The robust phase estimation (RPE) protocol was designed to be an efficient and robust way to calibrate quantum operations. The robustness of RPE refers to its ability to estimate a single parameter, usually gate amplitude, even when other parameters are poorly calibrated or when the gate experiences significant errors. Here we demonstrate the robustness of RPE to errors that affect initialization, measurement, and gates. In each case, the error threshold at which RPE begins to fail matches quantitatively with theoretical bounds. We conclude that RPE is an effective and reliable tool for calibration of one-qubit rotations and that it is particularly useful for automated calibration routines and sensor tasks.
The robust phase estimation (RPE) protocol was designed to be an efficient and robust way to calibrate quantum operations. The robustness of RPE refers to its ability to estimate a single parameter, usually gate amplitude, even when other parameters are poorly calibrated or when the gate experiences significant errors. Here we demonstrate the robustness of RPE to errors that affect initialization, measurement, and gates. In each case, the error threshold at which RPE begins to fail matches quantitatively with theoretical bounds. We conclude that RPE is an effective and reliable tool for calibration of one-qubit rotations and that it is particularly useful for automated calibration routines and sensor tasks.
Accurate calibration of control parameters in quan-tum gates is crucial for high-fidelity operations, yet it represents a significant time and resource challenge, necessitating periods of downtime for quantum computers. Robust Phase Estimation (RPE) [8] has emerged as a practical and effective calibration technique aimed at tackling this challenge. It combines a provably efficient number of control pulses with a classical post-processing algorithm to estimate the phase accumulated by a quantum gate. We introduce Bayesian Robust Phase Estimation (BRPE), an in-novative approach that integrates Bayesian parameter estimation into the classical post-processing phase to reduce the sampling overhead. Our numerical analysis shows that BRPE markedly reduces phase estimation errors, requiring approximately 50% fewer samples than standard RPE. Specifically, in an ideal, noise-free setting, it achieves up to a 96% reduction in average absolute estimation error for a fixed sample cost of 88 shots when compared to RPE. Under a depolarizing noise model, it attains up to a 47% reduction for a fixed cost of 1 76 shots. Additionally, we adapt BRPE for Ramsey spectroscopy applications and successfully implement it experimentally in a trapped ion system.
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the error in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors, but is both time consuming, (when one only wants to learn a few key parameters), and requires resources, like perfect state preparation and measurement, that might not be available. With the goal of efficiently estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge two key parameters (amplitude and off-resonance errors) in a single-qubit gate with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins, New J. Phys. 11, 073023 (2009)].
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors but is both time consuming (when one wants to learn only a few key parameters) and usually inaccurate without resources such as perfect state preparation and measurement, which might not be available. With the goal of efficiently and accurately estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge key systematic parameters (specifically, amplitude and off-resonance errors) in a universal single-qubit gate set with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling, and do so without entanglement and entirely within a single-qubit Hilbert space. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins et al., New J. Phys. 11, 073023 (2009)].
We demonstrate an experimental implementation of robust phase estimation (RPE) to learn the phase of a single-qubit rotation on a trapped Yb^{+} ion qubit. We show this phase can be estimated with an uncertainty below 4×10^{-4} rad using as few as 176 total experimental samples, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We crossvalidate the results of RPE with the more resource-intensive protocol of gate set tomography.
The calibration of high-quality two-qubit entangling gates is an essential component in engineering large-scale, fault-tolerant quantum computers. However, many standard calibration techniques are based on randomized circuits that are only quadratically sensitive to calibration errors. As a result, these approaches are inefficient, requiring many experimental shots to achieve acceptable performance. In this work, we demonstrate that robust phase estimation can enable high-precision, Heisenberg-limited estimates of coherent errors in multi-qubit gates. Equipped with an efficient estimator, the calibration problem may be reduced to a simple optimization loop that minimizes the estimated coherent error. We experimentally demonstrate our calibration protocols by improving the operation of a two-qubit controlled-Z gate on a superconducting processor, and we validate the improved performance with gate set tomography. Our methods are applicable to gates in other quantum hardware platforms such as ion traps and neutral atoms, and on other multi-qubit gates, such as CNOT or iSWAP.
Robust Phase Estimation (RPE) is a quantum algorithm to determine the relative phases of eigenstates of a unitary operator. This code implements the classical portion of the RPE algorithm, useful both in simulation (e.g., Sandia's pyGSTi or IBM's Qiskit simulators) and on actual quantum hardware (e.g., IBM's Qiskit Quantum Experience). It additionally implements improvements in these dependent software packages, for both required core function of the RPE and improved usability. SAND2020-12547 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.