Error counting in a quantum error-correcting code and the ground-state energy of a spin glass

Details Error counting in a quantum error-correcting code and the ground-state energy of a spin glass Error counting in a quantum error-correcting code and the ground-state energy of a spin glass

2004-05-14

arxiv.org/abs/cond-mat/0405313v1

Journal of the Physical Society of Japan, 73:2701-2707, 2004

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 7 figures, JPSJ style, latex style file included

Scientific paper

10.1143/JPSJ.73.2701

Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the ground-state energy of the +/-J Ising spin glass model on the square lattice with symmetric and asymmetric bond distributions. This is a highly non-trivial example in which insights from quantum information lead directly to an explicit result on a physical quantity in the statistical mechanics of disordered systems.

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