Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator

TL;DR

This paper proposes a method to simulate non-abelian topological phases, specifically Floquet spin liquids, using programmable quantum simulators like Rydberg atom arrays, enabling exploration of complex topological phenomena such as Majorana modes.

Contribution

It introduces a novel Floquet-based approach to realize non-abelian spin liquids in quantum simulators, including practical implementation schemes and methods for probing topological excitations.

Findings

Feasible implementation in Rydberg atom arrays.

Simulation of non-abelian excitations and Majorana modes.

Potential for exploring topological phases and braiding experiments.

Abstract

Understanding topological matter is an outstanding challenge across several disciplines of physical science. Programmable quantum simulators have emerged as a powerful approach to studying such systems. While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-abelian excitations remains an open problem. We introduce and analyze a new approach to simulating topological matter based on periodic driving. Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-abelian spin liquid in Kitaev's honeycomb model. We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms. One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations. We describe methods for probing the non-abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments. Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter. Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.