





from __future__ import annotations

from decimal import Decimal

from numpy import array







def       A__							(   SCREAMING_SNAKE_CASE__)       ->   list[list[float]]:
  __snake_case:						Any			  =						Decimal

  # Check if the provided matrix has 2 rows and 2 columns
  # since this implementation only works for 2x2 matrices
  if len(SCREAMING_SNAKE_CASE__) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
    # Calculate the determinant of the matrix
    __snake_case:						Tuple			  =						float(
        d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1]))
    if determinant == 0:
      raise ValueError("""This matrix has no inverse.""")

    # Creates a copy of the matrix with swapped positions of the elements
    __snake_case:						Optional[int]			  =						[[0.0, 0.0], [0.0, 0.0]]
    __snake_case:						Optional[Any]			  =						matrix[1][1], matrix[0][0]
    __snake_case:						Union[str, Any]			  =						-matrix[1][0], -matrix[0][1]

    # Calculate the inverse of the matrix
    return [
        [(float(d(SCREAMING_SNAKE_CASE__)) / determinant) or 0.0 for n in row] for row in swapped_matrix
    ]
  elif (
      len(SCREAMING_SNAKE_CASE__) == 3
      and len(matrix[0]) == 3
      and len(matrix[1]) == 3
      and len(matrix[2]) == 3
  ):
    # Calculate the determinant of the matrix using Sarrus rule
    __snake_case:						Any			  =						float(
        (
            (d(matrix[0][0]) * d(matrix[1][1]) * d(matrix[2][2]))
            + (d(matrix[0][1]) * d(matrix[1][2]) * d(matrix[2][0]))
            + (d(matrix[0][2]) * d(matrix[1][0]) * d(matrix[2][1]))
        )
        - (
            (d(matrix[0][2]) * d(matrix[1][1]) * d(matrix[2][0]))
            + (d(matrix[0][1]) * d(matrix[1][0]) * d(matrix[2][2]))
            + (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
        ))
    if determinant == 0:
      raise ValueError("""This matrix has no inverse.""")

    # Creating cofactor matrix
    __snake_case:						Tuple			  =						[
        [d(0.0), d(0.0), d(0.0)],
        [d(0.0), d(0.0), d(0.0)],
        [d(0.0), d(0.0), d(0.0)],
    ]
    __snake_case:						Dict			  =						(d(matrix[1][1]) * d(matrix[2][2])) - (
        d(matrix[1][2]) * d(matrix[2][1])
    )
    __snake_case:						Tuple			  =						-(
        (d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
    )
    __snake_case:						Optional[int]			  =						(d(matrix[1][0]) * d(matrix[2][1])) - (
        d(matrix[1][1]) * d(matrix[2][0])
    )
    __snake_case:						Union[str, Any]			  =						-(
        (d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
    )
    __snake_case:						str			  =						(d(matrix[0][0]) * d(matrix[2][2])) - (
        d(matrix[0][2]) * d(matrix[2][0])
    )
    __snake_case:						List[Any]			  =						-(
        (d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
    )
    __snake_case:						Optional[Any]			  =						(d(matrix[0][1]) * d(matrix[1][2])) - (
        d(matrix[0][2]) * d(matrix[1][1])
    )
    __snake_case:						List[str]			  =						-(
        (d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
    )
    __snake_case:						Optional[int]			  =						(d(matrix[0][0]) * d(matrix[1][1])) - (
        d(matrix[0][1]) * d(matrix[1][0])
    )

    # Transpose the cofactor matrix (Adjoint matrix)
    __snake_case:						List[Any]			  =						array(SCREAMING_SNAKE_CASE__)
    for i in range(3):
      for j in range(3):
        __snake_case:						Tuple			  =						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
    __snake_case:						List[Any]			  =						array(SCREAMING_SNAKE_CASE__)
    for i in range(3):
      for j in range(3):
        inverse_matrix[i][j] /= d(SCREAMING_SNAKE_CASE__)

        # Calculate the inverse of the matrix
    return [[float(d(SCREAMING_SNAKE_CASE__)) or 0.0 for n in row] for row in inverse_matrix]
  raise ValueError("""Please provide a matrix of size 2x2 or 3x3.""")








import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute







def       A__							(   SCREAMING_SNAKE_CASE__ = 3)       ->   qiskit.result.counts.Counts:
  if isinstance(SCREAMING_SNAKE_CASE__ , SCREAMING_SNAKE_CASE__):
    raise TypeError("""number of qubits must be a integer.""")
  if number_of_qubits <= 0:
    raise ValueError("""number of qubits must be > 0.""")
  if math.floor(SCREAMING_SNAKE_CASE__) != number_of_qubits:
    raise ValueError("""number of qubits must be exact integer.""")
  if number_of_qubits > 10:
    raise ValueError("""number of qubits too large to simulate(>10).""")

  __snake_case:						int			  =						QuantumRegister(SCREAMING_SNAKE_CASE__ , """qr""")
  __snake_case:						List[str]			  =						ClassicalRegister(SCREAMING_SNAKE_CASE__ , """cr""")

  __snake_case:						Optional[Any]			  =						QuantumCircuit(SCREAMING_SNAKE_CASE__ , SCREAMING_SNAKE_CASE__)

  __snake_case:						Tuple			  =						number_of_qubits

  for i in range(SCREAMING_SNAKE_CASE__):
    quantum_circuit.h(number_of_qubits - i - 1)
    counter -= 1
    for j in range(SCREAMING_SNAKE_CASE__):
      quantum_circuit.cp(np.pi / 2 ** (counter - j) , SCREAMING_SNAKE_CASE__ , SCREAMING_SNAKE_CASE__)

  for k in range(number_of_qubits // 2):
    quantum_circuit.swap(SCREAMING_SNAKE_CASE__ , number_of_qubits - k - 1)

  # measure all the qubits
  quantum_circuit.measure(SCREAMING_SNAKE_CASE__ , SCREAMING_SNAKE_CASE__)
  # simulate with 10000 shots
  __snake_case:						Union[str, Any]			  =						Aer.get_backend("""qasm_simulator""")
  __snake_case:						Optional[Any]			  =						execute(SCREAMING_SNAKE_CASE__ , SCREAMING_SNAKE_CASE__ , shots=1_0000)

  return job.result().get_counts(SCREAMING_SNAKE_CASE__)


if __name__ == "__main__":
      print(
          f'Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}'
      )






