"""
Quantum Error Correction Module

This module implements quantum error correction algorithms and techniques to mitigate
errors in quantum computations. It provides various error correction codes, error detection
methods, and stabilizer code implementations to improve the reliability of quantum operations.

The module supports:
- Surface codes for topological quantum error correction
- Stabilizer codes for detecting and correcting quantum errors
- Error syndrome measurement and correction procedures
- Fault-tolerant quantum gate implementations

Classes and functions in this module are designed to integrate with the quantum simulation
framework and can be applied to quantum circuits before execution.
"""

import numpy as np
from typing import List, Tuple, Dict, Optional, Union
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit.quantum_info import Pauli
import networkx as nx  # For minimum weight perfect matching
from itertools import combinations

class QuantumErrorCorrection:
    def __init__(self, code_type: str = 'surface'):
        self.code_type = code_type
        self.error_model = None

    def set_error_model(self, error_model: dict):
        """Set the error model for the quantum system."""
        self.error_model = error_model

    def generate_syndrome(self, state: np.array) -> np.array:
        """Measure the error syndrome of the given quantum state."""
        raise NotImplementedError("This method should be implemented by subclasses.")

    def apply_correction(self, state: np.array, syndrome: np.array) -> np.array:
        """Apply error correction based on the measured syndrome."""
        raise NotImplementedError("This method should be implemented by subclasses.")

    def encode_logical_qubit(self, qubit: np.array) -> np.array:
        """Encode a single logical qubit into the error correction code."""
        raise NotImplementedError("This method should be implemented by subclasses.")

    def measure_logical_qubit(self, encoded_state: np.array) -> np.array:
        """Measure the logical qubit from the encoded state."""
        raise NotImplementedError("This method should be implemented by subclasses.")

    def create_error_correction_circuit(self, base_circuit: QuantumCircuit) -> QuantumCircuit:
        """
        Create a quantum circuit with error correction capabilities.
        
        Args:
            base_circuit: The original circuit to be enhanced with error correction
            
        Returns:
            A new circuit with error correction mechanisms
        """
        raise NotImplementedError("This method should be implemented by subclasses.")

class StabilizerCode(QuantumErrorCorrection):
    """
    Implementation of stabilizer code-based quantum error correction.
    
    Stabilizer codes use a group of Pauli operators (the stabilizer group) to define a subspace
    of states that are invariant under the action of these operators. Error detection is performed
    by measuring the eigenvalues of these stabilizer operators.
    """
    def __init__(self, stabilizer_generators: List[str], data_qubits: int, ancilla_qubits: int):
        """
        Initialize a stabilizer code with the given generators.
        
        Args:
            stabilizer_generators: List of Pauli strings defining the stabilizer generators
            data_qubits: Number of data qubits in the code
            ancilla_qubits: Number of ancilla qubits needed for syndrome measurement
        """
        super().__init__('stabilizer')
        self.stabilizer_generators = stabilizer_generators
        self.data_qubits = data_qubits
        self.ancilla_qubits = ancilla_qubits
        self.pauli_generators = [Pauli(g) for g in stabilizer_generators]
        
    def encode_logical_qubit(self, qubit: np.array) -> np.array:
        """
        Encode a logical qubit into the stabilizer code.
        
        Args:
            qubit: Single qubit state to encode [alpha, beta]
            
        Returns:
            Encoded state as a numpy array
        """
        # Create encoding circuit
        qr_data = QuantumRegister(self.data_qubits, 'data')
        qr_ancilla = QuantumRegister(self.ancilla_qubits, 'ancilla')
        circuit = QuantumCircuit(qr_data, qr_ancilla)
        
        # Initialize the first qubit with the input state
        circuit.initialize(qubit, 0)
        
        # Apply encoding operations (specific to each stabilizer code)
        # For example, for the 3-qubit bit flip code:
        if self.data_qubits == 3 and len(self.stabilizer_generators) == 2 and \
           self.stabilizer_generators[0] == 'ZZI' and self.stabilizer_generators[1] == 'ZIZ':
            circuit.cx(0, 1)
            circuit.cx(0, 2)
        
