Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras

Authors:Andrew Rowan Barlow (1 and 2), Hans-Martin Rieser (1), Markus Lange (1) ((1) Institute for AI Safety and Security, Deutsches Zentrum für Luft- und Raumfahrt, Ulm/St. Augustin, Germany, (2) Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Heidelberg, Germany)

Abstract:Variational hybrid quantum models are a common paradigm for realising machine learning on quantum hardware. Nonetheless, they are challenging to train due to several problems intrinsic to the loss landscapes formed by variational quantum circuits. To mitigate these issues, researchers have extended the idea of subspace controllability leading to an increase in the success rate of variational models in finding the global minimum for quantum-based tasks. However, it remains unknown whether these results extend to classical-based tasks, and if any advantages are realised over a hyperparameter search. We begin to address this question by employing controllable circuits in a multi- classification task using MNIST-1D. Our results show that over a hyperparameter search, the majority of quantum models that achieve the lowest training and validation losses are subspace controllable. These results indicate that the hyperparameter search can be restricted to such models, in turn reducing computational cost and time.

arXiv:2609.24475 [quant-ph]

(or arXiv:2609.24475v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.24475 arXiv-issued DOI via DataCite (pending registration)