Free-Fermion Subsystem Codes
نویسندگان
چکیده
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 Hamiltonian terms the of code and exact spectrum eigenstates can be found via generalized Jordan-Wigner transformation. Such solutions characterized frustration graph Hamiltonian: vertices terms, which neighboring if anticommute. provide methods for embedding given in anticommutation relations model present first known example an exactly solvable with two-dimensional free-fermion description topological qubits. This viewed as free-fermionized version Bacon-Shor code. Using graph-theoretic tools to study unit cell, we give efficient algorithm deciding translation-invariant is solvable, explicitly construct solution. Further, examine energetics these models from perspective show that relevant gaps correspond quantities: skew energy median eigenvalue oriented graph. Finally, numerically search have large spectral above ground-state configuration thus exhibit particularly robust thermal suppression errors. These results suggest optimal will low dimensionality odd coordination numbers, primary limit energetic error difference between different symmetry sectors rather than single-particle excitations free fermions.2 MoreReceived 2 February 2022Revised 21 June 2022Accepted 29 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030321Published American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasMajorana fermionsQuantum correctionTechniquesExact many-body systemsGraph theoryQuantum Information
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ژورنال
عنوان ژورنال: PRX quantum
سال: 2022
ISSN: ['2691-3399']
DOI: https://doi.org/10.1103/prxquantum.3.030321