VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians
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Quantum Physics arXiv:2606.15061 (quant-ph) [Submitted on 13 Jun 2026] Title:VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians Authors:Elijah Pelofske, Stephan Eidenbenz View a PDF of the paper titled VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians, by Elijah Pelofske and 1 other authors View PDF HTML (experimental) Abstract:Quantum Phase Estimation (QPE) is the quantum algorithmic workhorse for computing ground state energies of quantum Hamiltonians with quantum computers. Ground state energy calculation of physical systems is perhaps the most promising use case for quantum computing in terms of scientific and commercial value with a plausible path to outperformance of classical alternatives. This path, however, hinges on the availability of initial states for QPE with significant overlap with the true ground state. Using extensive (classical) numerical computations, we study whether the NISQ-era algorithm VQE (Variational Quantum Eigensolver) could be used to efficiently prepare high-overlap states of disordered fully-connected anisotropic Heisenberg spin glass quantum Hamiltonians with up to $15$ qubits. We find that (i) -- consistent with widely held, but rarely numerically illustrated beliefs -- VQE is generally unable to efficiently converge to the ground state for our Hamiltonians, which is a well-known issue with VQE due to a variety of factors including vanishing gradients and local minima; (ii) low energy states do not necessarily have large ground-state overlap, but there is typically a correlation between the two measures; (iii) adding more than three layers to the VQE ansatz neither improves overlap nor the energies found; and (iv) the best-found overlap scaling as a function of the Hamiltonian system size is not strongly exponentially decreasing, suggesting potential for VQE to be a heuristic state preparation algorithm for QPE. Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Numerical Analysis (math.NA) Cite as: arXiv:2606.15061 [quant-ph] (or arXiv:2606.15061v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.15061 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Elijah Pelofske [view email] [v1] Sat, 13 Jun 2026 02:35:48 UTC (3,180 KB) Full-text links: Access Paper: View a PDF of the paper titled VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians, by Elijah Pelofske and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.dis-nn cs cs.NA math math.NA 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?)