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Quantum Error Correction Fault Tolerance

High-dimensional Expansion of Product Codes is Stronger than Robust and Agreement Testability

arXiv
Authors: Gleb Kalachev

Year

2023

Paper ID

56056

Status

Preprint

Abstract Read

~2 min

Abstract Words

88

Citations

N/A

Abstract

We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes. It was shown before that this property is equivalent to robust testability and agreement testability for products of two codes with linear distance. First, we show that robust testability for product of many codes with linear distance is equivalent to agreement testability. Second, we provide an example of product of three codes with linear distance which is robustly testable but not product expanding.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2023 reference point for readers tracking recent quantum research.
  • We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2308.02889 [2] arXiv https://arxiv.org/abs/2308.02889 [3] Publisher https://arxiv.org/abs/2308.02889

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