



'''simple docstring'''




def        lowerCAmelCase_     (			_lowerCamelCase:     list[int] ,   _lowerCamelCase:     list[int] ,   _lowerCamelCase:     int      ):
		return not any(
		    neighbour == 1 and colored_vertices[i] == color
		    for i, neighbour in enumerate(_lowerCamelCase      )      )






def        lowerCAmelCase_     (			_lowerCamelCase:     list[list[int]] ,   _lowerCamelCase:     int ,   _lowerCamelCase:     list[int] ,   _lowerCamelCase:     int      ):

		# Base Case
		if index == len(_lowerCamelCase      ):
				return True

		# Recursive Step
		for i in range(_lowerCamelCase      ):
				if valid_coloring(graph[index] ,   _lowerCamelCase ,   _lowerCamelCase      ):
						# Color current vertex
						__SCREAMING_SNAKE_CASE :	List[Any]					 =	i
						# Validate coloring
						if util_color(_lowerCamelCase ,   _lowerCamelCase ,   _lowerCamelCase ,   index + 1      ):
								return True
						# Backtrack
						__SCREAMING_SNAKE_CASE :	str					 =	-1
		return False






def        lowerCAmelCase_     (			_lowerCamelCase:     list[list[int]] ,   _lowerCamelCase:     int      ):
		__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	[-1] * len(_lowerCamelCase      )

		if util_color(_lowerCamelCase ,   _lowerCamelCase ,   _lowerCamelCase ,   0      ):
				return colored_vertices

		return []




'''simple docstring'''




import qiskit


def        lowerCAmelCase_     (			_lowerCamelCase:     int = 2      ):
		__SCREAMING_SNAKE_CASE :	Dict					 =	qubits

		# Using Aer's simulator
		__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	qiskit.Aer.get_backend("""aer_simulator"""      )

		# Creating a Quantum Circuit acting on the q register
		__SCREAMING_SNAKE_CASE :	str					 =	qiskit.QuantumCircuit(_lowerCamelCase ,   _lowerCamelCase      )

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

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

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

		# 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
		__SCREAMING_SNAKE_CASE :	str					 =	qiskit.execute(_lowerCamelCase ,   _lowerCamelCase ,   shots=10_00      )

		return job.result().get_counts(_lowerCamelCase      )


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