Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits

Quantum Physics arXiv:2609.27053 (quant-ph) [Submitted on 22 Sep 2026] Title:Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits Authors:Vishal S. Ngairangbam, Michael Spannowsky View a PDF of the paper titled Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits, by Vishal S. Ngairangbam and 1 other authors View PDF HTML (experimental) Abstract:Employing problem-specific non-universal Variational Quantum Circuits aligned with a suitable state preparation has become a standard approach to counter the difficulty in training universal ansätze. However, due to their non-universality, diagnosing their reachability and trainability remains reference-state-specific. In this work, we establish the equivalence of maximal reachability and generic reachability over arbitrary reference states as a consequence of the \emph{principal orbit-type theorem}. Thereafter, assuming that the global minimum of the cost function is achieved on a subset that can be described as the image of a smooth function, we derive necessary and sufficient conditions for non-zero probability of reachability under generically sampled reference states. Furthermore, when the solution set is assumed to be realised through a real analytic map that embeds a solution manifold, we show that local surjectivity is generically obtained on the entire solution manifold if it is attained at a single point. As a practical design rule, the need for local surjectivity automatically translates to a necessary dimensional criterion: reachability requires the target set's topological dimension to be at least as large as the co-dimension of the generic orbit. Numerical simulations show that finite-depth optimisation consistently fails when the dimensional obstruction applies, while unobstructed cases show improved convergence. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.27053 [quant-ph] (or arXiv:2609.27053v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.27053 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vishal Ngairangbam [view email] [v1] Tue, 22 Sep 2026 20:51:19 UTC (1,894 KB) Full-text links: Access Paper: View a PDF of the paper titled Equivalence of maximal and generic reachability for non-universal Variational Quantum Circuits, by Vishal S. Ngairangbam and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)