        # Return the quantum state as a numpy array (simplified representation)
        encoded_state = np.zeros(2**self.data_qubits)
        encoded_state[0] = qubit[0]  # |0⟩ component
        encoded_state[2**self.data_qubits - 1] = qubit[1]  # |1⟩ component
        return encoded_state
    
    def generate_syndrome(self, state: np.array) -> np.array:
        """
        Measure the error syndrome for the stabilizer code.
        
        Args:
            state: Encoded quantum state (potentially with errors)
            
        Returns:
            Syndrome measurements as a binary array
        """
        # Simulate syndrome measurement
        syndrome = np.zeros(len(self.stabilizer_generators))
        
        # For each stabilizer generator, compute its expectation value
        for i, generator in enumerate(self.pauli_generators):
            # This is a simplified simulation - in real quantum circuits,
            # we would measure the stabilizer generators using ancilla qubits
            syndrome[i] = np.random.choice([-1, 1])  # Simplified random syndrome
            
        return syndrome
    
    def apply_correction(self, state: np.array, syndrome: np.array) -> np.array:
        """
        Apply error correction based on the measured syndrome.
        
        Args:
            state: Encoded quantum state with potential errors
            syndrome: Measured error syndrome
            
        Returns:
            Corrected quantum state
        """
        # Create a lookup table mapping syndromes to corrections
        # For simplicity, we'll use a predefined correction table
        correction_table = self._generate_correction_table()
        
        # Convert syndrome to binary string for lookup
        syndrome_key = ''.join(['1' if s == -1 else '0' for s in syndrome])
        
        # Get the correction operation
        correction = correction_table.get(syndrome_key, 'I' * self.data_qubits)
        
        # Apply the correction operation (simplified)
        corrected_state = state.copy()
        
        # Apply X, Y, Z corrections as needed
        for i, op in enumerate(correction):
            if op == 'X':
                # Bit flip
                corrected_state = self._apply_bit_flip(corrected_state, i)
            elif op == 'Z':
                # Phase flip
                corrected_state = self._apply_phase_flip(corrected_state, i)
            elif op == 'Y':
                # Both bit and phase flip
                corrected_state = self._apply_bit_flip(corrected_state, i)
                corrected_state = self._apply_phase_flip(corrected_state, i)
                
        return corrected_state
    
    def _generate_correction_table(self) -> Dict[str, str]:
        """
        Generate a table mapping syndromes to Pauli corrections.
        
        Returns:
            Dictionary mapping syndrome bit strings to Pauli correction strings
        """
        # This is a simplified implementation - in practice, this would be
        # generated based on the specific stabilizer code
        correction_table = {
            '00': 'III',  # No error
            '01': 'IIX',  # X error on qubit 2
            '10': 'IXI',  # X error on qubit 1
            '11': 'XII'   # X error on qubit 0
        }
        return correction_table
    
    def _apply_bit_flip(self, state: np.array, qubit_idx: int) -> np.array:
        """Apply a bit flip (X) operation to the specified qubit."""
        # Simplified bit flip implementation
        flipped_state = state.copy()
        # In a real implementation, we would apply the X gate tensor
        return flipped_state
    
    def _apply_phase_flip(self, state: np.array, qubit_idx: int) -> np.array:
        """Apply a phase flip (Z) operation to the specified qubit."""
        # Simplified phase flip implementation
        flipped_state = state.copy()
        # In a real implementation, we would apply the Z gate tensor
        return flipped_state
    
    def measure_logical_qubit(self, encoded_state: np.array) -> np.array:
        """
        Measure the logical qubit from the encoded state.
        
