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arXiv · 2301.04250

Non-Abelian Anyons with Rydberg Atoms

Nora M. Bauer·Elias Kokkas·Victor Ale·George Siopsis
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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.

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Nora M. Bauer, Elias Kokkas, Victor Ale, George Siopsis. 2023-01-10. Non-Abelian Anyons with Rydberg Atoms. https://doi.org/10.1103/physreva.107.062407

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