Citation:Iqbal, Mohsin, et al. "Qutrit Toric Code and Parafermions in Trapped Ions." arXiv preprint arXiv:2411.04185 (2024).
Web: https://arxiv.org/abs/2411.04185
Tags: Hardware, Kitaev-quantum-double, Defects/boundaries
In this nice experimental paper, the quantinuum team experimentally realized the Z3 toric code, and coherently manipulated its non-abelian defects. It's cool that they can do this! The encoding puts every qutrit into two qubits. Since the code is not as native as qubit codes, the fidelity is 96% - much lower than comparable toric code experiments.
The main experiment they did was to create a ground state with defects, move anyons around defects, and then verify that the anyon type changed as expected.
It seems like this work is mainly a stepping stone towards the S_3 model, which also requires mapping into a qutrit. To quote the authors, in reference to the S_3 model: "Our findings show that digital quantum processors have advanced to the point where they can throw off the shackles of the underlying qubit architecture and explore the much larger class of topologically ordered systems that is naturally formulated with local Hilbert space dimensions greater than two. Tantalisingly, that class includes models with universal quantum computational power, some of which are closely related to the model presented here".