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- W4385644803 abstract "Statistical mechanics mappings provide key insights on quantum error correction. However, existing mappings assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with coherent errors, taken as X or Z rotations (replacing bit or phase flips), to a two-dimensional (2D) Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal both commonalities and qualitative differences in correcting coherent and incoherent errors. For both, the error-correcting phase maps, as we explicitly show by linking 2D networks to 1D fermions, to a Z_{2}-nontrivial 2D insulator. However, beyond a rotation angle ϕ_{th}, instead of a Z_{2}-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This ϕ_{th} is the theoretically achievable storage threshold. We numerically find ϕ_{th}≈0.14π. The corresponding bit-flip rate sin^{2}(ϕ_{th})≈0.18 exceeds the known incoherent threshold p_{th}≈0.11." @default.
- W4385644803 created "2023-08-08" @default.
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- W4385644803 date "2023-08-08" @default.
- W4385644803 modified "2023-10-14" @default.
- W4385644803 title "Coherent-Error Threshold for Surface Codes from Majorana Delocalization" @default.
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- W4385644803 doi "https://doi.org/10.1103/physrevlett.131.060603" @default.
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