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We discuss and review several thermodynamic criteria that have beenintroduced to characterize the thermal stability of a self-correcting quantummemory. We first examine the use of symmetry-breaking fields in analyzing theproperties of self-correcting quantum memories in the thermodynamic limit: weshow that the thermal expectation values of all logical operators vanish forany stabilizer and any subsystem code in any spatial dimension. On the positiveside, we generalize the results in [R. Alicki et al., arXiv:0811.0033] toobtain a general upper bound on the relaxation rate of a quantum memory atnonzero temperature, assuming that the quantum memory interacts via a Markovianmaster equation with a thermal bath. This upper bound is applicable to quantummemories based on either stabilizer or subsystem codes.

Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes