Qudit lattice surgery

Abstract

We observe that lattice surgery, a model of fault-tolerant qubit computation, generalises straightforwardly to arbitrary finite-dimensional qudits. The generalised model is based on the group algebras $\mathbb{C}{\mathbb{Z}}_d$ for $d\ge 2$. It still requires magic state injection for universal quantum computation. We relate the model to the ZX-calculus, a diagrammatic language based on Hopf-Frobenius algebras.

arXiv comment23 pages, many figures. Fixed some small errors in v3