Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
Abstract
We discuss and review several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields in analyzing the properties of self-correcting quantum memories in the thermodynamic limit: we show that the thermal expectation values of all logical operators vanish for any stabilizer and any subsystem code in any spatial dimension. On the positive side, we generalize the results in [R. Alicki et al., arXiv:0811.0033] to obtain a general upper bound on the relaxation rate of a quantum memory at nonzero temperature, assuming that the quantum memory interacts via a Markovian master equation with a thermal bath. This upper bound is applicable to quantum memories based on either stabilizer or subsystem codes.
Cite
@article{arxiv.0907.2807,
title = {Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes},
author = {Stefano Chesi and Daniel Loss and Sergey Bravyi and Barbara M. Terhal},
journal= {arXiv preprint arXiv:0907.2807},
year = {2015}
}
Comments
23 pages. v2: revised introduction, various additional comments, and a new section on gapped hamiltonians