Robust Lindbladian Estimation for Quantum Dynamics

TL;DR

This paper improves Lindbladian estimation methods for quantum process tomography by developing algorithms for logarithm search and integrating gate set tomography techniques to enhance robustness against errors, demonstrated on simulated and real quantum hardware data.

Contribution

It introduces practical algorithmic improvements for Lindbladian logarithm search and combines them with gate set tomography to better handle experimental errors.

Findings

Logarithm search algorithms are effective for Lindbladian fitting in realistic quantum settings.

Augmentation with gate set tomography enhances robustness against SPAM errors.

Techniques successfully applied to both simulated and real superconducting-qubit data.

Abstract

We revisit the problem of fitting Lindbladian models to the outputs of quantum process tomography. A sequence of prior theoretical works approached the problem by considering whether there exists a Lindbladian generator close to a matrix logarithm of the tomographically estimated transfer matrix. This technique must take into account the non-uniqueness of the matrix logarithm, so that in general multiple branches of the logarithm must be checked. In contrast, all practical demonstrations of Lindbladian fitting on real experimental data have to our knowledge eschewed logarithm search, instead adopting direct numerical optimisation or ad-hoc approaches tailored to a particular experimental realisation. In our work, we introduce algorithmic improvements to logarithm search, demonstrating that it can be applied in practice to settings relevant for current quantum computing hardware. We additionally augment the task of Lindbladian fitting with techniques from gate set tomography to improve robustness against state preparation and measurement (SPAM) errors, which can otherwise obfuscate estimates of the model underlying the process of interest. We benchmark our techniques extensively using simulated tomographic data employing a range of realistic error models, before demonstrating their application to tomographic data collected from real superconducting-qubit hardware.