




import math

import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute







def lowerCamelCase__   (			_lowercase = 1 ,						_lowercase = 1      ):

     '''simple docstring'''


     if isinstance(lowercase_ ,						lowercase_      ) or isinstance(lowercase_ ,						lowercase_      ):
          raise TypeError('''inputs must be integers.'''      )
     if (bit_a < 0) or (bit_a < 0):
          raise ValueError('''inputs must be positive.'''      )
     if (math.floor(lowercase_      ) != bit_a) or (math.floor(lowercase_      ) != bit_a):
          raise ValueError('''inputs must be exact integers.'''      )
     if (bit_a > 1) or (bit_a > 1):
          raise ValueError('''inputs must be less or equal to 1.'''      )

     # build registers
     UpperCAmelCase_			:							Union[str, Any]   =			QuantumRegister(2 ,						'''qr'''      )
     UpperCAmelCase_			:							List[Any]   =			ClassicalRegister(2 ,						'''cr'''      )

     UpperCAmelCase_			:							str   =			QuantumCircuit(lowercase_ ,						lowercase_      )

     # entanglement the qubits
     quantum_circuit.h(1      )
     quantum_circuit.cx(1 ,						0      )

     # send the information
     UpperCAmelCase_			:							Dict   =			str(lowercase_      ) + str(lowercase_      )

     if c_information == "11":
          quantum_circuit.x(1      )
          quantum_circuit.z(1      )
     elif c_information == "10":
          quantum_circuit.z(1      )
     elif c_information == "01":
          quantum_circuit.x(1      )
     else:
          quantum_circuit.i(1      )

     # unentangled the circuit
     quantum_circuit.cx(1 ,						0      )
     quantum_circuit.h(1      )

     # measure the circuit
     quantum_circuit.measure(lowercase_ ,						lowercase_      )

     UpperCAmelCase_			:							Tuple   =			Aer.get_backend('''aer_simulator'''      )
     UpperCAmelCase_			:							Any   =			execute(lowercase_ ,						lowercase_ ,						shots=1000      )

     return job.result().get_counts(lowercase_      )


if __name__ == "__main__":
     print(F"""Counts for classical state send: {superdense_coding(1,1)}""")





'''simple docstring'''







from __future__ import annotations

import math
from itertools import permutations






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if 1 < number < 4:
				# 2 and 3 are primes
				return True
		elif number < 2 or number % 2 == 0 or number % 3 == 0:
				# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
				return False

		# All primes number are in format of 6k +/- 1
		for i in range(5						,							int(math.sqrt(lowercase_  ) + 1  )						,							6  ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True






def 		_lowercase		(	lowercase_ = 7  ):



		'''simple docstring'''







		_snake_case	       =       "".join(str(lowercase_  ) for i in range(1						,							n + 1  )  )
		_snake_case	       =       [int("".join(lowercase_  )  ) for i in permutations(lowercase_						,							lowercase_  )]
		_snake_case	       =       [num for num in perm_list if is_prime(lowercase_  )]
		return max(lowercase_  ) if pandigitals else 0


if __name__ == "__main__":
						print(F'''{solution() = }''')





