A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling

Quantum Physics arXiv:2607.07942 (quant-ph) [Submitted on 8 Jul 2026] Title:A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling Authors:Dario Picozzi View a PDF of the paper titled A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling, by Dario Picozzi View PDF Abstract:Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini-Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient $n$-qubit ansatz, which parametrises states by a binary tree and whose Fubini-Study pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of $k$ computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in $k$; a variant reaches near-optimal $O(nk/\log n)$ scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in $k$ (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.07942 [quant-ph] (or arXiv:2607.07942v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.07942 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Dario Picozzi [view email] [v1] Wed, 8 Jul 2026 21:38:39 UTC (2,637 KB) Full-text links: Access Paper: View a PDF of the paper titled A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling, by Dario PicozziView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)