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.
Cite
@article{arxiv.1311.0019,
title = {Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems},
author = {Courtney G. Brell and Simon Burton and Guillaume Dauphinais and Steven T. Flammia and David Poulin},
journal= {arXiv preprint arXiv:1311.0019},
year = {2015}
}
Comments
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