Non-abelian topological order (TO) is a coveted state of matter that despite extensive efforts has remained elusive. I will present the first unambiguous realization of non-abelian TO and demonstrate control of its anyons. Using an adaptive circuit, we create the ground state wavefunction of D4 TO on a kagome lattice of 27 qubits on Quantinuum’s H2 trapped-ion quantum processor and obtain fidelity per site exceeding 98.4%. Moreover we are able to experimentally confirm the various features that are unique to non-abelian phases of matter including: 1) a non-square ground state degeneracy of 22, 2) an excited state with a single anyon on a torus, and 3) a non-trivial phase factor upon tracing three non-abelian anyons in the shape of Borromean rings in spacetime.
This talk is based on this arXiv paper.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Topological Quantum Computation.
