1209.5289 (Fabio L. Pedrocchi et al.)

Local 3D spin Hamiltonian as a thermally stable surface code    [PDF]

Fabio L. Pedrocchi, Adrian Hutter, James R. Wootton, Daniel Loss

We study a 2D toric code embedded in a 3D Heisenberg ferromagnet in a broken-symmetry state at finite temperature. Stabilizer operators of the toric code are locally coupled to individual spins of the ferromagnet. The effects of the Goldstone modes of the ferromagnet in the ordered phase lead to an energy penalty for anyons that grows linearly with $L$, the linear size of the toric code. This $O(L)$ energy barrier for logical errors leads to a lifetime of the quantum memory that grows exponentially with $L$, assuming that the toric code is weakly coupled to a thermal bath with temperature below the phase transition of the ferromagnet. This provides a stable quantum memory with strictly local bounded-strength interactions in less than four dimensions.

View original: http://arxiv.org/abs/1209.5289