K-P Quantum Neural Networks

Elija Perrier

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arXiv · 2504.01673

K-P Quantum Neural Networks

Elija Perrier

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Abstract

We present an extension of K-P time-optimal quantum control solutions using global Cartan $KAK$ decompositions for geodesic-based solutions. Extending recent time-optimal constant-$\theta$ control results, we integrate Cartan methods into equivariant quantum neural network (EQNN) for quantum control tasks. We show that a finite-depth limited EQNN ansatz equipped with Cartan layers can replicate the constant-$\theta$ sub-Riemannian geodesics for K-P problems. We demonstrate how for certain classes of control problem on Riemannian symmetric spaces, gradient-based training using an appropriate cost function converges to certain global time-optimal solutions when satisfying simple regularity conditions. This generalises prior geometric control theory methods and clarifies how optimal geodesic estimation can be performed in quantum machine learning contexts.

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BibTeX RIS

Elija Perrier. 2025-04-02. K-P Quantum Neural Networks. https://arxiv.org/abs/2504.01673

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