A Symbol-Pair Decoder for CSS Codes

TL;DR

This paper introduces a symbol-pair decoder for CSS quantum codes, leveraging classical codes over the symbol-pair metric to enhance quantum error correction capabilities.

Contribution

It establishes a relation between symplectic and symbol-pair weights, enabling the lifting of classical symbol-pair decoders to quantum CSS codes.

Findings

Improved error correction for CSS codes using symbol-pair metrics.

Established a relation between symplectic and symbol-pair weights.

Enhanced decoding methods for cyclic code-based CSS codes.

Abstract

The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work allows us to lift decoders for classical codes over the Hamming metric to decoders for stabilizer quantum codes. A natural question to consider: Can we do something similar with decoders for classical codes considered over other metrics? i.e., Can we lift decoders for classical codes over other metrics to obtain decoders for stabilizer quantum codes? In our current work, we answer this question in the affirmative by considering classical codes over the symbol-pair metric. In particular, we present a relation between the symplectic weight and the symbol-pair weight and use it to improve the error correction capability of CSS-codes (a well-studied class of stabilizer codes) obtained from cyclic codes.