''' 
Module: quantum_simulator.py
Description: A prototype quantum circuit simulator with basic gate functionalities. 
This module simulates quantum operations on qubit states using numpy arrays. 
It currently supports: 
 - Hadamard gate (H)
 - Pauli-X gate (X)
 - A stub implementation for the CNOT gate 

Future enhancements will expand this functionality to fully simulate multi-qubit systems and additional gates.

Extensive inline documentation and logging are provided for clarity.
'''

import numpy as np
import logging

# Configure logging for the module
logging.basicConfig(level=logging.DEBUG, format='%(asctime)s - %(levelname)s - %(message)s')

# Define common quantum states for convenience
ket_zero = np.array([[1.0], [0.0]], dtype=complex)  # |0> state
ket_one = np.array([[0.0], [1.0]], dtype=complex)   # |1> state


def apply_hadamard(qubit_state: np.ndarray) -> np.ndarray:
    '''
    Apply the Hadamard gate to a single qubit.

    The Hadamard matrix transforms the basis states as:
    H|0> = 1/√2 (|0> + |1>)
    H|1> = 1/√2 (|0> - |1>)
    
    Parameters:
        qubit_state (np.ndarray): A 2x1 numpy array representing the qubit state.

    Returns:
        np.ndarray: The resulting state after applying the Hadamard gate.
    '''
    logging.debug('Applying Hadamard gate to state: %s', qubit_state.flatten())
    H = (1/np.sqrt(2)) * np.array([[1, 1], [1, -1]], dtype=complex)
    result = np.dot(H, qubit_state)
    logging.debug('Resulting state after Hadamard: %s', result.flatten())
    return result


def apply_pauli_x(qubit_state: np.ndarray) -> np.ndarray:
    '''
    Apply the Pauli-X (NOT) gate to a single qubit.

    The Pauli-X gate flips the state:
    X|0> = |1>
    X|1> = |0>
    
    Parameters:
        qubit_state (np.ndarray): A 2x1 numpy array representing the qubit state.

    Returns:
        np.ndarray: The resulting state after applying the Pauli-X gate.
    '''
    logging.debug('Applying Pauli-X gate to state: %s', qubit_state.flatten())
    X = np.array([[0, 1], [1, 0]], dtype=complex)
    result = np.dot(X, qubit_state)
    logging.debug('Resulting state after Pauli-X: %s', result.flatten())
    return result


def apply_cnot(control: np.ndarray, target: np.ndarray) -> (np.ndarray, np.ndarray):
    '''
    Stub for CNOT gate application on a two-qubit system.

    The CNOT gate flips the target qubit if the control qubit is in the |1> state. 
    Currently, this function is a stub and does not fully simulate a multi-qubit system.

    Parameters:
        control (np.ndarray): A 2x1 numpy array representing the control qubit state.
        target (np.ndarray): A 2x1 numpy array representing the target qubit state.

    Returns:
        tuple: A tuple containing the (control, target) qubit states after applying the CNOT gate.
    '''
    logging.debug('CNOT gate stub invoked. Control state: %s, Target state: %s', control.flatten(), target.flatten())
    # This is a simplified demonstration. In a full simulation the joint state would be used.
    # For now, if control is in state |1>, simply apply Pauli-X to the target qubit.
    if np.allclose(control, ket_one):
        logging.debug('Control qubit is |1>; applying Pauli-X to target qubit.')
        target = apply_pauli_x(target)
    else:
        logging.debug('Control qubit is not |1>; target qubit remains unchanged.')
    return control, target


def simulate_quantum_circuit():
    '''
    Demonstration function for simulating a simple quantum circuit.

    This function applies a sequence of gate operations to an initial qubit state and prints the results.
    It simulates the following operations:
      1. Start with a |0> state.
      2. Apply a Hadamard gate to create a superposition.
      3. Apply a Pauli-X gate to flip the state.
      4. Demonstrate a CNOT operation (stub) on a two-qubit system.
    '''
    logging.info('Starting quantum circuit simulation...')
    # Start with a |0> state
    initial_state = ket_zero.copy()
    logging.info('Initial state |0>: %s', initial_state.flatten())

    # Apply Hadamard gate
    state_after_h = apply_hadamard(initial_state)

    # Apply Pauli-X gate
    state_after_x = apply_pauli_x(state_after_h)

    # For CNOT simulation, define control and target qubits
    control_qubit = ket_zero.copy()  # For demonstration, starting with |0>
    target_qubit = ket_one.copy()      # And |1> for the target
    logging.info('Before CNOT - Control: %s, Target: %s', control_qubit.flatten(), target_qubit.flatten())
    control_qubit, target_qubit = apply_cnot(control_qubit, target_qubit)
    logging.info('After CNOT (stub) - Control: %s, Target: %s', control_qubit.flatten(), target_qubit.flatten())

    logging.info('Quantum circuit simulation complete.')


if __name__ == '__main__':
    # Execute the simulation if the module is run directly
    simulate_quantum_circuit() 