  A two-dimensional topologically ordered quantum memory is well protected
against error if the energy gap is large compared to the temperature, but this
protection does not improve as the system size increases. We review and
critique some recent proposals for improving the memory time by introducing
long-range interactions among anyons, noting that instability with respect to
small local perturbations of the Hamiltonian is a generic problem for such
proposals. We also discuss some broader issues regarding the prospects for
scalable quantum memory in two-dimensional systems.
