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

TL;DR

This paper reviews thermodynamic criteria for quantum memory stability, showing logical operators' expectation values vanish at all dimensions, and provides an upper bound on relaxation rates for stabilizer and subsystem codes interacting with thermal baths.

Contribution

It generalizes previous results to establish a universal upper bound on relaxation rates for quantum memories based on stabilizer and subsystem codes.

Findings

Logical operators' thermal expectation values vanish in all spatial dimensions.

Established a universal upper bound on quantum memory relaxation rates.

Applicable to memories interacting via Markovian dynamics with thermal baths.

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.