Low-temperature coherence properties of Z2 quantum memory

We investigate low-temperature coherence properties of the Z2 quantum memory which is capable of storing the information of a single logical qubit. We show that the memory has superposition of macroscopically distinct states for some values of a control parameter and at sufficiently low temperature and that the code states of this memory have no instability except for the inevitable one. However, we also see that the coherence power of this memory is limited by space and time. We also briefly discuss the resonating valence bond memory, which is an improvement of the Z2 quantum memory, and the relations of our results to the obscured symmetry breaking in statistical physics.