SymmetryProtected InfiniteTemperature Quantum Memory from Subsystem Codes
Abstract
We study a mechanism whereby quantum information present in the initial state of a quantum manybody system can be protected for arbitrary times due to a combination of symmetry and spatial locality. Remarkably, the mechanism is sufficiently generic that the dynamics can be fully ergodic upon resolving the protecting symmetry and fixing the encoded quantum state, resulting in an infinitetemperature quantum memory. After exemplifying the mechanism in a strongly nonintegrable twodimensional (2D) spin model inspired by the surface code, we find it has a natural interpretation in the language of noiseless subsystems and stabilizer subsystem codes. This interpretation yields a number of further examples, including a nonintegrable Hamiltonian with quantum memory based on the BaconShor code. The lifetime of the encoded quantum information in these models is infinite provided the dynamics respect the stabilizer symmetry of the underlying subsystem code. In the presence of symmetryviolating perturbations, we make contact with previous work leveraging the concept of prethermalization to show that the encoded quantum information retains a parametrically long lifetime under dynamics with an enlarged continuous symmetry group. We identify conditions on the underlying subsystem code that enable such a prethermal enhancement of the memory lifetime.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05710
 Bibcode:
 2021arXiv211005710W
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 20 pages, 9 figures