text: import qcircuits as qc
  import numpy as np
  import random
  
  
  # Grover's algorithm (search)
  # Given a boolean function f, Grover's algorithm finds an x such that
  # f(x) = 1.
  # If there are N values of x, and M possible solutions, it requires
  # O(sqrt(N/M)) time.
  # Here, we construct a search problem with 1 solution amongst 1024
  # possible answers, and find the solution with 25 applications of
  # the Grover iteration operator.
  
  
  # Construct a Boolean function that is 1 in exactly one place
  def construct_problem(d=10):
      num_inputs = 2**d
      answers = np.zeros(num_inputs, dtype=np.int32)
      answers[np.random.randint(0, num_inputs)] = 1
  
      def f(*bits):
          index = sum(v * 2**i for i, v in enumerate(bits))
  
          return answers[index]
  
      return f
  
  
  def grover_algorithm(d, f):
      # The operators we will need
      Oracle = qc.U_f(f, d=d+1)
      H_d = qc.Hadamard(d)
      H = qc.Hadamard()
      N = 2**d
      zero_projector = np.zeros((N, N))
      zero_projector[0, 0] = 1
      Inversion = H_d((2 * qc.Operator.from_matrix(zero_projector) - qc.Identity(d))(H_d))
      Grover = Inversion(Oracle, qubit_indices=range(d))
  
      # Initial state
      state = qc.zeros(d) * qc.ones(1)
      state = (H_d * H)(state)
  
      # Number of Grover iterations
      angle_to_rotate = np.arccos(np.sqrt(1 / N))
      rotation_angle = 2 * np.arcsin(np.sqrt(1 / N))
      iterations = int(round(angle_to_rotate / rotation_angle))
      for i in range(iterations):
          state = Grover(state)
  
      measurements = state.measure(qubit_indices=range(d))
      return measurements
  
  
  if __name__ == '__main__':
      d = 10
  
      f = construct_problem(d)
      bits = grover_algorithm(d, f)
  
      print('Measurement: {}'.format(bits))
      print('Evaluate f at measurement: {}'.format(f(*bits)))