Entropic barriers for two-dimensional quantum memories.
Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.
Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom and School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
Benjamin J
BJ
Brown
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
Abbas
A
Al-Shimary
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
Jiannis K
JK
Pachos