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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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03358122
Contributor : Robert Booth Connect in order to contact the contributor
Submitted on : Wednesday, September 29, 2021 - 11:06:10 AM
Last modification on : Thursday, February 3, 2022 - 3:57:53 PM

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  • HAL Id : hal-03358122, version 1
  • ARXIV : 2109.13810

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Robert Booth, Aleks Kissinger, Damian Markham, Clément Meignant, Simon Perdrix. Outcome determinism in measurement-based quantum computation with qudits. 2021. ⟨hal-03358122⟩

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