Error models in quantum computation: an application of model selection

TL;DR

This paper demonstrates how model selection techniques, specifically the Akaike Information Criterion, can be used to detect and analyze error types in quantum computing experiments, even with limited state information.

Contribution

It introduces a method applying model selection to identify error types in quantum systems, addressing the challenge of limited state and process descriptions.

Findings

Error detection scales polynomially with qubits and error size

Model selection effectively distinguishes error types in quantum experiments

Method applicable up to 25 qubits in the example

Abstract

Threshold theorems for fault-tolerant quantum computing assume that errors are of certain types. But how would one detect whether errors of the "wrong" type occur in one's experiment, especially if one does not even know what type of error to look for? The problem is that for many qubits a full state description is impossible to analyze, and a full process description is even more impossible to analyze. As a result, one simply cannot detect all types of errors. Here we show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike Information Criterion. The example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size.