
"""simple docstring"""

def 							A		(       snake_case   :Any       ,      snake_case   :int       ,      snake_case   :List[Any]       ,      snake_case   :Tuple       ,      snake_case   :Optional[int]       ,      snake_case   :Tuple	)   ->			Union[str, Any]:
 if index == r:
  for j in range(snake_case	):
   print(data[j]       ,      end=' '	)
  print(' '	)
  return
 #  When no more elements are there to put in data[]
 if i >= n:
  return
 # current is included, put next at next location
 __UpperCamelCase       						= arr[i]
 combination_util(snake_case       ,      snake_case       ,      snake_case       ,      index + 1       ,      snake_case       ,      i + 1	)
 # current is excluded, replace it with
 # next (Note that i+1 is passed, but
 # index is not changed)
 combination_util(snake_case       ,      snake_case       ,      snake_case       ,      snake_case       ,      snake_case       ,      i + 1	)
 # The main function that prints all combinations
 # of size r in arr[] of size n. This function
 # mainly uses combinationUtil()






def 							A		(       snake_case   :List[Any]       ,      snake_case   :str       ,      snake_case   :Tuple	)   ->			int:
 # A temporary array to store all combination one by one
 __UpperCamelCase       						= [0] * r
 # Print all combination using temporary array 'data[]'
 combination_util(snake_case       ,      snake_case       ,      snake_case       ,      0       ,      snake_case       ,      0	)


if __name__ == "__main__":
      # Driver code to check the function above
      UpperCamelCase			:       List[str]									=				[1_0, 2_0, 3_0, 4_0, 5_0]
      print_combination(arr, len(arr), 3)
      # This code is contributed by Ambuj sahu





"""simple docstring"""

import numpy as np
import qiskit






def 							A		(       snake_case   :int = 8       ,      snake_case   :int | None = None	)   ->			str:
 __UpperCamelCase       						= np.random.default_rng(seed=snake_case	)

 # Roughly 25% of the qubits will contribute to the key.
 # So we take more than we need.
 __UpperCamelCase       						= 6 * key_len
 # Measurement basis for Alice's qubits.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)
 # The set of states Alice will prepare.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)
 # Measurement basis for Bob's qubits.
 __UpperCamelCase       						= rng.integers(2       ,      size=snake_case	)

 # Quantum Circuit to simulate BB84
 __UpperCamelCase       						= qiskit.QuantumCircuit(snake_case       ,      name='BB84'	)

 # Alice prepares her qubits according to rules above.
 for index, _ in enumerate(snake_case	):
  if alice_state[index] == 1:
   bbaa_circ.x(snake_case	)
  if alice_basis[index] == 1:
   bbaa_circ.h(snake_case	)
 bbaa_circ.barrier()

 # Bob measures the received qubits according to rules above.
 for index, _ in enumerate(snake_case	):
  if bob_basis[index] == 1:
   bbaa_circ.h(snake_case	)

 bbaa_circ.barrier()
 bbaa_circ.measure_all()

 # Simulate the quantum circuit.
 __UpperCamelCase       						= qiskit.Aer.get_backend('aer_simulator'	)
 # We only need to run one shot because the key is unique.
 # Multiple shots will produce the same key.
 __UpperCamelCase       						= qiskit.execute(snake_case       ,      snake_case       ,      shots=1       ,      seed_simulator=snake_case	)
 # Returns the result of measurement.
 __UpperCamelCase       						= job.result().get_counts(snake_case	).most_frequent()

 # Extracting the generated key from the simulation results.
 # Only keep measurement results where Alice and Bob chose the same basis.
 __UpperCamelCase       						= ''.join(
     [
         result_bit
         for alice_basis_bit, bob_basis_bit, result_bit in zip(
             snake_case       ,      snake_case       ,      snake_case	)
         if alice_basis_bit == bob_basis_bit
     ]	)

 # Get final key. Pad with 0 if too short, otherwise truncate.
 __UpperCamelCase       						= gen_key[:key_len] if len(snake_case	) >= key_len else gen_key.ljust(snake_case       ,      '0'	)
 return key


if __name__ == "__main__":
      print(f'''The generated key is : {bbaa(8, seed=0)}''')
      from doctest import testmod

      testmod()



