transform_gradient(self, x: np.ndarray) -> np.ndarray:
        """
        Gradient of the nonlinear transformation G'(x).
        
        Args:
            x: Input state vector
            
        Returns:
            Gradient vector
        """
        return np.cos(x) + 3*(x**2) + np.sin(x)
    
    def energy_functional(self, x: np.ndarray) -> float:
        """
        Calculate the energy functional E(x).
        
        Args:
            x: State vector
            
        Returns:
            Energy value
        """
        Gx = self.nonlinear_transform(x)
        return x.dot(self.W).dot(x) + self.config.regularization * np.sum(Gx**2)
    
    def energy_gradient(self, x: np.ndarray) -> np.ndarray:
        """
        Calculate the gradient of the energy functional ∇E(x).
        
        Args:
            x: State vector
            
        Returns:
            Gradient vector
        """
        Gx = self.nonlinear_transform(x)
        Gx_prime = self.transform_gradient(x)
        return 2*self.W.dot(x) + 2*self.config.regularization * (Gx * Gx_prime)
    
    def optimize(self) -> Tuple[np.ndarray, List[float]]:
        """
        Perform gradient descent optimization to find minimal energy state.
        
        Returns:
            Tuple of (optimal state vector, energy history)
        """
        self.energy_history = []
        self.state_history = []
        
        prev_energy = float('inf')
        
        for i in range(self.config.iterations):
            # Calculate gradient and update state
            grad = self.energy_gradient(self.x)
            self.x -= self.config.learning_rate * grad
            
            # Calculate and store energy
            current_energy = self.energy_functional(self.x)
            self.energy_history.append(current_energy)
            self.state_history.append(self.x.copy())
            
            # Check convergence
            if abs(current_energy - prev_energy) < self.config.convergence_threshold:
                print(f"Converged at iteration {i}")
                break
                
            prev_energy = current_energy
            
        return self.x, self.energy_history
    
    def visualize_optimization(self):
        """Generate visualization of the optimization process"""
        plt.figure(figsize=(12, 8))
        
        # Plot energy history
        plt.subplot(2, 1, 1)
        plt.plot(self.energy_history)
        plt.title('Energy Convergence')
        plt.xlabel('Iteration')
        plt.ylabel('Energy')
        plt.yscale('log')
        
        # Plot final state distribution
        plt.subplot(2, 1, 2)
        plt.hist(self.x, bins=50, density=True)
        plt.title('Final State Distribution')
        plt.xlabel('State Value')
        plt.ylabel('Density')
        
        plt.tight_layout()
        plt.show()

# Example usage and validation
if __name__ == "__main__":
    # Configure the algorithm
    config = QuantumSynergyConfig(
        dimension=100,
        regularization=0.01,
        learning_rate=1e-3,
        iterations=200
    )
    
    # Initialize and run the algorithm
    qsr = QuantumSynergyStateReconstruction(config)
    final_state, energies = qsr.optimize()
    
   
    
    # Print final statistics
    print(f"Final energy: {energies[-1]:.6f}")
    print(f"State norm: {np.linalg.norm(final_state):.6f}")
    print(f"Optimization steps: {len(energies)}")
    
     # Visualize results
    qsr.visualize_optimization()