One-Shot any Code

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 $p_{\rm RG}>0$ for joint local stochastic physical and measurement noise, the logical failure probability over $T$ correction rounds is bounded by \begin{equation*} O(T n)\exp[-\Omega(m^\alpha)] \end{equation*} for a constant $\alpha>0$; we say that the \textit{threshold} is $p_{\rm RG}$ and \textit{error suppression} is $\Omega(m^{\alpha})$. Moreover, if the input code is equipped with a single-shot decoder with threshold $p_c>0$ and error suppression $\Omega(n^{\beta})$, then the output code \textit{enhances} the error suppression to $\Omega(m^{\alpha} n^{\beta})$, while maintaining the decoder-independent threshold $p_{\rm RG}$, and thus \textit{enhanced} if $p_c < p_{\rm RG}$.

arXiv:2610.02137 [quant-ph]

(or arXiv:2610.02137v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.02137 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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