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

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.