Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes
| Autor: | Venn, F., Béri, B. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Phys. Rev. Research 2, 043412 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.2.043412 |
| Popis: | 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. Comment: 16 pages, 12 figures |
| Databáze: | arXiv |
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