2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23962Upper 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.15 pages, 7 figures, JPSJ style, latex style file includedDisordered Systems and Neural NetworksStatistical MechanicsQuantum Physicstext