Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

TL;DR

This paper proposes a method to detect fractional statistics in quantum simulators of spin liquids using quasiparticle interferometry, demonstrating robustness against noise and providing a way to test quantum coherence in these devices.

Contribution

It introduces a generic approach to probe fractional statistics in topological spin liquids with a specific implementation using combinatorial gauge symmetry.

Findings

Design of a quasiparticle interferometry scheme for fractional statistics detection

Assessment of scheme robustness against disorder and dephasing

Scheme serves as a test of quantum coherence in quantum simulators

Abstract

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of $\mathbb{Z}_2$ topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing -- effects that are generally pervasive in noisy quantum programmable devices. A useful counterpart of our scheme is that it provides a clear test of the `quantumness' of these devices, since the signatures that we are looking for crucially hinge on quantum coherence and quantum interference effects in the system.