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- W4386977881 abstract "Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best trade-offs between efficiency and speed, but one question that was left open is how they handle worst-case or adversarial errors, i.e. what is the order of magnitude of the smallest weight of an error pattern that will be wrongly decoded. We initiate such a study involving a simple hard-decision and deterministic version of a renormalisation decoder. We exhibit an uncorrectable error pattern whose weight scales like $d^{1/2}$ and prove that the decoder corrects all error patterns of weight less than $frac{5}{6} d^{log_{2}(6/5)}$, where $d$ is the minimum distance of the toric code." @default.
- W4386977881 created "2023-09-23" @default.
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- W4386977881 date "2023-09-21" @default.
- W4386977881 modified "2023-10-18" @default.
- W4386977881 title "Analysis of the Error-Correcting Radius of a Renormalisation Decoder for Kitaev's Toric Code" @default.
- W4386977881 doi "https://doi.org/10.48550/arxiv.2309.12165" @default.
- W4386977881 hasPublicationYear "2023" @default.
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