





import qiskit




def _a (  SCREAMING_SNAKE_CASE__      :  int			,				SCREAMING_SNAKE_CASE__      :  int       )	->    qiskit.result.counts.Counts:

       '''simple docstring'''






       SCREAMING_SNAKE_CASE__       :      Optional[int]     =						qiskit.Aer.get_backend("aer_simulator"       )

       # Create a Quantum Circuit acting on the q register
       SCREAMING_SNAKE_CASE__       :      str     =						qiskit.QuantumCircuit(lowerCAmelCase__			,				lowerCAmelCase__       )

       # 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
       SCREAMING_SNAKE_CASE__       :      Tuple     =						qiskit.execute(lowerCAmelCase__			,				lowerCAmelCase__			,				shots=10_00       )

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


if __name__ == "__main__":
  _lowerCamelCase :    Dict  							= single_qubit_measure(2, 2)
  print(f"Total count for various states are: {counts}")













from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def _a (  SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  complex			,				SCREAMING_SNAKE_CASE__      :  str = "x"			,				SCREAMING_SNAKE_CASE__      :  float = 10**-10			,				SCREAMING_SNAKE_CASE__      :  int = 1			,				)	->    complex:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						symbols(SCREAMING_SNAKE_CASE__       )
							SCREAMING_SNAKE_CASE__       :      str     =						lambdify(SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__       )
							SCREAMING_SNAKE_CASE__       :      int     =						lambdify(SCREAMING_SNAKE_CASE__			,				diff(SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__       )       )

							SCREAMING_SNAKE_CASE__       :      Any     =						starting_point

							while True:
														if diff_function(SCREAMING_SNAKE_CASE__       ) != 0:
																					SCREAMING_SNAKE_CASE__       :      Any     =						prev_guess - multiplicity * func(SCREAMING_SNAKE_CASE__       ) / diff_function(
																					    SCREAMING_SNAKE_CASE__       )
														else:
																					raise ZeroDivisionError("Could not find root"       ) from None

														# Precision is checked by comparing the difference of consecutive guesses
														if abs(next_guess - prev_guess       ) < precision:
																					return next_guess

														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						next_guess


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

		# Find root of polynomial
		# Find fourth Root of 5
		print(f"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}")

		# Find value of e
		print(
		    '''The root of log(y) - 1 = 0 is ''',
		    f"{newton_raphson('log(y) - 1', 2, variable='y')}",
		)

		# Exponential Roots
		print(
		    '''The root of exp(x) - 1 = 0 is''',
		    f"{newton_raphson('exp(x) - 1', 1_0, precision=0.005)}",
		)

		# Find root of cos(x)
		print(f"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")






