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PreprintarXiv licencearXiv

One-Shot any Code

  • Andrew C. Yuan
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Abstract

We first provide a simple proof showing that any single-shot code is self-correcting. We then show that any [[n,k]] CSS quantum low-density parity-check (QLDPC) code can be transformed into an [[nm,k]] CSS QLDPC code with single-shot (SS) quantum error correction and an efficient local decoder which runs in O(log m) parallel time. Below a constant threshold pRG>0 for joint local stochastic physical and measurement noise, the logical failure probability over T correction rounds is bounded by O(T n)exp[−Ω(mα)] for a constant α>0; we say that the \textit{threshold} is pRG and \textit{error suppression} is Ω(mα). Moreover, if the input code is equipped with a single-shot decoder with threshold pc>0 and error suppression Ω(nβ), then the output code \textit{enhances} the error suppression to Ω(mα nβ), while maintaining the decoder-independent threshold pRG, and thus \textit{enhanced} if pc < pRG.

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Cite

BibTeXRIS
BibTeX
@misc{yuan2026oneshot,
  title = {{One-Shot any Code}},
  author = {Andrew C. Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02137},
  eprint = {2610.02137},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02137},
}
RIS
TY  - UNPB
TI  - One-Shot any Code
AU  - Andrew C. Yuan
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02137
UR  - https://arxiv.org/abs/2610.02137
AB  - We first provide a simple proof showing that any single-shot code is self-correcting. We then show that any [[n,k]] CSS quantum low-density parity-check (QLDPC) code can be transformed into an [[nm,k]] CSS QLDPC code with single-shot (SS) quantum error correction and an efficient local decoder which runs in O(log m) parallel time. Below a constant threshold p_RG>0 for joint local stochastic physical and measurement noise, the logical failure probability over T correction rounds is bounded by O(T n)exp[−Ω(m^α)] for a constant α>0; we say that the \textit{threshold} is p_RG and \textit{error suppression} is Ω(m^α). Moreover, if the input code is equipped with a single-shot decoder with threshold p_c>0 and error suppression Ω(n^β), then the output code \textit{enhances} the error suppression to Ω(m^α n^β), while maintaining the decoder-independent threshold p_RG, and thus \textit{enhanced} if p_c < p_RG.
ER  -