Explainable quantum regression algorithm with encoded data structure

Quantum Physics [Submitted on 17 Apr 2026] Explainable quantum regression algorithm with encoded data structure C.-C. Joseph Wang, F. Perkkola, I. Salmenperä, A. Meijer-van de Griend, J. K. Nurminen 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: arXiv admin note: substantial text overlap with arXiv:2307.03334 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 Submission history From: C.-C. Joseph Wang [view email] [v1] Fri, 17 Apr 2026 03:42:12 UTC (625 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)