Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes

• URL: http://arxiv.org/abs/2006.13055v1
• Date: Tue, 23 Jun 2020 14:29:25 GMT
• Title: Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
• Authors: F. Venn and B. B\'eri
• Abstract summary: We numerically study coherent errors in surface codes on planar graphs. In particular, we show that a graph class exists where logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between resilience against coherent $X$- and $Z$-rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into three distinct classes, each resulting in qualitatively distinct final-state distributions. In particular, we show that a graph class exists where the logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold. In these classes, therefore, the logical level noise above the error-correction threshold can retain significant amount of coherence even for large-distance codes. To perform our analysis, we develop a Majorana-fermion representation of planar-graph surface codes and describe the characterization of logical-state storage using fermion-linear-optics-based simulations. We thereby generalize the approach introduced for the square lattice by Bravyi \textit{et al}. [npj Quantum Inf. 4, 55 (2018)] to surface codes on general planar graphs.

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