Thursday, July 25, 2013

1307.6222 (Benjamin J. Brown et al.)

Glassy topological quantum memories in two-dimensions    [PDF]

Benjamin J. Brown, Abbas Al-Shimary, Jiannis K. Pachos
Recently, three-dimensional topological glassy memories have been introduced that exhibit coherence times that increase polynomially with system size. This partial self-correction is desirable for storing quantum information. Based on dimensional arguments, such a behaviour is not expected to be present in local two-dimensional systems. Nevertheless, three-dimensional memories are daunting in terms of complexity and they lack experimental amenability. Here we present a two-dimensional topologically ordered model decorated with a defect grid, which exhibits fragile glassy behaviour. We numerically demonstrate that the equilibration times of the system depend super-exponentially on the inverse temperature of the environment and polynomially on the size of the system. Both of these hallmarks of fragile glassy behaviour are also direct manifestations of partial self-correction. This result has applications to engineering reliable quantum memories with current technology, e.g. with Josephson junctions or ion traps.
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