Abstract
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-based methods for MBQC with qudit graph states, which we call Zd-flow, when the local dimension is an odd prime. Our main results are a proof that Zd-flow is sufficient to obtain a strong form of outcome determinism, and a partial converse to that result in the case of qubits and qutrits. Along the way, we find a suitable generalization of the concept of measurement planes to this setting and characterize the allowed measurements in a qudit MBQC. We also provide a polynomial time algorithm for finding an optimal Zd-flow whenever one exists.
