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.
Highlights
One of the most interesting features of two-dimensional quantum systems with anyonic excitations [1] is their application to quantum information science, where the topological nature of the anyons offers some intrinsic protection of quantum coherence [2]
These topologically ordered systems are insensitive to local perturbations [3,4,5], have a ground-space degeneracy that is a function of the topology of the system [6,7], and can realize quantum gates by braiding anyons, which are naturally robust to error because of their topological nature [2,8]
We adapt two algorithms used in decoding Abelian anyon systems: a clustering renormalization group (RG) decoder introduced by Bravyi and Haah [34] and the perfect matching decoder [31]
Summary
One of the most interesting features of two-dimensional quantum systems with anyonic excitations [1] is their application to quantum information science, where the topological nature of the anyons offers some intrinsic protection of quantum coherence [2]. Non-Abelian anyon systems have excitations that can be used to implement topological quantum computation [10,11], and so they are of interest for quantum-information-processing schemes as well as quantum error correction. The local check operators can be measured using standard circuitry [32] on an ordinary, circuit-model quantum computer This second scenario we consider is not contingent on the existence of physical systems that naturally present topological quantum order; it could, in principle, be used in any quantum-computing architecture with nearest-neighbor interactions on a two-dimensional lattice. In this setting, our results provide an efficient decoding algorithm for the corresponding quantum error-correcting code. This provides the first efficient decoding schemes for a family of nonadditive quantum codes, i.e., codes without explicit Pauli-matrix tensor product structure
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
