Pauli-string grouping for VQE measurement reduction on a sparse-connectivity quantum annealer

Quantum Physics arXiv:2609.20861 (quant-ph) [Submitted on 10 Sep 2026] Title:Pauli-string grouping for VQE measurement reduction on a sparse-connectivity quantum annealer Authors:Raul Martinez, Miguel Sanchez-Beato, Mario Calonge View a PDF of the paper titled Pauli-string grouping for VQE measurement reduction on a sparse-connectivity quantum annealer, by Raul Martinez and 1 other authors View PDF HTML (experimental) Abstract:The Variational Quantum Eigensolver (VQE) requires a large number of measurements to evaluate molecular Hamiltonians. Expressing a molecular Hamiltonian as a linear combination of Pauli strings creates a measurement bottleneck: non-commuting Pauli strings cannot be measured simultaneously. Consequently, mutually commuting Pauli strings must be grouped and measured together to minimise the number of quantum-state preparations. This task maps to the minimum clique cover problem on a commutativity graph, an NP-hard problem typically addressed using classical heuristics. Although an Ising-model formulation has recently been explored on fully connected CMOS Ising machines and demonstrated on physical quantum annealers only at small scale, the embedding cost that governs its behaviour on hardware with sparse connectivity, where each logical variable must be represented by a chain of physical qubits, has not been characterised. In this work, we formulate the Pauli-grouping problem as a standard QUBO colouring model and study its scalability on a D-Wave quantum annealer. Across a series of molecular systems and for both qubit-wise and full commutativity, we quantify the growth in the number of logical variables and the QUBO interaction density, characterise the physical-qubit and chain-length overhead required for embedding on the Zephyr topology, and compare the annealer's time-to-solution and solution quality with those of heuristic classical baselines. This analysis identifies the threshold of molecular complexity beyond which hardware connectivity prevents viable embedding, and shows that a second, practical limit is reached earlier. The threshold therefore measures how far current annealers are from the regime in which pre-optimising a VQE measurement scheme on hardware would be worth considering. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Cite as: arXiv:2609.20861 [quant-ph] (or arXiv:2609.20861v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.20861 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Raul Martinez Pavon [view email] [v1] Thu, 10 Sep 2026 11:59:59 UTC (961 KB) Full-text links: Access Paper: View a PDF of the paper titled Pauli-string grouping for VQE measurement reduction on a sparse-connectivity quantum annealer, by Raul Martinez and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math.OC 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?)