Implicit Differentiation for Measurement-Efficient Bilevel Quantum-Classical Optimization

Quantum Physics arXiv:2608.07717 (quant-ph) [Submitted on 7 Aug 2026] Title:Implicit Differentiation for Measurement-Efficient Bilevel Quantum-Classical Optimization Authors:Tobias Rohe, Markus Baumann, Federico Harjes Ruiloba, Maximilian Zorn, Jonas Stein, Claudia Linnhoff-Popien View a PDF of the paper titled Implicit Differentiation for Measurement-Efficient Bilevel Quantum-Classical Optimization, by Tobias Rohe and 5 other authors View PDF HTML (experimental) Abstract:Quantum optimization has shown promising results for quadratic unconstrained binary optimization (QUBO) problems. Real-world applications, however, often involve polynomial coefficients that depend on tunable external factors - such as demand forecasts or risk preferences - giving rise to bilevel optimization structures. We show how variational quantum algorithms (VQAs) can efficiently handle such parametric problems, making three contributions. First, we propose a bilevel optimization model for diagonal cost Hamiltonians where coefficients depend on a tunable outer parameter: an outer loop adjusts this parameter - reshaping the cost landscape - while an inner VQA optimizes circuit variables. Second, since derivative-free probing methods incur a multiplicative overhead when each outer evaluation requires a complete inner solve, we develop correlator-reuse implicit differentiation (CR-ID), which obtains outer gradients by reusing quantum measurements already collected during inner energy estimation, requiring essentially no additional circuit executions. Experiments across three coefficient families show that CR-ID consistently improves budget-normalized efficiency by ~4\% in 1D and over 14\% in multi-dimensional settings, showing a significant performance advantage compared to finite-difference methods. Third, we show that this property is architecture-dependent: VQE admits exact reuse gradients, whereas QAOA introduces a state-dependent term that creates a cost-bias trade-off. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.07717 [quant-ph] (or arXiv:2608.07717v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.07717 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tobias Rohe [view email] [v1] Fri, 7 Aug 2026 19:03:43 UTC (404 KB) Full-text links: Access Paper: View a PDF of the paper titled Implicit Differentiation for Measurement-Efficient Bilevel Quantum-Classical Optimization, by Tobias Rohe and 5 other authorsView 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?)