Self-dual random-plaquette gauge model and the quantum toric code

Details Self-dual random-plaquette gauge model and the quantum toric code Self-dual random-plaquette gauge model and the quantum toric code

2003-10-30

arxiv.org/abs/hep-th/0310279v2

Nucl. Phys. B686 (2004) 377-396

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 13 figures

Scientific paper

10.1016/j.nuclphysb.2004.03.006

We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, p_c=0.889972..., and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

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