docs: def single_qubit_randomized_benchmarking(
          sampler: sim.Sampler,
          qubit: devices.GridQubit,
          use_xy_basis: bool = True,
          *,
          num_clifford_range: Sequence[int] = range(10, 100, 10),
          num_circuits: int = 20,
          repetitions: int = 1000) -> RandomizedBenchMarkResult:
      """Clifford-based randomized benchmarking (RB) of a single qubit.
  
      A total of num_circuits random circuits are generated, each of which
      contains a fixed number of single-qubit Clifford gates plus one
      additional Clifford that inverts the whole sequence and a measurement in
      the z-basis. Each circuit is repeated a number of times and the average
      |0> state population is determined from the measurement outcomes of all
      of the circuits.
  
      The above process is done for different circuit lengths specified by the
      integers in num_clifford_range. For example, an integer 10 means the
      random circuits will contain 10 Clifford gates each plus one inverting
      Clifford. The user may use the result to extract an average gate fidelity,
      by analyzing the change in the average |0> state population at different
      circuit lengths. For actual experiments, one should choose
      num_clifford_range such that a clear exponential decay is observed in the
      results.
  
      See Barends et al., Nature 508, 500 for details.
  
      Args:
          sampler: The quantum engine or simulator to run the circuits.
          qubit: The qubit under test.
          use_xy_basis: Determines if the Clifford gates are built with x and y
              rotations (True) or x and z rotations (False).
          num_clifford_range: The different numbers of Cliffords in the RB study.
          num_circuits: The number of random circuits generated for each
              number of Cliffords.
          repetitions: The number of repetitions of each circuit.
  
      Returns:
          A RandomizedBenchMarkResult object that stores and plots the result.
      """
  
      cliffords = _single_qubit_cliffords()
      c1 = cliffords.c1_in_xy if use_xy_basis else cliffords.c1_in_xz
      cfd_mats = np.array([_gate_seq_to_mats(gates) for gates in c1])
  
      gnd_probs = []
      for num_cfds in num_clifford_range:
          excited_probs_l = []
          for _ in range(num_circuits):
              circuit = _random_single_q_clifford(qubit, num_cfds, c1, cfd_mats)
              circuit.append(ops.measure(qubit, key='z'))
              results = sampler.run(circuit, repetitions=repetitions)
              excited_probs_l.append(np.mean(results.measurements['z']))
          gnd_probs.append(1.0 - np.mean(excited_probs_l))
  
      return RandomizedBenchMarkResult(num_clifford_range, gnd_probs)