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Title: Universality Classes of Stabilizer Code Hamiltonians

Abstract

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. 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.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Washington Univ., St. Louis, MO (United States). Dept. of Physics
  2. Indiana Univ., Bloomington IN (United States). Dept. of Physics
Publication Date:
Research Org.:
Indiana Univ., Bloomington IN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
OSTI Identifier:
1630819
Grant/Contract Number:  
SC0020343; NSF 1411229
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 123; Journal Issue: 23; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Weinstein, Zack, Ortiz, Gerardo, and Nussinov, Zohar. Universality Classes of Stabilizer Code Hamiltonians. United States: N. p., 2019. Web. https://doi.org/10.1103/PhysRevLett.123.230503.
Weinstein, Zack, Ortiz, Gerardo, & Nussinov, Zohar. Universality Classes of Stabilizer Code Hamiltonians. United States. https://doi.org/10.1103/PhysRevLett.123.230503
Weinstein, Zack, Ortiz, Gerardo, and Nussinov, Zohar. Tue . "Universality Classes of Stabilizer Code Hamiltonians". United States. https://doi.org/10.1103/PhysRevLett.123.230503. https://www.osti.gov/servlets/purl/1630819.
@article{osti_1630819,
title = {Universality Classes of Stabilizer Code Hamiltonians},
author = {Weinstein, Zack and Ortiz, Gerardo and Nussinov, Zohar},
abstractNote = {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. 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.},
doi = {10.1103/PhysRevLett.123.230503},
journal = {Physical Review Letters},
number = 23,
volume = 123,
place = {United States},
year = {2019},
month = {12}
}

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