Error counting in a quantum error-correcting code and the ground-state energy of a spin glass
Disordered Systems and Neural Networks
2007-05-23 v1 Statistical Mechanics
Quantum Physics
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.
Cite
@article{arxiv.cond-mat/0405313,
title = {Error counting in a quantum error-correcting code and the ground-state energy of a spin glass},
author = {Hidetoshi Nishimori and Peter Sollich},
journal= {arXiv preprint arXiv:cond-mat/0405313},
year = {2007}
}
Comments
15 pages, 7 figures, JPSJ style, latex style file included