Experimental simulation of anyonic fractional statistics with an NMR quantum information processor

TL;DR

This paper demonstrates the simulation of anyonic fractional statistics using an NMR quantum processor, showcasing creation, braiding, and fusion of anyons with observed phase differences indicative of their unique statistics.

Contribution

It provides an experimental simulation of anyonic fractional statistics on a quantum processor, implementing key anyon manipulations in a 7-qubit NMR system.

Findings

Observed a $rac{ heta}{2}$ phase difference confirming fractional statistics.

Successfully simulated anyon creation, braiding, and fusion.

Demonstrated phase differences distinct from fermions and bosons.

Abstract

Anyons have exotic statistical properties, fractional statistics, differing from Bosons and Fermions. They can be created as excitations of some Hamiltonian models. Here we present an experimental demonstration of anyonic fractional statistics by simulating a version of the Kitaev spin lattice model proposed by Han et al[Phys. Rev.Lett. 98, 150404 (2007)] using an NMR quantum information processor. We use a 7-qubit system to prepare a 6-qubit pseudopure state to implement the ground state preparation and realize anyonic manipulations, including creation, braiding and anyon fusion. A $\pi/2\times 2$ phase difference between the states with and without anyon braiding, which is equivalent to two successive particle exchanges, is observed. This is different from the $\pi\times 2$ and $2\pi \times 2$ phases for Fermions and Bosons after two successive particle exchanges, and is consistent with the fractional statistics of anyons.