Braiding Non-Abelian Anyons on a Programmable Superconducting Processor

Dongling Deng

Institute for Interdisciplinary Information Sciences, Tsinghua University

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topologically-ordered phases of matter. They are the building blocks of topological quantum computing. In this talk, I will first give a brief introduction to non-Abelian anyons and then report two recent experimental quantum digital simulation of braiding non-Abelian anyons on a programable superconducting processor. In the first experiment, we prepare the ground states of the toric-code model with twists, and demonstrate that twists behave as Ising anyons, exhibiting the same fusion rules and non-Abelian braiding statistics of the Ising type. They can be explored to encode topological logical qubits and both single- and two-qubit logic gates can be implemented by braiding them. In the second experiment, we exploit efficient quantum circuits to prepare the non-Abelian topologically ordered ground states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. In particular, we create two pairs of Fibonacci quasiparticle excitations by acting string operators on the prepared ground states and demonstrate their nontrivial mutual statistics by braiding them with sequences supporting universal single-qubit logic gates.

References:

[1] Xu et al., Chin. Phys. Lett. 40, 060301 (2023).

[2] Xu et al., arXiv:2404.00091v1