University of Tasmania
Browse
133050 - Modified belief propagation decoders for quantum.pdf (1.6 MB)

Modified belief propagation decoders for quantum low-density parity-check codes

Download (1.6 MB)
journal contribution
posted on 2023-05-20, 04:05 authored by Rigby, A, Jan OlivierJan Olivier, Peter JarvisPeter Jarvis
Quantum low-density parity-check codes can be decoded using a syndrome based GF(4) belief propagation decoder. However, the performance of this decoder is limited both by unavoidable 4-cycles in the code’s factor graph and the degenerate nature of quantum errors. For the subclass of CSS codes, the number of 4-cycles can be reduced by breaking an error into an X and Z component and decoding each with an individual GF(2) based decoder. However, this comes at the expense of ignoring potential correlations between these two error components. We present a number of modified belief propagation decoders that address these issues. We propose a GF(2) based decoder for CSS codes that reintroduces error correlations by reattempting decoding with adjusted error probabilities. We also propose the use of an augmented decoder, which has previously been suggested for classical binary low-density parity-check codes. This decoder iteratively reattempts decoding on factor graphs that have a subset of their check nodes duplicated. The augmented decoder can be based on a GF(4) decoder for any code, a GF(2) decoder for CSS code, or even a supernode decoder for a dual-containing CSS code. For CSS codes, we further propose a GF(2) based decoder that combines the augmented decoder with error probability adjustment. We demonstrate the performance of these new decoders on a range of different codes, showing that they perform favorably compared to other decoders presented in literature.

History

Publication title

Physical Review A

Volume

100

Article number

12330

Number

12330

Pagination

1-21

ISSN

2469-9926

Department/School

School of Engineering

Publisher

American Physical Society

Place of publication

USA

Rights statement

© 2019 American Physical Society. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in philosophy and religious studies

Usage metrics

    University Of Tasmania

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC