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

• DOI: 10.48550/arxiv.2305.03766
• Publication Date: 2024-02-14
• Authors: Mohsin Iqbal; Nathanan Tantivas...; 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; Henrik Dreyer
• Keywords: Quantum Physics; Condensed Matter - Strongly Correlated Electrons; Multidisciplinary; Strongly Correlated Electrons (cond-mat.str-el); FOS: Physical sciences; Quantum Physics (quant-ph); 530

Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian TO and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian TO. In this work, we present the first unambiguous realization of non-Abelian TO 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 $D_4$ TO on a kagome lattice of 27 qubits, with fidelity per site exceeding $98.4\%$. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunneling 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 TO. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.<br/>6 + 20 pages, 6 + 5 figures, 3 tables v2: Changed title, added a reference<br/>