Clifford-deformed Surface Codes

TitleClifford-deformed Surface Codes
Publication TypeJournal Article
Year of Publication2022
AuthorsDua, A, Kubica, A, Jiang, L, Flammia, ST, Gullans, M
Date Published1/19/2022
KeywordsDisordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech)

Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of single-qubit Clifford operators. We first analyze CDSCs on the 3×3 square lattice and find that depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSCs with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations at finite bias outperform the thresholds and subthreshold logical error rates of the best known translationally invariant codes.