Robust Phase Estimation

Is a kind of iterative phase estimation formalized by Kimmel, Low, Yoder Phys. Rev. A 92, 062315 (2015). It is ideal for measuring gate calibration errors.

• Robust Phase Estimation
  • Estimate phase of RZ(angle, qubit)
    • Generate RPE experiment
    • Acquire data
    • Extract the estimate of the phase
  • Estimate phase of RX(angle, qubit)
  • Hadamard-like rotation
  • Group multiple experiments to run simultaneously
  • Upper bound on the point estimate variance
  • Visualize the rotation at each depth by plotting x and y expectations
  • Multi qubit gates
  • Characterizing a universal 1q gate set with approximately orthogonal rotation axes
  • Customizing the noise model

API Reference

do_rpe(qc, rotation, changes_of_basis, …)	A wrapper around experiment generation, data acquisition, and estimation that runs robust phase estimation.
bloch_rotation_to_eigenvectors(theta, phi)	Provides convenient conversion from a 1q rotation about some Bloch vector to the two eigenvectors of rotation that lay along the rotation axis.
get_change_of_basis_from_eigvecs(eigenvectors)	Generates a unitary matrix that sends each computational basis state to the corresponding eigenvector.
change_of_basis_matrix_to_quil(qc, qubits, …)	Helper to return a native quil program for the given qc to implement the change_of_basis matrix.
generate_rpe_experiments(rotation, …)	Generate a dataframe containing all the experiments needed to perform robust phase estimation to estimate the angle of rotation of the given rotation program.
get_additive_error_factor(M_j, …)	Calculate the factor in Equation V.17 of [RPE].
num_trials(depth, max_depth, …)	Calculate the optimal number of shots per program with a given depth.
acquire_rpe_data(qc, experiments, …)	Run each experiment in the sequence of experiments.

Analysis

_p_max(M_j)	Calculate an upper bound on the probability of error in the estimate on the jth iteration.
_xci(h)	Calculate the maximum error in the estimate after h iterations given that no errors occurred in all previous iterations.
get_variance_upper_bound(num_depths, …)	Equation V.9 in [RPE]
estimate_phase_from_moments(xs, ys, x_stds, …)	Estimate the phase in an iterative fashion as described in section V.
robust_phase_estimate(results, qubits)	Provides the estimate of the phase for an RPE experiment with results.
plot_rpe_iterations(xs, ys, x_stds, y_stds, …)	Creates a polar plot of the estimated location of the state in the plane perpendicular to the axis of rotation for each iteration of RPE.