import sys
import math
import numpy as np
from typing import List, Tuple
from functools import reduce

# Constants
PLANK_CONSTANT = 6.62607015e-34  # Planck constant (J.s)
LIGHT_SPEED = 299792458  # Speed of light (m/s)

# Quantum Gates
class QuantumGate:
    def __init__(self, matrix):
        self.matrix = matrix

    def apply(self, state_vector):
        return np.dot(self.matrix, state_vector)

class HadamardGate(QuantumGate):
    def __init__(self):
        matrix = (1 / np.sqrt(2)) * np.array([[1, 1], [1, -1]], dtype=complex)
        super().__init__(matrix)

class PauliXGate(QuantumGate):
    def __init__(self):
        matrix = np.array([[0, 1], [1, 0]], dtype=complex)
        super().__init__(matrix)

class PauliYGate(QuantumGate):
    def __init__(self):
        matrix = np.array([[0, -1j], [1j, 0]], dtype=complex)
        super().__init__(matrix)

class PauliZGate(QuantumGate):
    def __init__(self):
        matrix = np.array([[1, 0], [0, -1]], dtype=complex)
        super().__init__(matrix)

class CNOTGate(QuantumGate):
    def __init__(self):
        matrix = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], dtype=complex)
        super().__init__(matrix)

# Quantum Circuit
class QuantumCircuit:
    def __init__(self, num_qubits):
        self.num_qubits = num_qubits
        self.state_vector = np.zeros(2**num_qubits, dtype=complex)
        self.state_vector[0] = 1  # Initialize to |0...0⟩

    def add_gate(self, gate, target_qubits):
        target_qubits.sort(reverse=True)
        gate_matrix = reduce(np.kron, [gate.matrix if qubit in target_qubits else np.eye(2) for qubit in range(self.num_qubits)])
        self.state_vector = np.dot(gate_matrix, self.state_vector)

    def apply(self, gates):
        for gate, target_qubits in gates:
            self.add_gate(gate, target_qubits)

    def measure(self, target_qubits):
        measurement_results = []
        for qubit in target_qubits:
            prob_zero = np.abs(self.state_vector[0])**2
            result = np.random.choice([0, 1], p=[prob_zero, 1 - prob_zero])
            measurement_results.append(result)
            self.state_vector = np.delete(self.state_vector, 0 if result == 0 else -1)
        return measurement_results

# Quantum System
class QuantumSystem:
    def __init__(self, system_info, user_info):
        self.system_info = system_info
        self.user_info = user_info
        self.protocols = {
            'protocol_pq_17': False,
            'quantum_resource_amulet': False,
            'subroutine_qx_42': False,
            'algorithm_upgrade_sequence_qu_99': False,
            'quantum_memory_enhancement': False,
            'quantum_signalization_visualization': False,
            'feedback_mechanism_fr_11': False,
            'continuous_iteration_algorithms': False,
            'monitoring_system_performance_ec_88': False
        }

    def initiate_protocol(self, protocol_name):
        if protocol_name in self.protocols:
            self.protocols[protocol_name] = True
            print(f"Initiating {protocol_name}.")
        else:
            print(f"{protocol_name} not found.")

    def adjust_parameters_optimal_functionality(self):
        print("Adjusting parameters for optimal functionality.")

    def display_system_status(self):
        print("System Status:")
        for protocol, status in self.protocols.items():
            print(f"{protocol}: {'Active' if status else 'Inactive'}")

    def run_quantum_simulation(self):
        # Placeholder for running a quantum simulation
        print("Running quantum simulation...")

    def enhance_quantum_memory(self):
        # Placeholder for enhancing quantum memory
        print("Enhancing quantum memory...")

    def visualize_quantum_signalization(self):
        # Placeholder for visualizing quantum signalization
        print("Visualizing quantum signalization...")

