Explainable quantum regression algorithm with encoded data structure
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Quantum Physics arXiv:2604.15666 (quant-ph) [Submitted on 17 Apr 2026] Title:Explainable quantum regression algorithm with encoded data structure Authors:C.-C. Joseph Wang, F. Perkkola, I. Salmenperä, A. Meijer-van de Griend, J. K. Nurminen View a PDF of the paper titled Explainable quantum regression algorithm with encoded data structure, by C.-C. Joseph Wang and 4 other authors View PDF HTML (experimental) Abstract:Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. However, variational quantum algorithms (derived from randomized hardware-efficient ansatz or adaptive ansatz) become a black box, not trustworthy for model interpretation, and not to mention for application deployment in informing critical decisions. In this paper, we construct the first interpretable quantum regression algorithm, in which the quantum state exactly encodes the classical data table and the variational parameters correspond directly to the regression coefficients, which are real numbers by construction, providing a high degree of model interpretability and minimal cost to optimize due to the right expressiveness. We also exploit the encoded data structure to reduce the gate complexity of computing the regression map. To reduce circuit depth in nonlinear regression, our algorithm can be extended by directly constructing nonlinear features via classical preprocessing, such as independent encoded column vectors. By design, the model performance is determined by the cost function measurement results $\mathcal{C}$ synchronous to the mean squared errors (MSE) for the regression models. We derived the read-out errors induced by one-hot encoding and compact encoding; the required physical qubit resources are exponentially compressed for the compact encoding to be favorable for noisy quantum devices. We also derive the cost function dependent sample complexity $ \in \mathcal{O}\left(\sigma^{2}(\mathcal{C}) \ln (1/\alpha)/\epsilon^{2}\right)$ under the error budget $\epsilon$ and confidence tolerance $\alpha$. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15666 [quant-ph] (or arXiv:2604.15666v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.15666 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: C.-C. Joseph Wang [view email] [v1] Fri, 17 Apr 2026 03:42:12 UTC (625 KB) Full-text links: Access Paper: View a PDF of the paper titled Explainable quantum regression algorithm with encoded data structure, by C.-C. Joseph Wang and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)