Robustness of Topological Order in the Toric Code with Open Boundaries

Abstract

We analyze the robustness of topological order in the toric code in an open boundary setting in the presence of perturbations. The boundary conditions are introduced on a cylinder, and are classified into condensing and non-condensing classes depending on the behavior of the excitations at the boundary under perturbation. For the non-condensing class, we see that the topological order is more robust when compared to the case of periodic boundary conditions while in the condensing case topological order is lost as soon as the perturbation is turned on. In most cases, the robustness can be understood by the quantum phase diagram of a equivalent Ising model.

12 pages, 14 figures. Presentation improved, clarifying texts added, version to appear in Physical Review B

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Cited by in corpus (14)

• Magic-state resource theory for the ground state of the transverse-field Ising model
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• An Operational Definition of Topological Order
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state
• Stability of topological purity under random local unitaries
• Error-correction properties of an interacting topological insulator
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Kibble-Zurek mechanism and errors of gapped quantum phases
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Free fermion representation of the topological surface code
• Robustness of a state with Ising topological order against local projective measurements