Pauli channels can be estimated from syndrome measurements in quantum error correction

TL;DR

This paper proves that stabilizer codes can be used to accurately estimate Pauli noise channels, including correlated errors and measurement errors, without assuming low error rates, enabling improved quantum error correction.

Contribution

It provides a rigorous proof that stabilizer codes can estimate Pauli channels with correlations, even with frequent high-weight errors and measurement errors, extending previous results beyond low-error regimes.

Findings

Stabilizer codes can estimate correlated Pauli channels.

The method works even with frequent high-weight errors.

Measurement errors can be incorporated into the estimation framework.

Abstract

The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome measurements done anyway during quantum error correction. While these measurements preserve the encoded quantum state, it is currently not clear how much information about the noise can be extracted in this way. So far, apart from the limit of vanishing error rates, rigorous results have only been established for some specific codes. In this work, we rigorously resolve the question for arbitrary stabilizer codes. The main result is that a stabilizer code can be used to estimate Pauli channels with correlations across a number of qubits given by the pure distance. This result does not rely on the limit of vanishing error rates, and applies even if high weight errors occur frequently. Moreover, it also allows for measurement errors within the framework of quantum data-syndrome codes. Our proof combines Boolean Fourier analysis, combinatorics and elementary algebraic geometry. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.