A Scheme for Simulation of Quantum Gates by Abelian Anyons

Heng Fan

Seth Lloyd

Yao Shen, Fulin Zhang, Yu-Zhu Chen +1 more

David J. Clarke, Kirill Shtengel, Parsa Bonderson +1 more

Yao Shen, Qing Ai, Gui‐Lu Long

Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian anyons in the Kitaev model. Two pairs of anyons (six spins) are used to realize single-qubit gates, while ten spins are needed for the CNOT gate. Based on these quantum gates, we show how to realize the Grover algorithm in a two-qubit system.

Wade Bloomquist, Zhenghan Wang

Abstract We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality. We are interested in the possible gate sets which can emerge in this setting. As a first step, we prove that for abelian anyons, all gates from these mapping class group representations are normalizer gates. Results of Van den Nest then allow us to conclude that for abelian anyons this quantum computing scheme can be simulated efficiently on a classical computer. With an eye toward more general anyon models we additionally show that for Fibonnaci anyons, quantum representations of mapping class groups give rise to gates which are not generalized Clifford gates.