




import qiskit

def 			_SCREAMING_SNAKE_CASE			(							lowercase	:       int	,							lowercase	:       int     ):


      '''simple docstring'''



      lowerCamelCase_		     =    qiskit.Aer.get_backend('aer_simulator'     )

      # Create a Quantum Circuit acting on the q register
      lowerCamelCase_		     =    qiskit.QuantumCircuit(lowercase	,							lowercase     )

      # Apply X (NOT) Gate to Qubits 0 & 1
      circuit.x(0     )
      circuit.x(1     )

      # Map the quantum measurement to the classical bits
      circuit.measure([0, 1]	,							[0, 1]     )

      # Execute the circuit on the qasm simulator
      lowerCamelCase_		     =    qiskit.execute(lowercase	,							lowercase	,							shots=10_00     )

      # Return the histogram data of the results of the experiment.
      return job.result().get_counts(lowercase     )


if __name__ == "__main__":
 lowerCamelCase				:		Optional[Any]     =   single_qubit_measure(2, 2)
 print(F"""Total count for various states are: {counts}""")









from collections.abc import Callable

import numpy as np

def 			_SCREAMING_SNAKE_CASE			(							lowercase	:       Callable	,							lowercase	:       float	,							lowercase	:       float	,							lowercase	:       float	,							lowercase	:       float     ):


      '''simple docstring'''



      lowerCamelCase_		     =    int(np.ceil((x_end - xa) / step_size     )     )
      lowerCamelCase_		     =    np.zeros((n + 1,)     )
      lowerCamelCase_		     =    ya
      lowerCamelCase_		     =    xa

      for k in range(lowercase     ):
            lowerCamelCase_		     =    y[k] + step_size * ode_func(lowercase	,							y[k]     )
            lowerCamelCase_		     =    y[k] + (
                (step_size / 2) * (ode_func(lowercase	,							y[k]     ) + ode_func(x + step_size	,							lowercase     ))
            )
            x += step_size

      return y


if __name__ == "__main__":
 import doctest

 doctest.testmod()



