Complete flow-preserving rewrite rules for MBQC patterns with Pauli measurements

Thomas McElvanney, Miriam Backens

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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In the one-way model of measurement-based quantum computation (MBQC), computation proceeds via measurements on some standard resource state. So-called flow conditions ensure that the overall computation is deterministic in a suitable sense, with Pauli flow being the most general of these. Existing work on rewriting MBQC patterns while preserving the existence of flow has focused on rewrites that reduce the number of qubits. In this work, we show that introducing new Z-measured qubits, connected to any subset of the existing qubits, preserves the existence of Pauli flow. Furthermore, we give a unique canonical form for stabilizer ZX-diagrams inspired by recent work of Hu & Khesin [17]. We prove that any MBQClike stabilizer ZX-diagram with Pauli flow can be rewritten into this canonical form using only rules which preserve the existence of Pauli flow and that each of these rules can be reversed while also preserving the existence of Pauli flow. Hence we have complete graphical rewriting for MBQC-like stabilizer ZX-diagrams with Pauli flow.
Original languageEnglish
Title of host publication19th International Conference on Quantum Physics and Logic
PublisherOpen Publishing Association
Publication statusAccepted/In press - 1 Jun 2022

Publication series

NameElectronic proceedings in theoretical computer science
ISSN (Electronic)2075-2180

Bibliographical note

QPL2022 Proceedings not yet available from EPTCS as of 21/09/2023.


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