• Open Access

Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry

Hao Song (宋昊), Janik Schönmeier-Kromer, Ke Liu (刘科 子竞), Oscar Viyuela, Lode Pollet, and M. A. Martin-Delgado
Phys. Rev. Lett. 129, 230502 – Published 30 November 2022
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Abstract

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multibody couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms.

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  • Received 17 December 2021
  • Accepted 11 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.230502

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Hao Song (宋昊)1,2,3, Janik Schönmeier-Kromer4,5, Ke Liu (刘科 子竞)4,5,*, Oscar Viyuela6,7, Lode Pollet4,5,8, and M. A. Martin-Delgado3,†

  • 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
  • 3Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
  • 4Arnold Sommerfeld Center for Theoretical Physics, University of Munich, Theresienstr. 37, 80333 München, Germany
  • 5Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany
  • 6Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 7Department of Physics, Harvard University, Cambridge, Massachusetts 02318, USA
  • 8Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

  • *ke.liu@lmu.de
  • mardel@fis.ucm.es

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Issue

Vol. 129, Iss. 23 — 2 December 2022

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