Information theoretic approach to readout error mitigation for quantum computers

TL;DR

This paper presents an information theoretic foundation for iterative Bayesian unfolding to mitigate readout errors in quantum computers, distinguishing between structural and unstructural mitigation strategies for different quantum computing tasks.

Contribution

It introduces a flexible, information theoretic approach to readout error mitigation, extending iterative Bayesian unfolding to both deterministic and broad-distribution quantum outputs.

Findings

Structural mitigation corrects errors with few repetitions for deterministic outputs.

Unstructural mitigation effectively reduces errors in specific observables for broad distributions.

Application to a 127-qubit GHZ state demonstrates the method's practical effectiveness.

Abstract

We show that the method of iterative bayesian unfolding for mitigating readout errors in quantum computers can be derived from an information theoretic analysis. This inspires more flexible applications of this error mitigation scheme. In particular, we distinguish between structural mitigation and unstructural mitigation. Structural mitigation addresses nearly deterministic quantum computation, where the computer is expected to output a single or few outcome bitstrings. It is shown that the readout errors alone can be corrected by few repetitions of the computation. In contrast, unstructural mitigation is designed for quantum simulation, where the computer outputs bitstrings broadly distributed. In this case, one is interested in mitigating certain observables of interest. As most observables of interest are dependent on few bits and not the whole bitstring, it is sufficient to mitigate the marginal distributions over these dependent bits. As long as the cross-talk of readout errors can be ignored, it is shown that the iterative bayesian unfolding applied locally for these marginal distributions gives similar results as mitigation using least squared errors. We illustrate our analysis using the data of the preparation of the GHZ state in a 127-qubit quantum computer.