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SUMMARY:Coherent error threshold for surface codes from Majorana delocaliz
 ation - Dr Jan Behrends\, University of Cambridge (TCM)
DTSTART:20230130T140000Z
DTEND:20230130T143000Z
UID:TALK196312@talks.cam.ac.uk
CONTACT:Dr M. Simoncelli
DESCRIPTION:Statistical mechanics mappings provide key insights on quantum
  error correction. However\, existing mappings assume incoherent noise\, t
 hus ignoring coherent errors due to\, e.g.\, spurious gate rotations. We m
 ap the surface code with coherent errors\, taken as X- or Z-rotations (rep
 lacing bit or phase flips)\, to a two-dimensional (2D) Ising model with co
 mplex couplings\, and further to a 2D Majorana scattering network. Our map
 pings 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-n
 ontrivial 2D insulator. However\, beyond a rotation angle ϕc\, instead of
  a Z2-trivial insulator as for incoherent errors\, coherent errors map to 
 a Majorana metal. This ϕc is the theoretically achievable storage thresho
 ld. We numerically find ϕc≈0.14π. The corresponding bit-flip rate sin^
 2(ϕc)≈0.18 exceeds the known incoherent threshold pth≈0.11.
LOCATION:Mott Seminar Room 531\, Cavendish Laboratory
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