Experimental simulation of fractional statistics of abelian anyons in the Kitaev lattice-spin model

TL;DR

This paper demonstrates the fractional statistics of abelian anyons through a quantum simulation of the Kitaev lattice-spin model using nuclear magnetic resonance, providing a new way to observe and manipulate anyons.

Contribution

It presents the first experimental simulation of abelian anyons' fractional statistics in the Kitaev model using NMR techniques, bridging theory and potential quantum computing applications.

Findings

Successfully simulated anyonic fractional statistics

Encoded four-body interactions into two-body Ising chain interactions

Revealed distinct anyonic statistical properties in a controllable quantum system

Abstract

In two-dimensions, the laws of physics even permit the existence of anyons which exhibit fractional statistics ranging continuously from bosonic to fermionic behaviour. They have been responsible for the fractional quantum Hall effect and proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, the fractional statistics of anyons has never been observed in nature directly. Here we report the demonstration of fractional statistics of anyons by simulation of the first Kitaev lattice-spin model on a nuclear magnetic resonance system. We encode four-body interactions of the lattice-spin model into two-body interactions of an Ising spin chain in molecules. It can thus efficiently prepare and operate the ground state and excitations of the model Hamiltonian. This quantum system with convenience of manipulation and detection of abelian anyons reveals anyonic statistical properties distinctly. Our experiment with interacted Hamiltonian could also prove useful in the long run to the control and application of anyons.