Measuring Chern–Simons level k by braiding anyons

Artem Belov; Andrey Morozov

doi:10.1140/epjc/s10052-024-13734-1

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 91
https://doi.org/10.1140/epjc/s10052-024-13734-1

Regular Article - Theoretical Physics

Measuring Chern–Simons level k by braiding $S U {(2)}_{k}$ anyons

Artem Belov¹^,3^a and Andrey Morozov¹^,2^,3

¹ NRC “Kurchatov Institute”, 123182, Moscow, Russia
² Institute for Information Transmission Problems, 127994, Moscow, Russia
³ Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia

^a belov.artem@phystech.su

Received: 29 August 2024
Accepted: 24 December 2024
Published online: 27 January 2025

Abstract

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 $S U {(2)}_{k}$ $$SU(2)_k$$ 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.

© The Author(s) 2025

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