Adrian Hutter, James R. Wootton, Daniel Loss
We study the two-dimensional toric code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields. It has been shown that such interactions allow to increase the lifetime of the stored quantum information arbitrarily by making L, the linear size of the memory, larger [Phys. Rev. A 82 022305 (2010)]. We show that for these systems the choice of boundary conditions (open boundaries as opposed to periodic boundary conditions) is not a mere technicality; the influence of anyons produced at the boundaries becomes in fact dominant for large enough L. This influence can be both beneficial or detrimental. In particular, we study an effective Hamiltonian proposed in [Phys. Rev. B 83 115415 (2011)] that describes repulsion between anyons and anyon holes. For this system, we find a lifetime of the stored quantum information that grows exponentially in L^2, even for an architecture with open boundaries. However, L is upper-bounded through the breakdown of the perturbative threatment of the underlying Hamiltonian.
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http://arxiv.org/abs/1206.0991
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