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Quantum Error Correction Fault Tolerance Open Quantum Systems Decoherence

Khovanov homology and quantum error-correcting codes

arXiv
Authors: Rostislav Akhmechet, Milena Harned, Pranav Venkata Konda, Felix Shanglin Liu, Nikhil Mudumbi, Eric Yuang Shao, Zheheng Xiao

Year

2024

Paper ID

38104

Status

Preprint

Abstract Read

~2 min

Abstract Words

82

Citations

N/A

Abstract

Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with desirable properties. We explore Khovanov homology and some of its many extensions, namely reduced, annular, and mathfrak{sl}3 homology, to generate new families of quantum codes and to establish several properties about codes that arise in this way, such as behavior of distance under Reidemeister moves or connected sums.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.11252 [2] arXiv https://arxiv.org/abs/2410.11252 [3] Publisher https://arxiv.org/abs/2410.11252

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