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YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation

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arXiv:2603.29379v1 Announce Type: new Abstract: We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-pla

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Quantum Physics [Submitted on 31 Mar 2026] YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation Jaroslav Kysela, Katharina Ludwig, Nitica Sakharwade, Anette Messinger, Wolfgang Lechner We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the YZ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal YZ-plane-only measurement pattern and establish a connection between YZ-plane-only and XZ-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that YZ-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation. Comments: 15 pages, 8 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.29379 [quant-ph] (or arXiv:2603.29379v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.29379 Focus to learn more Submission history From: Jaroslav Kysela [view email] [v1] Tue, 31 Mar 2026 07:49:33 UTC (254 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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