Non–Pauli Errors Can Be Efficiently Sampled in Qudit Surface Codes

Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modeled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we quantify remaining correlations after syndrome measurement for a qud...

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Bibliographic Details
Published in:Physical review letters 2023-11, Vol.131 (20), p.200602-200602, Article 200602
Main Authors: Ma, Yue, Hanks, Michael, Kim, M. S.
Format: Article
Language:English
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Summary:Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modeled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we quantify remaining correlations after syndrome measurement for a qudit 2D surface code subject to non-Pauli errors via loops on the lattice, using percolation theory. Below the error correction threshold, remaining correlations are sparse and locally constrained. Syndromes for qudit surface codes are therefore efficiently samplable for non-Pauli errors, independent of the exact forms of the error and decoder.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.131.200602