Can long-range interactions stabilize quantum memory at nonzero temperature?

TL;DR

This paper reviews the potential of long-range interactions to stabilize 2D topological quantum memories at finite temperature, highlighting challenges and limitations of such approaches.

Contribution

It critically analyzes recent proposals involving long-range interactions for quantum memory stabilization and discusses broader scalability issues.

Findings

Long-range interactions do not necessarily improve stability against local perturbations.

Instability under small local perturbations is a common problem for proposed long-range interaction schemes.

Scalability of 2D quantum memories remains a significant challenge.

Abstract

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.