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

Autor:	Belov, Artem, Morozov, Andrey
Rok vydání:	2024
Předmět:	High Energy Physics - Theory Quantum Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 12 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.14188 Zobrazit plný text záznamu View this record from Arxiv