Error Counting in a Quantum Error-correcting Code and the Ground-State Energy of a Spin Glass
Hidetoshi Nishimori, Peter Sollich · Journal of the Physical Society of Japan · 2004
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.