title: Self-correcting quantum memories beyond the percolation threshold.
abstract: We analyze several high dimensional generalizations of the toric code at a nonzero temperature. We find that in a large enough dimension, there can be a distinct separation between the critical temperature Tc, given by thermodynamic singularities, and the percolation temperature Tp, given by the percolation of defects. We argue that the regime Tp<T<Tc is a range of temperatures where a self-correcting quantum memory can operate despite having percolating defects. We present analytic arguments and numerical evidence in support of this scenario, including a mean-field treatment and Monte Carlo simulations. Near Tc, simulations observe a large hysteretic behavior, which may have applications by allowing the self-correcting phase to survive in a "superheated" regime.
authors.affiliation: Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California 93106, USA and Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
authors.forename: Matthew B
authors.initials: MB
authors.lastname: Hastings
authors.affiliation: Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Grant H
authors.initials: GH
authors.lastname: Watson
authors.affiliation: Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Roger G
authors.initials: RG
authors.lastname: Melko