Time-dependent Hamiltonian identification

Mohan Sarovar, Jun Zhang

Francisco Soto, Braulio Misael Villegas-Martínez, H. M. Moya-Cessa

Shi‐Yao Hou, Hang Li, Gui‐Lu Long

Sidney Golden

A minimum principle is described which has von Neumann’s equation of motion of the statistical operator as its ultimate solution. When the statistical operator is initially restricted to be a projection of trace unity, the minimum principle has Schrödinger’s time−dependent equation as its ultimate solution. As a result, the present minimum principle is shown to be a generalization of one first introduced by McLachlan, with a modification of the Dirac−Frenkel variational principle as a necessary consequence. In physical terms, the quantity that is minimized is shown to be the mean−squared deviation of an effective time−dependent Hamiltonian, which can be attributed to a time−dependent statistical operator initially chosen to describe a system, from the actual time−dependent Hamiltonian of the system. Examples of approximate solutions to von Neumann’s equation and Schrödinger’s equation that are obtained by use of the minimum principle confirm this identification.

Ladislav Šamaj

Antonio Guerra, Daniel Uzcategui-Contreras, Aldo Delgado +1 more

Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a physics-informed deep learning approach based on Physics-Informed Neural Networks to estimate these operators over the full time domain. By incorporating physical constraints such as unitarity and leveraging the second-order Magnus expansion on the evolution operator, the proposed framework enables the estimation of unitary matrices at different time intervals. The model is trained using simulated unitary operators and evaluated on quantum systems ranging from 2 to 6 qubits. For larger many-body systems, specifically those with 7 and 8 qubits, the same methodology is employed to reconstruct an effective time-dependent Hamiltonian, from which the corresponding time-evolution operator is computed over the entire temporal domain. The proposed framework achieves fidelities exceeding 0.92 using a limited number of unitary samples, indicating a potential reduction in measurement and data acquisition costs. These results highlight the effectiveness of the approach for data-driven simulation and identification of quantum dynamical systems, with direct relevance to quantum computing and quantum simulation applications.