model) can serve as a self-correcting quantum memory due to the errors induced by a thermal environment.

In other words, increasing the size of such a system does not prolong the protection of its ground-state space from decoherence. These negative results point toward the fundamental question whether topologically ordered quantum states, and hence self-correcting quantum memories, can exist at all on a macroscopic scale. In the following, we will demonstrate that self-correcting properties of two-dimensional (2D) stabilizer Hamiltonians can indeed be established when we allow for long-range repulsive interactions between the elementary excitations (anyons). While the purpose of the present work is of principal nature, we note that such interacting models can be expected to be realized in physical systems. We discuss this issue in greater detail at the end, where we also show how tunable repulsive long-range interactions could be mediated via photons in an optical cavity.

The outline of the paper is as follows: In Sec. \[sec:model\] we introduce a toric code model with repulsive long-range interactions between anyons. In Sec. \[app:simulation\] we describe how to simulate the dynamics of the model in contact with Ohmic or super-Ohmic thermal baths. A discussion of the decoherence caused by anyon 