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.

• Received 29 March 2023
• Revised 19 July 2023
• Accepted 20 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.200602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society