BOOTH Robert
Supervision : Damian MARKHAM
Cosupervision : PERDRIX Simon
Measurementbased quantum computation beyond qubits
Measurementbased quantum computation (MBQC) is an alternative model for quantum computation, which makes careful use of the properties of the measurement of entangled quantum systems to perform transformations on an input. It differs fundamentally from the standard quantum circuit model in that measurementbased computations are naturally irreversible. This is an unavoidable consequence of the quantum description of measurements, but begets an obvious question: when does an MBQC implement an effectively reversible computation? The measurement calculus is a framework for reasoning about MBQC with the remarkable feature that every computation can be related in a canonical way to a graph. This allows one to use graphtheoretical tools to reason about MBQC problems, such as the reversibility question, and the resulting study of MBQC has had a large range of applications.
However, the vast majority of the work on MBQC has focused on architectures using the simplest possible quantum system: the qubit. It remains an open question how much of this work can be lifted to other quantum systems. In this thesis, we begin to tackle this question, by introducing analogs of the measurement calculus for higher and infinitedimensional quantum systems. More specifically, we consider the case of qubits when the local dimension is an odd prime, and of continuousvariable systems familiar from the quantum physics of free particles. In each case, a calculus is introduced and given a suitable interpretation in terms of quantum operations. We then relate the resulting models to the standard circuit models, using graphtheoretical tools called ``flow'' conditions.
Defence : 02/22/2022
Jury members :
Dan Browne, Professor at University College London [rapporteur]
Robert Raussendorf, Professor at University of British Columbia [rapporteur]
Ross Duncan, Fellow at University of Strathclyde
Claudia Faggian, Chargée de Recherche CNRS à l'IRIF
Elham Kashefi, Directrice de Recherche CRNS au LIP6
Simon Perdrix, Directeur de Recherche Inria au LORIA Nancy
Damian Markham, Charge de Recherche CNRS au LIP6
20222023 Publications

2023
 R. Booth, D. Markham : “Flow conditions for continuous variable measurementbased quantum computing”, Quantum, vol. 7, pp. 1146, (Verein) (2023)
 R. Booth, A. Kissinger, D. Markham, C. Meignant, S. Perdrix : “Outcome determinism in measurementbased quantum computation with qudits”, Journal of Physics A: Mathematical and Theoretical, vol. 56 (11), pp. 115303, (IOP Publishing) (2023)

2022
 R. Booth : “Measurementbased quantum computation beyond qubits”, thesis, phd defence 02/22/2022, supervision Markham, Damian, cosupervision : Perdrix, Simon (2022)
 R. Booth, U. Chabaud, P.‑E. Emériau : “Contextuality and Wigner negativity are equivalent for continuousvariable quantum measurements”, Physical Review Letters, vol. 129 (23), pp. 230401, (American Physical Society) (2022)
 R. Booth, T. Carette : “Complete ZXcalculi for the stabiliser fragment in odd prime dimensions”, Leibniz International Proceedings in Informatics (LIPIcs), vol. 241, 47^{th} International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Vienna, Austria, pp. 24:124:15, (Schloss Dagstuhl  LeibnizZentrum für Informatik), (ISBN: 9783959772563) (2022)