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Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2023

Outcome determinism in measurement-based quantum computation with qudits

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 proofs that Zd-flow is a necessary and sufficient condition for a strong form of outcome determinism. Along the way, we find a suitable generalisation of the concept of measurement planes to this setting and characterise the allowed measurements in a qudit MBQC. We also provide a polynomial-time algorithm for finding an optimal Zd-flow whenever one exists.

Dates and versions

hal-03358122 , version 1 (29-09-2021)

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Robert I. Booth, Aleks Kissinger, Damian Markham, Clément Meignant, Simon Perdrix. Outcome determinism in measurement-based quantum computation with qudits. Journal of Physics A: Mathematical and Theoretical, 2023, 56 (11), pp.115303. ⟨10.1088/1751-8121/acbace⟩. ⟨hal-03358122⟩
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