Learning logical Pauli noise in quantum error correction

TL;DR

This paper introduces a method to efficiently characterize the logical error channel in quantum computers using syndrome data, specifically for stabilizer codes under Pauli noise, reducing experimental and computational effort.

Contribution

It proves that the logical error channel can be estimated from syndrome data for any stabilizer, subsystem, or data syndrome code, given the code can correct the noise.

Findings

Logical error channel estimation from syndrome data is possible for stabilizer codes.

The method applies to arbitrary stabilizer, subsystem, and data syndrome codes.

Estimation requires minimal conditions, only that the code can correct the noise.

Abstract

The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for specific applications and develop protocols that require little additional effort. In this work, we focus on the characterization of quantum computers in the context of stabilizer quantum error correction. For arbitrary stabilizer codes, subsystem codes, and data syndrome codes, we prove that the logical error channel induced by Pauli noise can be estimated from syndrome data under minimal conditions. More precisely, for any such code, we show that the estimation is possible as long as the code can correct the noise.