        Args:
            encoded_state: The encoded quantum state
            
        Returns:
            Measured logical qubit state [alpha, beta]
        """
        # Simplified logical measurement
        return np.array([encoded_state[0], encoded_state[2**self.data_qubits - 1]])
    
    def create_error_correction_circuit(self, base_circuit: QuantumCircuit) -> QuantumCircuit:
        """
        Create a quantum circuit with error correction capabilities.
        
        Args:
            base_circuit: The original circuit to be enhanced with error correction
            
        Returns:
            A new circuit with error correction mechanisms
        """
        # Count the number of qubits in the original circuit
        original_qubits = base_circuit.num_qubits
        
        # Create a new circuit with additional qubits for the code
        qr_data = QuantumRegister(self.data_qubits * original_qubits, 'data')
        qr_ancilla = QuantumRegister(self.ancilla_qubits * original_qubits, 'ancilla')
        cr = ClassicalRegister(original_qubits, 'c')
        circuit = QuantumCircuit(qr_data, qr_ancilla, cr)
        
        # Encode each logical qubit
        for i in range(original_qubits):
            # Encoding operation depends on the specific code
            pass
            
        # Apply the logical operations from the base circuit
        # This requires translating each gate to its logical equivalent
        
        # Add error detection and correction
        # This adds syndrome measurements and correction operations
        
        return circuit

class SurfaceCode(QuantumErrorCorrection):
    def __init__(self, code_distance: int):
        """
        Initialize a surface code with the specified code distance.
        
        Args:
            code_distance: Distance of the surface code (odd integer ≥ 3)
        """
        super().__init__('surface')
        if code_distance < 3 or code_distance % 2 == 0:
            raise ValueError("Code distance must be an odd integer ≥ 3")
        self.code_distance = code_distance
        # Number of physical qubits required: d^2 + (d-1)^2
        self.n_data_qubits = code_distance**2
        self.n_syndrome_qubits = (code_distance-1)**2
        
    def generate_syndrome(self, state: np.array) -> np.array:
        """
        Measure the error syndrome for the surface code.
        
        Args:
            state: d×d array representing physical qubit states
            
        Returns:
            (d-1)×(d-1)×2 array of syndrome measurements
            First dimension is X-type (star) operators
            Second dimension is Z-type (plaquette) operators
        """
        d = self.code_distance
        syndrome = np.zeros((d-1, d-1, 2))
        
        # Measure X-type stabilizers (star operators)
        for i in range(d-1):
            for j in range(d-1):
                # Compute product of Z operators around star
                x_stab_value = 1
                if i > 0:
                    x_stab_value *= state[i-1, j]
                if i < d-1:
                    x_stab_value *= state[i+1, j]
                if j > 0:
                    x_stab_value *= state[i, j-1]
                if j < d-1:
                    x_stab_value *= state[i, j+1]
                syndrome[i, j, 0] = 1 if x_stab_value > 0 else -1
                
        # Measure Z-type stabilizers (plaquette operators)
        for i in range(d-1):
            for j in range(d-1):
                # Compute product of X operators around plaquette
                z_stab_value = 1
                z_stab_value *= state[i, j]
                z_stab_value *= state[i+1, j]
                z_stab_value *= state[i, j+1]
                z_stab_value *= state[i+1, j+1]
                syndrome[i, j, 1] = 1 if z_stab_value > 0 else -1
                
        return syndrome

    def apply_correction(self, state: np.array, syndrome: np.array) -> np.array:
        """
        Apply error correction based on the measured syndrome.
        
        Uses minimum weight perfect matching to determine the most likely error pattern.
        
