  Here we investigate the effect lattice geometry has on the lifetime of
two-dimensional topological quantum memories. Initially, we introduce various
lattice patterns and show how the error-tolerance against bit-flips and
phase-flips depends on the structure of the underlying lattice. Subsequently,
we investigate the dependence of the lifetime of the quantum memory on the
structure of the underlying lattice when it is subject to a finite temperature.
Importantly, we provide a simple effective formula for the lifetime of the
memory in terms of the average degree of the lattice. Finally, we propose
optimal geometries for the Josephson junction implementation of topological
quantum memories.
