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Free-Fermion Subsystem Codes

Chapman, Adrian and Flammia, Steven T. and Kollár, Alicia J. (2022) Free-Fermion Subsystem Codes. PRX Quantum, 3 (3). Art. No. 030321. ISSN 2691-3399. doi:10.1103/prxquantum.3.030321.

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We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of the code and whose exact spectrum and eigenstates can be found via a generalized Jordan-Wigner transformation. Such solutions are characterized by the frustration graph of the Hamiltonian: the graph whose vertices are Hamiltonian terms, which are neighboring if the terms anticommute. We provide methods for embedding a given frustration graph in the anticommutation relations of a spin model and present the first known example of an exactly solvable spin model with a two-dimensional free-fermion description and exact topological qubits. This model can be viewed as a free-fermionized version of the two-dimensional Bacon-Shor code. Using graph-theoretic tools to study the unit cell, we give an efficient algorithm for deciding if a given translation-invariant spin model is solvable, and explicitly construct the solution. Further, we examine the energetics of these exactly solvable models from the graph-theoretic perspective and show that the relevant gaps of the spin model correspond to known graph-theoretic quantities: the skew energy and the median eigenvalue of an oriented graph. Finally, we numerically search for models that have large spectral gaps above the ground-state spin configuration and thus exhibit particularly robust thermal suppression of errors. These results suggest that optimal models will have low dimensionality and odd coordination numbers, and that the primary limit to energetic error suppression is the skew energy difference between different symmetry sectors rather than single-particle excitations of the free fermions.

Item Type:Article
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URLURL TypeDescription Paper
Chapman, Adrian0000-0003-2303-7589
Flammia, Steven T.0000-0002-3975-0226
Additional Information:Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 2 February 2022; revised 21 June 2022; accepted 29 June 2022; published 10 August 2022) A.C. acknowledges support from EPSRC under Agreement EP/T001062/1, and from EU H2020-FETFLAG-03-2018 under Grant Agreement No. 820495 (AQTION). This work is supported in part by the Australian Research Council (ARC) via the Centre of Excellence in Engineered Quantum Systems (EQuS) project number CE170100009. A.J.K. acknowledges support from AFOSR Grant No. FA95502110129 and NSF Grant No. PHY2047732.
Group:AWS Center for Quantum Computing, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/T001062/1
European Research Council (ERC)820495
Australian Research CouncilCE170100009
Air Force Office of Scientific Research (AFOSR)FA9550-21-1-0129
Issue or Number:3
Record Number:CaltechAUTHORS:20220811-457365000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116236
Deposited By: George Porter
Deposited On:12 Aug 2022 02:07
Last Modified:12 Aug 2022 02:07

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