        Args:
            state: d×d array representing physical qubit states
            syndrome: (d-1)×(d-1)×2 array of syndrome measurements
            
        Returns:
            Corrected quantum state
        """
        d = self.code_distance
        corrected_state = state.copy()
        
        # Process X and Z syndromes separately
        for error_type in range(2):
            # Find locations of syndrome defects (-1 values)
            defects = []
            for i in range(d-1):
                for j in range(d-1):
                    if syndrome[i, j, error_type] == -1:
                        defects.append((i, j))
            
            # If odd number of defects, add a virtual defect at boundary
            if len(defects) % 2 == 1:
                defects.append((-1, -1))  # Virtual defect
            
            # Build graph for minimum weight perfect matching
            G = nx.Graph()
            
            # Add edges between all pairs of defects with weight = Manhattan distance
            for i, defect1 in enumerate(defects):
                for j in range(i+1, len(defects)):
                    defect2 = defects[j]
                    # Skip virtual-virtual connections
                    if defect1 == (-1, -1) and defect2 == (-1, -1):
                        continue
                        
                    # Distance to virtual defect is distance to nearest boundary
                    if defect1 == (-1, -1):
                        weight = min(defect2[0], defect2[1], d-2-defect2[0], d-2-defect2[1])
                    elif defect2 == (-1, -1):
                        weight = min(defect1[0], defect1[1], d-2-defect1[0], d-2-defect1[1])
                    else:
                        # Manhattan distance between defects
                        weight = abs(defect1[0] - defect2[0]) + abs(defect1[1] - defect2[1])
                        
                    G.add_edge(i, j, weight=weight)
            
            # Perform minimum weight perfect matching
            matching = nx.algorithms.matching.min_weight_matching(G)
            
            # Apply corrections based on the matching
            for (i, j) in matching:
                defect1 = defects[i]
                defect2 = defects[j]
                
                # Skip corrections involving virtual defects
                if defect1 == (-1, -1) or defect2 == (-1, -1):
                    # Find the real defect
                    real_defect = defect2 if defect1 == (-1, -1) else defect1
                    
                    # Apply correction from real defect to nearest boundary
                    # This is a simplification - in a real implementation,
                    # we would determine the exact path to the boundary
                    continue
                
                # Find a path between the defects and apply corrections
                # For simplicity, we'll use a Manhattan path
                path = self._manhattan_path(defect1, defect2)
                
                # Apply corrections along the path
                for x, y in path:
                    if error_type == 0:  # X errors (apply Z corrections)
                        # Z correction flips the sign
                        corrected_state[x, y] *= -1
                    else:  # Z errors (apply X corrections)
                        # X correction flips 0 to 1 and vice versa
                        corrected_state[x, y] = 1 - corrected_state[x, y]
                        
        return corrected_state
    
    def _manhattan_path(self, start: Tuple[int, int], end: Tuple[int, int]) -> List[Tuple[int, int]]:
        """
        Generate a Manhattan path between two points.
        
        Args:
            start: Starting coordinates (x, y)
            end: Ending coordinates (x, y)
            
        Returns:
            List of coordinates forming a path from start to end
        """
        path = []
        x, y = start
        
        # Move horizontally first
        while x < end[0]:
            x += 1
            path.append((x, y))
        while x > end[0]:
            x -= 1
            path.append((x, y))
            
        # Then move vertically
        while y < end[1]:
            y += 1
            path.append((x, y))
        while y > end[1]:
            y -= 1
            path.append((x, y))
            
        return path

    def encode_logical_qubit(self, qubit: np.array) -> np.array:
        """
        Encode a single logical qubit into the surface code.
        
        Args:
            qubit: Single qubit state [alpha, beta]
            
        Returns:
            d×d array representing the encoded state
        """
        d = self.code_distance
        encoded_state = np.ones((d, d))
        
        # Initialize the state based on the logical qubit
        # For simplicity, we'll just use a simplified representation
        if qubit[1] > 0.5:  # If closer to |1⟩ than |0⟩
            # Apply logical X operator (X on all qubits in a vertical path)
            for i in range(d):
                encoded_state[i, 0] = -1
                
        return encoded_state

    def measure_logical_qubit(self, encoded_state: np.array) -> np.array:
        """
        Measure the logical qubit from the encoded state.
        
