Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T73: Quantum Error Correction Foundations and Theory II
11:30 AM–2:18 PM,
Thursday, March 9, 2023
Room: Room 405
Sponsoring
Unit:
DQI
Chair: Arne Grimsmo, University of Sydney
Abstract: T73.00014 : Surface code error correction in a modular quantum computer*
2:06 PM–2:18 PM
Presenter:
Denis Sedov
(ITMO University)
Authors:
Denis Sedov
(ITMO University)
Renyu Wang
(University of California, Riverside)
Leonid P Pryadko
(University of California, Riverside)
modules connected along the edges, assuming that error probability for
two-qubit gates across the boundary be larger than that for
intra-modular gates. First, we prove a general structure theorem for
modular stabilizer codes: the total number of logical qubits supported
by individual modules after separation cannot exceed the dimension $k$
of the original code. Second, we use a statistical-mechanical map to
get semi-analytical estimates for the maximum-likelihood
error-correction threshold as a function of the module size $L$.
Namely, with ideal measurements, one gets a planar modulated
random-bond Ising model (MRBIM), and otherwise, assuming
phenomenological error model and repeated measurements, a
cubic-lattice MRBIM. We construct the corresponding phase diagrams
approximately using the mean-field effective couplings between block
spins, and exactly in 2D using the loop-counting technique. Finally,
we also locate the threshold using circuit simulations and
minimum-weight perfect matching decoder.
*L.P.P. was financially supported by the NSF Division of Physics via grant 2112848.
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