Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements

[2307.01800] Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2307.01800 (quant-ph) This paper has been withdrawn by S. Virmani [Submitted on 4 Jul 2023 ( v1 ), last revised 1 May 2026 (this version, v2)] Title: Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements Authors: Sahar Atallah , Michael Garn , Yukuan Tao , Shashank Virmani View a PDF of the paper titled Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements, by Sahar Atallah and 3 other authors No PDF available, click to view other formats Abstract: In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit undergoes at most $D$ diagonal gates, (iii) each qudit is destructively measured in the computational basis or bases unbiased to it, and (iv) each qudit is initialised within $\lambda^{-D}$ of a diagonal state according to a particular distance measure. In this work we explicitly compute $\lambda$ for any two qubit diagonal gate, thereby extending the computation of arXiv:2201.07655v2 beyond CZ gates. For any finite degree graph this allows us to describe a two parameter family of pure entangled quantum states (or three parameter family of thermal states) which have a non-trivial classically efficiently simulatable "phase" for the permitted measurements, even though other values of the parameters may enable ideal cluster state quantum computation. The main the technical tool involves considering separability in terms of "cylindrical" sets of operators. We also consider whether a different choice of set can strengthen the algorithm, and prove that they are optimal among a broad class of sets, but also show numerically that outside this class there are choices that can increase the size of the classically efficient regime. Comments: These results have been instead combined with newer results in arXiv:2604.27248 , together with an additional author Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2307.01800 [quant-ph] (or arXiv:2307.01800v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2307.01800 Focus to learn more arXiv-issued DOI via DataCite Submission history From: S. Virmani [ view email ] [v1] Tue, 4 Jul 2023 16:09:24 UTC (76 KB) [v2] Fri, 1 May 2026 00:22:46 UTC (1 KB) (withdrawn) Full-text links: Access Paper: View a PDF of the paper titled Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements, by Sahar Atallah and 3 other authors Withdrawn No license for this version due to withdrawn Current browse context: quant-ph < prev | next > new | recent | 2023-07 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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