Qudit lattice surgery

TL;DR

This paper extends the lattice surgery model, used for fault-tolerant quantum computing, from qubits to qudits of arbitrary dimension, connecting it to the ZX-calculus for a broader theoretical framework.

Contribution

It generalizes lattice surgery to qudits using group algebras and relates it to the ZX-calculus, expanding the theoretical understanding of fault-tolerant quantum computation.

Findings

Lattice surgery can be applied to qudits of any finite dimension.

The model is based on the group algebra $ ext{C} ext{Z}_d$ for $d \\geq 2$.

The approach maintains the need for magic state injection for universality.

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 $d \geq 2$. 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.