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

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• Thomas McElvanney (University of Birmingham)
• Friday 24 June 2022, 14:00-15:00
• LG23, SoCS and Zoom (see abstract for link).

If you have a question about this talk, please contact Anupam Das.

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 [arXiv:2109.10210]. We prove that any MBQC -like 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.

Joint work with Miriam Backens.

=== Zoom details ===

https://bham-ac-uk.zoom.us/j/81873335084?pwd=T1NaUFg2U1l6d0RLL2RlTzFBam1IUT09

Passcode: 217 Meeting ID: 818 7333 5084

This talk is part of the Lab Lunch series.

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• LG23, SoCS and Zoom (see abstract for link)
• Lab Lunch

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