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, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2023-03, Vol.56 (11), p.115303
Main Authors: Booth, Robert I, Kissinger, Aleks, Markham, Damian, Meignant, Clément, Perdrix, Simon
Format: Article
Language:English
Subjects:
determinism
flow
measurement-based quantum computation
Physics
Quantum Physics
qudit
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Summary: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 Z d -flow, when the local dimension is an odd prime. Our main results are a proof that Z d -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 Z d -flow whenever one exists.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/acbace