Simple, Efficient, and Generic Post-Selection Decoding for qLDPC codes

TL;DR

This paper introduces argument reweighting, a simple post-selection decoding method that significantly reduces logical errors in quantum LDPC codes, improving fault tolerance with minimal rejection rates.

Contribution

It presents a novel, broadly applicable post-selection decoding strategy that enhances existing decoders for quantum LDPC codes, demonstrating substantial error suppression.

Findings

Reduces logical error rates by nearly two orders of magnitude

Requires only a rejection rate of 1.44×10⁻⁵ for significant error suppression

Applicable across multiple decoders and qLDPC codes

Abstract

Quantum error correction is indispensable for scalable quantum computation. Although encoding logical qubits substantially enhances noise resilience, achieving logical error rates low enough for practical algorithms remains challenging on existing hardware. Here we introduce argument reweighting, a simple and broadly applicable post-selection decoding strategy that boosts the performance of maximum-likelihood-type decoders, including minimum-weight perfect matching and belief-propagation families. The method suppresses logical errors by performing additional decoding rounds under reweighted error models, enabling acceptance of high-confidence syndrome outcomes. Circuit-level simulations across multiple decoders and qLDPC codes show that argument reweighting substantially suppresses logical errors, requiring a rejection rate of only $1.44\times10^{-5}$ to reduce the logical error rate by almost two orders of magnitude for the $[[144,12,12]]$ bivariate bicycle code. These results establish argument reweighting as a practical and resource-efficient approach for enhancing quantum fault tolerance.