K-P Quantum Neural Networks

Code

• github.com/eperrier/k-p_qnn
  OfficialIn paperjax★ 0

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- 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- 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.

Tasks

Reproductions