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Non-Abelian anyons with Rydberg atoms

Nora M. Bauer*, Elias Kokkas†, Victor Ale‡, and George Siopsis§

  • Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA

  • *nbauer1@vols.utk.edu
  • †ikokkas@vols.utk.edu
  • ‡vale@vols.utk.edu
  • §siopsis@tennessee.edu
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Phys. Rev. A 107, 062407 – Published 6 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.062407

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 infinite Density Matrix Renormalization Group 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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Outline

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Phys. Rev. A 107, 062407– Published 6 June, 2023
  • Received 19 January 2023
  • Accepted 23 May 2023
Article part of CHORUS
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