Outcome determinism in measurement-based quantum computation with qudits

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