DECODABLE QUANTUM LDPC CODES BEYOND THE /n DISTANCE BARRIER USING HIGH-DIMENSIONAL EXPANDERS

Shai Evra, Tali Kaufman, Gilles Zemor

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Constructing quantum low-density parity-check (LDPC) codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional expanders, in particular Ramanujan complexes. These naturally give rise to very unbalanced quantum error correcting codes that have a large X-distance but a much smaller Z-distance. However, together with a classical expander LDPC code and a tensoring method that generalizes a construction of Hastings and also the Tillich-Zemor construction of quantum codes, we obtain quantum LDPC codes whose minimum distance exceeds the square root of the code length and whose dimension comes close to a square root of the code length. When the ingredient is a 2-dimensional Ramanujan complex, or the 2-skeleton of a 3-dimensional Ramanujan complex, we obtain a quantum LDPC code of minimum distance n1/2 log1/2 n. We then exploit the expansion properties of the complex to devise the first polynomial-time algorithm that decodes above the square root barrier for quantum LDPC codes. Using a 3-dimensional Ramanujan complex, we also obtain an overall quantum code of minimum distance n1/2 log n, which sets a new record for quantum LDPC codes.

Original languageEnglish
Pages (from-to)FOCS20-276 and FOCS20-316
JournalSIAM Journal on Computing
Volume53
Issue number6
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.

Keywords

  • chain complex
  • expander
  • quantum code

Fingerprint

Dive into the research topics of 'DECODABLE QUANTUM LDPC CODES BEYOND THE /n DISTANCE BARRIER USING HIGH-DIMENSIONAL EXPANDERS'. Together they form a unique fingerprint.

Cite this