Artem Belov | Searcharxiv

arXiv2026

Ising anyons in the $SU(2)_2$ Chern--Simons theory

The present work is motivated by the statement that the Ising minimal model $\mathcal{M}(4,3)$ is equivalent, at the level of observables, to the $SU(2)_2$ Chern--Simons theory. At first glance, however, these two theories appear to differ substantially. For instance, the number of irreducible highest-weight representations does not match the number of Ising anyons. For tensor products of low degree, these discrepancies are examined in this work. While representation structure differs, it does not affect the observables underlying topological quantum computation algorithms.

hep-th↗

arXiv2024

Measuring Chern-Simons level $k$ by braiding $SU(2)_k$ anyons

Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern-Simons level $k$ in the unknown material. For this purpose, we use the previously derived braiding rules for Chern-Simons $SU(2)_k$ anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern-Simons level $k$ can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations.

hep-th↗