Universality Classes of Stabilizer Code Hamiltonians

Weinstein, Zack; Ortiz, Gerardo; Nussinov, Zohar

doi:10.1103/PhysRevLett.123.230503

Title: Universality Classes of Stabilizer Code Hamiltonians

Journal Article · 02 December 2019 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.123.230503 · OSTI ID:1630819

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Washington Univ., St. Louis, MO (United States). Dept. of Physics; Indiana University
Indiana Univ., Bloomington IN (United States). Dept. of Physics
Washington Univ., St. Louis, MO (United States). Dept. of Physics

Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model’s universality class and effective dimension, insights may be gained on their finite temperature dynamics and robustness. In this work, our technique is demonstrated in particular on the 4D toric code and Haah’s code; we find that the former falls into the 4D Ising universality class, whereas Haah’s code exhibits dimensional reduction and falls into the 1D Ising universality class.

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Research Organization:: Indiana Univ., Bloomington IN (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0020343

OSTI ID:: 1630819

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 23 Vol. 123; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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