Non-Pauli errors can be efficiently sampled in qudit surface codes
arXiv:2303.16837 · doi:10.1103/PhysRevLett.131.200602
Abstract
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.
Main text 6 pages, 4 figures, Supplemental Material 6 pages, 7 figures
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- Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
- Reshaping quantum device noise via repetition code circuits