# Function to convert a ket to its corresponding integer representation
def ket_to_int_(ket: str) -> int:
    ket_int = 0
    for i in range(len(ket)):
        if ket[i] == "|1>":
            ket_int += (1 << (len(ket) - 1 - i))
    return ket_int

# Function to convert an integer to its corresponding ket representation
def int_to_ket(integer: int, num_qubits: int) -> str:
    ket = ""
    for i in range(num_qubits):
        if (integer & (1 << i)):
            ket += "|1>"
        else:
            ket += "|0>"
    return ket

# Function to compute the Kronecker product of two matrices
def kronecker_product(matrix1: np.ndarray, matrix2: np.ndarray) -> np.ndarray:
    result_rows, result_cols = matrix1.shape[0] * matrix2.shape[0], matrix1.shape[1] * matrix2.shape[1]
    result = np.zeros((result_rows, result_cols), dtype=np.complex64)
    for i1 in range(matrix1.shape[0]):
        for j1 in range(matrix1.shape[1]):
            for i2 in range(matrix2.shape[0]):
                for j2 in range(matrix2.shape[1]):
                    result[i1 * matrix2.shape[0] + i2, j1 * matrix2.shape[1] + j2] = matrix1[i1, j1] * matrix2[i2, j2]
    return result

# Function to compute the tensor product between two operators
def tensor_product(operator1: np.ndarray, operator2: np.ndarray) -> np.ndarray:
    return np.kron(operator1, operator2)

# Function to return the Pauli operator given a string of Pauli matrices
def pauli_operator(pauli_string: str) -> np.ndarray:
    if pauli_string == "I":
        return np.array([[1, 0], [0, 1]])
    elif pauli_string == "X":
        return np.array([[0, 1], [1, 0]])
    elif pauli_string == "Y":
        return np.array([[0, -1j], [1j, 0]])
    elif pauli_string == "Z":
        return np.array([[1, 0], [0, -1]])
    else:
        raise ValueError("Invalid Pauli string")

# Function to compute the expectation value of an operator given a state
def expectation_value(operator: np.ndarray, state: np.ndarray) -> float:
    return np.dot(state.T.conj(), np.dot(operator, state))[0][0].real

# Function to measure quantum state and return the outcome
def measure(state: np.ndarray) -> int:
    probabilities = np.abs(state)**2
    outcome = np.random.choice(range(len(probabilities)), p=probabilities)
    return outcome

# Function to apply a quantum gate to a quantum state
def apply_gate(gate: np.ndarray, state: np.ndarray) -> np.ndarray:
    return np.dot(gate, state)

# Function to apply the Hadamard gate to a quantum state
def apply_circuit_hadamard(state: np.ndarray) -> np.ndarray:
    hadamard_gate = 1/math.sqrt(2) * np.array([[1, 1], [1, -1]])
    return apply_gate(hadamard_gate, state)

# Function to apply the CNOT gate to a quantum state
def apply_circuit_cnot(state: np.ndarray, control_qubit: int, target_qubit: int) -> np.ndarray:
    cnot_gate = np.array([[1, 0, 0, 0],
                           [0, 1, 0, 0],
                           [0, 0, 0, 1],
                           [0, 0, 1, 0]])
    return apply_gate(cnot_gate, state)

# Function to apply a measurement to a quantum state
def apply_circuit_measure(state: np.ndarray, qubit: int) -> int:
    probabilities = np.abs(state)**2
    outcome = np.random.choice(range(len(probabilities)), p=probabilities)
    return outcome

# Function to run a quantum circuit
def run_circuit(circuit: QuantumCircuit) -> List[int]:
    measurement_results = []
    for gate, target_qubits in circuit.gates:
        if gate == "H":
            circuit.apply_gate(HadamardGate(), target_qubits)
        elif gate == "CNOT":
            circuit.apply_gate(CNOTGate(), target_qubits)
        elif gate == "M":
            measurement_results.append(circuit.measure(target_qubits))
    return measurement_results

# Example usage
if __name__ == "__main__":
    # Create a quantum circuit with 2 qubits
    circuit = QuantumCircuit(2)

    # Add a Hadamard gate to the first qubit
    circuit.add_gate(HadamardGate(), [0])

    # Add a CNOT gate between the first and second qubits
    circuit.add_gate(CNOTGate(), [0, 1])

    # Measure the second qubit
    circuit.add_gate("M", [1])

    # Run the circuit and get the measurement result
    measurement_result = run_circuit(circuit)
    print(f"Measurement result: {measurement_result}")