Coherence in quantum error-correcting codes

TL;DR

This paper demonstrates that stabilizer codes decohere coherent errors into probabilistic Pauli errors, enabling better quantification and optimization of logical error rates in quantum error correction.

Contribution

It proves that stabilizer code encoding and syndrome measurement decohere errors, bridging the gap between realistic coherent errors and the probabilistic models used in analysis.

Findings

Errors decohere into Pauli errors after syndrome measurement

Logical error rate is accurately quantified by average gate fidelity

Optimal recovery operators can be found by maximizing logical fidelity

Abstract

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome.