Qutrit Toric Code and Parafermions in Trapped Ions

Abstract

The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum information storage and processing. While topological orders are more readily accessible with qudits, experimental realisations have thus far been limited to lattice models of qubits. Here, we prepare a ground state of the Z3 toric code state on 24 qutrits in a trapped ion quantum processor with fidelity per qutrit exceeding 96.5(3)%. We manipulate two types of defects which go beyond the conventional qubit toric code: a parafermion, and its bound state which is related to charge conjugation symmetry. We further demonstrate defect fusion and the transfer of entanglement between anyons and defects, which we use to control topological qutrits. Our work opens up the space of long-range entangled states with qudit degrees of freedom for use in quantum simulation and universal error-correcting codes.

8+20 pages, 15 figures

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Cited by in corpus (8)

• Protocols for Creating Anyons and Defects via Gauging
• Soft symmetries of topological orders
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Synthesis of Single Qutrit Circuits from Clifford+R
• Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
• Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice