Non-degenerate Marginal-Likelihood Calibration with Application to Quantum Characterization

TL;DR

This paper introduces a novel marginal likelihood method within the Bayesian framework for quantum device characterization, improving accuracy and stability in modeling quantum data with Gaussian processes.

Contribution

It presents an exact marginalized likelihood approach that handles degeneracy in covariance matrices, enhancing quantum system modeling accuracy.

Findings

Improved predictive accuracy for quantum device data.

Enhanced computational stability for large datasets.

Effective uncertainty quantification in quantum measurements.

Abstract

We propose a marginal likelihood strategy within the Kennedy-O'Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized likelihood by integrating out the degenerate eigenspace of the covariance matrix, rather than approximating the original likelihood. Unlike approximation methods that compromise accuracy for computational efficiency, our method defines an exact likelihood -- distinct from the original but preserving all relevant information. This formulation achieves computational efficiency and stability, even for large datasets where the covariance matrix nears degeneracy. Applied to the characterization of a superconducting quantum device at Lawrence Livermore National Laboratory, the approach enhances the predictive accuracy of the Lindblad master equations for modeling Ramsey measurement data by effectively quantifying uncertainties consistent with the quantum data.