Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver

Quantum Physics arXiv:2608.12830 (quant-ph) [Submitted on 13 Aug 2026] Title:Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver Authors:Mingyu Kang, K.

Birgitta Whaley View a PDF of the paper titled Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver, by Mingyu Kang and K.

Birgitta Whaley View PDF HTML (experimental) Abstract:Quantum subspace diagonalization methods are promising algorithms for quantum chemistry on near-term quantum computers. These methods can estimate low-lying energies of molecular systems using shallow quantum circuits, at the cost of many circuit repetitions to estimate the projected matrix elements. Errors in these matrix elements can be converted into much larger eigenvalue errors by an ill-conditioned overlap matrix. We study this bottleneck for the nonorthogonal quantum eigensolver (NOQE), which constructs a compact multireference subspace from dressed unrestricted Hartree-Fock states. We prove a finite-shot perturbation bound showing that, after overlap thresholding, the eigenvalue sensitivity is controlled by the condition number of the retained overlap matrix rather than by a worst-case dimension factor. With a scalable thresholding scheme, the upper bound on the per-matrix-element shot count required to reach a target accuracy scales as $\mathcal{O}(M)$, improving on the previously known $\mathcal{O}(M^3)$ bound, where $M$ is the number of reference states. Numerical experiments on hydrogen chains and rings suggest that, in practice, the measurement cost of structured NOQE instances can grow even more slowly than this linear bound. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.12830 [quant-ph] (or arXiv:2608.12830v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.12830 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mingyu Kang [view email] [v1] Thu, 13 Aug 2026 05:05:55 UTC (67 KB) Full-text links: Access Paper: View a PDF of the paper titled Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver, by Mingyu Kang and K. Birgitta WhaleyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)