Quantum data must be stored within a physical system. One readily accessible physical system is the Heisenberg ferromagnet, which has as its ground space the set of all symmetric states. By storing quantum data within a symmetric code, one can benefit from (1) the fact that such codes are left unchanged by the underlying dynamics of the Heisenberg ferromagnet, and (2) the quantum error correction properties of these symmetric codes.
I calculate bounds on the error of such quantum storage under physically realistic conditions. This calculation does not rely on any specific properties of symmetric codes apart from the number of errors they can correct. Hence, all symmetric codes with QEC properties can be used. Also I use the fact that the spectral gap of the Heisenberg ferromagnet can grow with the system size.
2019 Quantum storage in quantum ferromagnets [Memory /QEC /PI code]
Y. Ouyang http://arxiv.org/abs/1904.01458
2019 Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations [Memory]