Syndrome resampling enhances quantum error correction thresholds

TL;DR

Syndrome resampling is a novel, decoder-agnostic method that significantly enhances quantum error correction thresholds and reduces logical errors without extra hardware, applicable to current quantum devices.

Contribution

The paper introduces syndrome resampling, a new technique that improves QEC thresholds and logical fidelities by biasing syndrome averages, applicable across various decoders and codes.

Findings

Substantially increases QEC thresholds for surface codes.

Reduces logical error rates by up to four orders of magnitude.

Effective with finite data and existing experimental QEC data.

Abstract

Quantum error correction (QEC) enables fault-tolerant quantum computation but requires operating quantum hardware at physical error rates below code-dependent thresholds, which remains challenging for current devices. We introduce syndrome resampling, a general method that increases QEC thresholds of any decoder and suppresses logical errors without additional hardware, decoding modifications, or code-specific assumptions beyond syndrome statistics. The method exploits the fact that syndromes with low probability are likely to lead to logical failure, therefore biasing syndrome averages towards most likely syndromes effectively increases logical fidelities. We establish a direct connection between the R\'enyi coherent information (RCI) and powers of the syndrome probability distribution, showing that resampling syndromes according to these powers combined with maximum likelihood decoding (MLD) realizes a family of optimal thresholds associated with phase transitions in the RCI. Numerical simulations of surface codes demonstrate that syndrome resampling substantially increases thresholds for both optimal and suboptimal decoders and reduces logical error rates by up to four orders of magnitude in experimentally relevant regimes. We further show that syndrome resampling can be effectively implemented from finite data and combined with decoding-based post-selection to achieve additional gains. Finally, applying the method to existing experimental QEC data yields up to two orders of magnitude reduction in logical error rates without requiring additional measurements. Our results provide a practical and decoder-agnostic route to improved logical fidelities in near-term QEC experiments.