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• W2051537112 abstract "We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a low-temperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits." @default.
• W2051537112 created "2016-06-24" @default.
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• W2051537112 date "2014-10-07" @default.
• W2051537112 modified "2023-09-25" @default.
• W2051537112 title "Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low-temperature regime" @default.
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• W2051537112 doi "https://doi.org/10.1103/physrevb.90.134302" @default.
• W2051537112 hasPublicationYear "2014" @default.
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