Few-Shot, Robust Calibration of Single Qubit Gates Using Bayesian Robust Phase Estimation

TL;DR

This paper introduces Bayesian Robust Phase Estimation (BRPE), a novel method that enhances quantum gate calibration by reducing sampling requirements and errors, demonstrated through numerical simulations and experimental trapped ion system implementation.

Contribution

BRPE integrates Bayesian estimation into RPE, significantly reducing sample overhead and estimation errors in quantum gate calibration.

Findings

Reduces phase estimation errors by up to 96% in ideal conditions.

Requires approximately 50% fewer samples than standard RPE.

Successfully applied in experimental trapped ion systems.

Abstract

Accurate calibration of control parameters in quantum 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) 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 innovative 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 $176$ shots. Additionally, we adapt BRPE for Ramsey spectroscopy applications and successfully implement it experimentally in a trapped ion system.