Non-Abelian topological order and anyons on a trapped-ion processor

Mohsin Iqbal, Nathanan Tantivasadakarn, Ruben Verresen, Sara L. Campbell, Joan M. Dreiling, Caroline Figgatt, John P. Gaebler, Jacob Johansen, Michael Mills, Steven A. Moses, Juan M. Pino, Anthony Ransford, Mary Rowe, Peter Siegfried, Russell P. Stutz, Michael Foss-Feig, Ashvin Vishwanath and Henrik Dreyer ()
Additional contact information
Mohsin Iqbal: Quantinuum
Nathanan Tantivasadakarn: California Institute of Technology
Ruben Verresen: Harvard University
Sara L. Campbell: Quantinuum
Joan M. Dreiling: Quantinuum
Caroline Figgatt: Quantinuum
John P. Gaebler: Quantinuum
Jacob Johansen: Quantinuum
Michael Mills: Quantinuum
Steven A. Moses: Quantinuum
Juan M. Pino: Quantinuum
Anthony Ransford: Quantinuum
Mary Rowe: Quantinuum
Peter Siegfried: Quantinuum
Russell P. Stutz: Quantinuum
Michael Foss-Feig: Quantinuum
Ashvin Vishwanath: Harvard University
Henrik Dreyer: Quantinuum

Nature, 2024, vol. 626, issue 7999, 505-511

Abstract: 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.

Date: 2024
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DOI: 10.1038/s41586-023-06934-4

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