
"""simple docstring"""


from __future__ import annotations

import numpy as np






def    _snake_case					(		snake_case__ :  np.ndarray  ):
	A ,   A     = np.shape(snake_case__  )
	if rows != columns:
		A     = (
		    '\'table\' has to be of square shaped array but got a '
		    F'{rows}x{columns} array:\n{table}'
		)
		raise ValueError(snake_case__  )

	A     = np.zeros((rows, columns)  )
	A     = np.zeros((rows, columns)  )
	for i in range(snake_case__  ):
		for j in range(snake_case__  ):
			A     = sum(lower[i][k] * upper[k][j] for k in range(snake_case__  )  )
			if upper[j][j] == 0:
				raise ArithmeticError('No LU decomposition exists'  )
			A     = (table[i][j] - total) / upper[j][j]
		A     = 1
		for j in range(snake_case__						,   snake_case__  ):
			A     = sum(lower[i][k] * upper[k][j] for k in range(snake_case__  )  )
			A     = table[i][j] - total
	return lower, upper


if __name__ == "__main__":
		import doctest

		doctest.testmod()




'''simple docstring'''





import qiskit





def   a_   (		_UpperCAmelCase    :      int = 2				)    ->  qiskit.result.counts.Counts:
      __snake_case :   Union[str, Any]													=    qubits

      # Using Aer's simulator
      __snake_case :   List[Any]													=    qiskit.Aer.get_backend('aer_simulator'				)

      # Creating a Quantum Circuit acting on the q register
      __snake_case :   Dict													=    qiskit.QuantumCircuit(_UpperCAmelCase ,_UpperCAmelCase				)

      # Adding a H gate on qubit 0 (now q0 in superposition)
      circuit.h(0				)

      for i in range(1 ,_UpperCAmelCase				):
            # Adding CX (CNOT) gate
            circuit.cx(i - 1 ,_UpperCAmelCase				)

      # Mapping the quantum measurement to the classical bits
      circuit.measure(list(range(_UpperCAmelCase				)				) ,list(range(_UpperCAmelCase				)				)				)

      # Now measuring any one qubit would affect other qubits to collapse
      # their super position and have same state as the measured one.

      # Executing the circuit on the simulator
      __snake_case :   Optional[Any]													=    qiskit.execute(_UpperCAmelCase ,_UpperCAmelCase ,shots=10_00				)

      return job.result().get_counts(_UpperCAmelCase				)


if __name__ == "__main__":
    print(F"""Total count for various states are: {quantum_entanglement(3)}""")



