Ground-state splitting of a surface-code cylinder (source code)

= Ground-state splitting of a surface-code cylinder

On a cylinder with equal anyon-condensing boundaries, the two topological ground states split only through a virtual string implementing a logical operator. A perturbation of strength $h$ produces a splitting of order $J$ times a path-counting factor times $(|h|/J)^d$, where $d$ is the shortest supported logical-string length.