Generalizing the matching decoder for the Chamon code

TL;DR

This paper develops a generalized matching decoder with belief propagation for the Chamon quantum error-correcting code, achieving a 10.5% threshold for depolarizing noise, enhancing decoding performance for complex codes.

Contribution

It introduces a novel generalized matching decoder augmented with belief propagation tailored for the Chamon code's complex structure.

Findings

Achieved a 10.5% threshold for depolarizing noise.

Demonstrated improved decoding performance for non-trivial quantum codes.

Enhanced the practicality of decoding algorithms for complex LDPC codes.

Abstract

Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct errors that have occurred with high likelihood. Matching decoders are very good at correcting local errors while also demonstrating fast run times that can keep pace with physical quantum devices. We implement variations of a matching decoder for a three-dimensional, non-CSS, low-density parity check code known as the Chamon code, which has a non-trivial structure that does not lend itself readily to this type of decoding. The non-trivial structure of the syndrome of this code means that we can supplement the decoder with additional steps to improve the threshold error rate, below which the logical failure rate decreases with increasing code distance. We find that a generalized matching decoder that is augmented by a belief-propagation step prior to matching gives a threshold of 10.5% for depolarizing noise.