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Quantum Error Correction Fault Tolerance

Finite-Degree Quantum LDPC Codes Reaching the Gilbert-Varshamov Bound

arXiv
Authors: Kenta Kasai

Year

2026

Paper ID

35701

Status

Preprint

Abstract Read

~2 min

Abstract Words

43

Citations

N/A

Abstract

We construct nested Calderbank-Shor-Steane code pairs with non-vanishing coding rate from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove relative linear distance with high probability. Moreover, for several finite degree settings, we prove Gilbert-Varshamov distance by a rigorous computer-assisted proof.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.24588 [2] arXiv https://arxiv.org/abs/2603.24588 [3] Publisher https://arxiv.org/abs/2603.24588

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