Calibration of Quantum Devices via Robust Statistical Methods

TL;DR

This paper introduces advanced statistical methods for calibrating quantum devices, demonstrating improved robustness and efficiency over existing techniques, and achieving significant reductions in measurement data needed for accurate quantum system characterization.

Contribution

It systematically compares various statistical algorithms for quantum calibration, highlighting their advantages, and applies them to superconducting qubit calibration with superior performance.

Findings

Reduced uncertainty in qubit calibration by factors of 10 and 3.

Achieved better calibration results than default tools with up to 99.5% less data.

Demonstrated robustness of methods under multi-modality and high dimensionality.

Abstract

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its performance is the numerical representation of the Bayesian probability distributions. In this work, we explore advanced statistical methods for this purpose, and numerically analyze their performance against the state-of-the-art in quantum parameter learning. In particular, we consider sequential importance resampling, tempered likelihood estimation, Markov Chain Monte Carlo, random walk Metropolis (RWM), Hamiltonian Monte Carlo (HMC) and variants (stochastic gradients with and without friction, energy conserving subsampling), block pseudo-marginal Metropolis-Hastings with subsampling, hybrid HMC-RWM approaches, and Gaussian rejection filtering. We demonstrate advantages of these approaches over existing ones, namely robustness under multi-modality and high dimensionality. We apply these algorithms to the calibration of superconducting qubits from IBMQ, surpassing the standard quantum limit and achieving better results than Qiskit's default tools. In Hahn echo and Ramsey experiments, we reduce the uncertainty by factors of 10 and 3 respectively, without increasing the number of measurements; conversely, we match the performance of Qiskit's methods while using up to to 99.5% less experimental data. We additionally investigate the roles of adaptivity, dataset ordering and heuristics in quantum characterization. Our findings have applications in challenging quantum characterization tasks, namely learning the dynamics of open quantum systems.