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

TL;DR

This paper establishes bounds on error patterns in the toric code and uses these to derive a lower bound on the ground-state energy of a spin glass model, linking quantum information theory with statistical mechanics.

Contribution

It provides the first explicit bounds connecting quantum error correction properties with physical quantities in disordered systems.

Findings

Bounds on error pattern classes in the toric code

Lower bound on the ground-state energy of the +/-J Ising spin glass

Insight into quantum information's impact on statistical mechanics

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.