Outcome determinism in measurement-based quantum computation with qudits

• URL: http://arxiv.org/abs/2109.13810v1
• Date: Tue, 28 Sep 2021 15:36:36 GMT
• Title: Outcome determinism in measurement-based quantum computation with qudits
• Authors: Robert I. Booth, Aleks Kissinger, Damian Markham, Cl\'ement Meignant, Simon Perdrix
• Abstract summary: In measurement-based quantum computing, computation is carried out by a sequence of measurements and corrections on an entangled state. 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 that Zd-flow is a necessary and sufficient condition for a strong form of outcome determinism.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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