We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-
dimensional qudits (ie qupits). We derive a simplified rule set that closely resembles the …

Rig groupoids provide a semantic model of Π, a universal classical reversible programming
language over finite types. We prove that extending rig groupoids with just two maps and …

Current efforts to build quantum computers focus mainly on the two-state qubit, which often
involves suppressing readily-available higher states. In this work, we break this abstraction …

We introduce the qudit ZH-calculus and show how to generalise the phase-free qubit rules
to qudits. We prove that for prime dimensions $ d $, the phase-free qudit ZH-calculus is …

Recent hardware demonstrations and advances in circuit compilation have made quantum
computing with higher-dimensional systems (qudits) on near-term devices an attractive …

We identify a novel qudit gate which we refer to as the gate. This is an alternate
generalization of the qutrit T gate to any odd prime dimension d, in the dth level of the …

A popular universal gate set for quantum computing with qubits is Clifford+ T, as this can be
readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T …

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most
one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd …

It is known that the matrices that can be exactly represented by a multiqubit circuit over the
Toffoli+ Hadamard, Clifford+ $ T $, or, more generally, Clifford-cyclotomic gate set are …

We present an exact synthesis algorithm for qutrit unitaries in $\mathcal {U} _ {3^ n}(\mathbb
{Z}[1/3, e^{2\pi i/3}]) $ over the Clifford $+ T $ gate set with at most one ancilla. This extends …