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.
Cite
@article{arxiv.2109.13810,
title = {Outcome determinism in measurement-based quantum computation with qudits},
author = {Robert I. Booth and Aleks Kissinger and Damian Markham and Clément Meignant and Simon Perdrix},
journal= {arXiv preprint arXiv:2109.13810},
year = {2023}
}
Comments
16 pages + 10 pages of appendices, 1 figure