Complete Flow-Preserving Rewrite Rules for MBQC Patterns with Pauli Measurements
arXiv:2205.02009 · doi:10.4204/EPTCS.394.5
Abstract
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. 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.
In Proceedings QPL 2022, arXiv:2311.08375
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- Inserting Planar-Measured Qubits into MBQC Patterns while Preserving Flow
- Nonunitary gates using measurements only
- Pauli Flow on Open Graphs with Unknown Measurement Labels