Non-Pauli errors can be efficiently sampled in qudit surface codes

• Published in: arXiv.org
• Main Authors: Ma, Yue, Hanks, Michael, Kim, M S
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.03.2023
• Subjects: Error correction; Fault tolerance; Percolation theory; Physics - Quantum Physics; Quantum computing
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2303.16837

Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modelled 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. Using belief propagation and percolation theory, we relate correlations to loops on the lattice. 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.