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  • Title: Non-Abelian topological order and anyons on a trapped-ion processor.
    Author: Iqbal M, Tantivasadakarn N, Verresen R, Campbell SL, Dreiling JM, Figgatt C, Gaebler JP, Johansen J, Mills M, Moses SA, Pino JM, Ransford A, Rowe M, Siegfried P, Stutz RP, Foss-Feig M, Vishwanath A, Dreyer H.
    Journal: Nature; 2024 Feb; 626(7999):505-511. PubMed ID: 38356069.
    Abstract:
    Non-Abelian topological order is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged1-4. These anyonic excitations are promising building blocks of fault-tolerant quantum computers5,6. However, despite extensive efforts, non-Abelian topological order and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian topological order. Here we present the realization of non-Abelian topological order in the wavefunction prepared in a quantum processor and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground-state wavefunction of D4 topological order on a kagome lattice of 27 qubits, with fidelity per site exceeding 98.4 per cent. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunnelling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon-a peculiar feature of non-Abelian topological order. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.
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