Non-Abelian Anyons with Rydberg Atoms

TL;DR

This paper demonstrates the theoretical creation and manipulation of non-Abelian anyons in Rydberg atom systems, providing a potential platform for fault-tolerant quantum computing through topological states.

Contribution

It introduces a method to generate non-Abelian anyons in Rydberg atom lattices with mixed-boundary punctures and details how to implement quantum gates via ancilla atoms.

Findings

Numerical identification of topologically distinct ground states.

Proposal for creating topological states with ancilla atoms.

Implementation of braiding operations for non-Abelian anyons.

Abstract

We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant quantum computing, have not been generated. To generate anyons with non-Abelian braiding statistics, we consider systems with mixed-boundary punctures. We obtain the topologically distinct ground states of the system numerically using the iDMRG technique. We discuss how these topological states can be created using ancilla atoms of a different type. We show that a system with 2N+2 punctures and an equal number of ancilla atoms leads to N logical qubits whose Hilbert space is determined by a set of stabilizing conditions on the ancilla atoms. Quantum gates can be implemented using a set of gates acting on the ancilla atoms that commute with the stabilizers and realize the braiding group of non-Abelian Ising anyons.