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

Hidetoshi Nishimori·Peter Sollich
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Abstract

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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Hidetoshi Nishimori, Peter Sollich. 2004-05-14. Error counting in a quantum error-correcting code and the ground-state energy of a spin glass. https://doi.org/10.1143/jpsj.73.2701

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