K-P Quantum Neural Networks

2025/04/02 by Perrier, Elija
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2504.01673

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-θ 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-θ 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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