Nonequilibrium Reliability of Quantum Memories

The ability to store quantum information without recourse to constant feedback processes would yield a significant advantage for future implementations of quantum information processing. In this Letter, limitations of the prototypical model, the Toric code in two dimensions, are elucidated along with a sufficient condition for overcoming these limitations. Specifically, the interplay between Hamiltonian perturbations and dynamically occurring noise is considered as a system in its ground state is brought into contact with a thermal reservoir. This proves that when utilizing the Toric code on $N^2$ qubits in a 2D lattice as a quantum memory, the information cannot be stored for a time $O(N)$. In contrast, the 2D Ising model protects classical information against the described noise model for exponentially long times. The results also have implications for the robustness of braiding operations in topological quantum computation.