José D. Martín-Guerrero

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task due to the combined effects of non-commutativity, control complexity, and the exponential growth of the Hilbert space. In this work, we present a physics-informed neural network (PINN) framework to address this problem through the learning of counter-diabatic quantum dynamics. Our approach combines a variational PINN formulation with a Magnus-expansion treatment of time-ordered evolution, enabling the adiabatic gauge potential and the scheduling function to be inferred directly from the underlying physics while enforcing the Euler-Lagrange structure of the protocol. The method is applied to several families of driven spin Hamiltonians, including nearest-neighbor, dipolar, and trapped-ion-inspired interactions, for systems of up to six qubits. The numerical results show that the proposed framework systematically improves over reference solutions based only on the Euler-Lagrange condition, yielding high normalized QFI together with favorable fidelity and extremal-balance metrics while preserving small phsical residuals. The analysis further shows that learning the scheduling function provides a clear performance advantage in most cases, and reveals non-trivial finite-size effects, with $q=3$ emerging as a particularly challenging regime. Although scalability remains limited by the exponential growth of the operator space and by automatic-differentiation costs, the results demonstrate that PINNs constitute a viable and physically grounded route for learning metrologically optimal control strategies in interacting quantum systems.

Robust and high-precision quantum control is crucial but challenging for scalable quantum computation and quantum information processing. Traditional adiabatic control suffers severe limitations on gate performance imposed by environmentally induced noise because of a quantum system's limited coherence time. In this work, we experimentally demonstrate an alternative approach {to quantum control} based on deep reinforcement learning (DRL) on a trapped $^{171}\mathrm{Yb}^{+}$ ion. In particular, we find that DRL leads to fast and robust {digital quantum operations with running time bounded by shortcuts to adiabaticity} (STA). Besides, we demonstrate that DRL's robustness against both Rabi and detuning errors can be achieved simultaneously without any input from STA. Our experiments reveal a general framework of digital quantum control, leading to a promising enhancement in quantum information processing.