Observable-Guided Generator Selection for Improving Trainability in Quantum Machine Learning with a $ \mathfrak{g} $-Purity Interpretation under Restricted Settings

Quantum Physics [Submitted on 17 Apr 2026] Observable-Guided Generator Selection for Improving Trainability in Quantum Machine Learning with a \mathfrak{g} -Purity Interpretation under Restricted Settings Hiroshi Ohno To study generator design for parameterized unitaries in quantum machine learning (QML), we propose an observable-guided generator selection algorithm for n -qubit Pauli-string generator pools. The proposed method selects generators based on two criteria: maintaining large first-order sensitivity in the gradients and suppressing second-order interference in the Hessian matrix. Under a restricted setting with Pauli-string observables and candidate generators, the selection problem can be formulated as a binary optimization problem that favors mutually anti-commuting generators. Numerical experiments on a synthetic dataset with a small-scale five-qubit circuit show that the selected generators yield faster training than random generator selection in our setting, while exhibiting similar expressibility. Furthermore, under additional algebraic assumptions, the proposed criteria admit an interpretation in terms of the \mathfrak{g} -purity of the observable: the first-order sensitivity is proportional to the \mathfrak{g} -purity, whereas the second-order interference, namely the off-diagonal elements of the Hessian matrix, is upper-bounded by it. These results suggest that observable-guided generator selection is a promising direction for improving trainability in restricted QML settings. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15693 [quant-ph]   (or arXiv:2604.15693v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15693 Focus to learn more Submission history From: Hiroshi Ohno [view email] [v1] Fri, 17 Apr 2026 04:37:27 UTC (55 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?)