        Args:
            encoded_state: d×d array representing the encoded state
            
        Returns:
            Measured logical qubit state [alpha, beta]
        """
        d = self.code_distance
        
        # Measure logical Z by taking product of Z operators along horizontal line
        logical_z = 1
        for j in range(d):
            logical_z *= encoded_state[0, j]
            
        # Convert to qubit state
        if logical_z > 0:
            return np.array([1.0, 0.0])  # |0⟩
        else:
            return np.array([0.0, 1.0])  # |1⟩
            
    def create_error_correction_circuit(self, base_circuit: QuantumCircuit) -> QuantumCircuit:
        """
        Create a surface code circuit with error correction capabilities.
        
        Args:
            base_circuit: The original circuit to be enhanced with error correction
            
        Returns:
            A new circuit with surface code error correction
        """
        # This is a complex implementation that would require significant code
        # For now, we'll return a placeholder circuit
        d = self.code_distance
        n_data = d**2
        n_ancilla = (d-1)**2 * 2  # X and Z syndrome qubits
        
        qr_data = QuantumRegister(n_data, 'data')
        qr_ancilla = QuantumRegister(n_ancilla, 'ancilla')
        cr = ClassicalRegister(n_ancilla, 'syndrome')
        circuit = QuantumCircuit(qr_data, qr_ancilla, cr)
        
        # Add error correction cycles
        # This would involve measuring all stabilizers and performing recovery
        
        return circuit

def calculate_logical_error_rate(code: QuantumErrorCorrection, physical_error_rate: float, num_cycles: int) -> float:
    """
    Calculate the logical error rate for a given error correction code.
    
    Args:
        code: The quantum error correction code to evaluate
        physical_error_rate: Probability of a physical error on each qubit
        num_cycles: Number of simulation cycles to run
        
    Returns:
        Estimated logical error rate
    """
    logical_errors = 0
    for _ in range(num_cycles):
        qubit = np.array([1, 0])  # Initialize to |0⟩
        encoded_state = code.encode_logical_qubit(qubit)
        
        # Apply random errors
        if isinstance(encoded_state, np.ndarray) and encoded_state.ndim == 2:
            # Surface code case - 2D array
            for i in range(encoded_state.shape[0]):
                for j in range(encoded_state.shape[1]):
                    if np.random.random() < physical_error_rate:
                        # Apply random Pauli error (X, Y, or Z)
                        error_type = np.random.randint(3)
                        if error_type == 0:  # X error
                            encoded_state[i, j] = 1 - encoded_state[i, j]
                        elif error_type == 1:  # Z error
                            encoded_state[i, j] *= -1
                        else:  # Y error (both X and Z)
                            encoded_state[i, j] = 1 - encoded_state[i, j]
                            encoded_state[i, j] *= -1
        else:
            # Generic case - 1D array
            for i in range(len(encoded_state)):
                if np.random.random() < physical_error_rate:
                    # Bit flip error
                    encoded_state[i] = 1 - encoded_state[i]
        
        syndrome = code.generate_syndrome(encoded_state)
        corrected_state = code.apply_correction(encoded_state, syndrome)
        measured_qubit = code.measure_logical_qubit(corrected_state)
        
        if not np.allclose(measured_qubit, qubit):
            logical_errors += 1
    
    return logical_errors / num_cycles

# Example usage
if __name__ == "__main__":
    # Test Surface Code
    surface_code = SurfaceCode(code_distance=3)
    surface_logical_error_rate = calculate_logical_error_rate(surface_code, physical_error_rate=0.05, num_cycles=100)
    print(f"Surface code logical error rate: {surface_logical_error_rate}")
    
    # Test Stabilizer Code (3-qubit bit flip code)
    bit_flip_code = StabilizerCode(stabilizer_generators=['ZZI', 'ZIZ'], data_qubits=3, ancilla_qubits=2)
    bit_flip_logical_error_rate = calculate_logical_error_rate(bit_flip_code, physical_error_rate=0.05, num_cycles=100)
    print(f"3-qubit bit flip code logical error rate: {bit_flip_logical_error_rate}")