Physics-Informed Neural Networks for Maximizing Quantum Fisher Information in Time-Dependent Many-Body Systems

• URL: http://arxiv.org/abs/2604.18506v1
• Date: Mon, 20 Apr 2026 16:56:31 GMT
• Title: Physics-Informed Neural Networks for Maximizing Quantum Fisher Information in Time-Dependent Many-Body Systems
• Abstract summary: We present a physics-informed neural network (PINN) framework to address the problem of learning counter-diabatic quantum dynamics.<n>We show that PINNs constitute a viable and physically grounded route for learning metrologically optimal control strategies in interacting quantum systems.
• Score: 2.586346262913921
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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