Berlin 2024 – scientific programme
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QI: Fachverband Quanteninformation
QI 7: Quantum Error Correction
QI 7.4: Talk
Monday, March 18, 2024, 15:45–16:00, HFT-TA 441
Coherent error threshold for surface codes from Majorana delocalization — Florian Venn1, •Jan Behrends2, and Benjamin Béri1,2 — 1DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK — 2T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge, CB3 0HE, UK
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 Z2-nontrivial 2D insulator. However, beyond a rotation angle φth, instead of a Z2-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This φth is the theoretically achievable storage threshold. We numerically find φth ≈ 0.14π. The corresponding bit-flip rate sin2(φth) ≈ 0.18 exceeds the known incoherent threshold pth ≈ 0.11.
Keywords: surface code; toric code; coherent errors; ising model; network models