Approximate level-by-level maximum-likelihood decoding based on the Chase algorithm for high-rate concatenated stabilizer codes

TL;DR

This paper introduces a new high-performance decoding algorithm for high-rate concatenated stabilizer codes in quantum error correction, leveraging the Chase algorithm to improve decoding accuracy and efficiency.

Contribution

It extends the level-by-level minimum-distance decoder by incorporating the Chase algorithm, enhancing decoding performance for high-rate concatenated stabilizer codes.

Findings

Outperforms conventional decoders for high-rate concatenated Hamming codes

Demonstrates improved decoding accuracy under bit-flip noise

Applicable to large-scale fault-tolerant quantum computation

Abstract

Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated codes have recently attracted attention due to theoretical advances in fault-tolerant protocols with constant-space-overhead and polylogarithmic-time-overhead, as well as practical developments of high-rate many-hypercube codes equipped with a high-performance level-by-level minimum-distance decoder (LMDD). We propose a general, high-performance decoder for high-rate concatenated stabilizer codes that extends LMDD by leveraging the Chase algorithm to generate a suitable set of candidate errors. Our simulation results demonstrate that the proposed decoder outperforms conventional decoders for high-rate concatenated Hamming codes under bit-flip noise.