Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems

Abstract

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.

34 pages, 9 figures; v2 matches the journal version and corrects a misstatement about the detailed balance condition of our Metropolis simulations. All conclusions from v1 are unaffected by this correction

References in corpus (15)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological Quantum Distillation
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Classification of Topological Defects in Abelian Topological States
• The structure of preserved information in quantum processes
• Efficient Decoders for Qudit Topological Codes
• On measurement-based quantum computation with the toric code states
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Topological degeneracy of non-Abelian states for dummies
• Decoding non-Abelian topological quantum memories
• Quantum Circuits for Measuring Levin-Wen Operators
• Self-Correcting Quantum Memories Beyond the Percolation Threshold
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
• Non-Abelian Chern-Simons Theory from a Hubbard-like Model
• Statistical dynamics of a non-Abelian anyonic quantum walk

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• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order