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KP Quantum Neural Networks

Created by
  • Haebom

Author

Elijah Perrier

Outline

This paper extends the KP time-optimal quantum control solution using the global Cartan $KAK$ decomposition for geodesic-based solutions. Extending recent results on time-optimal constant-θ control, we integrate the Cartan method into an homovariant quantum neural network (EQNN) for quantum control tasks. We show that the finite-depth-constrained EQNN ansatz with Cartan layers can replicate the constant-θ Ahrimani geodesics for the KP problem. We show how gradient-based training with an appropriate cost function can converge to certain global time-optimal solutions for certain types of control problems in Riemannian-symmetric spaces when simple regularity conditions are satisfied. This generalizes previous geometric control theory methods and clarifies how to perform optimal geodesic estimation in the context of quantum machine learning.

Takeaways, Limitations

Takeaways:
We present a novel solution to the KP-time optimal quantum control problem by incorporating the Cartan method into EQNN.
We show that finite-depth EQNN ansatz can replicate the constant-θ Ahriman geodesic.
We prove that gradient-based training for certain control problems in Riemann-symmetric spaces converges to a global-time optimal solution.
We clarify an optimal geodesic estimation method by linking geometric control theory and quantum machine learning.
Limitations:
Further studies are needed to determine whether the proposed method is applicable to all types of KP problems.
There are constraints that must satisfy simple regularity conditions.
Since the result is for a specific Riemannian symmetry space, its applicability to general quantum control problems may be limited.
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