Combining physics-informed neural networks with the freezing mechanism for general Hamiltonian learning

The precision required to characterize a Hamiltonian is central to developing advantageous quantum computers, providing powerful advances in quantum sensing and crosstalk mitigation. Traditional methods to determine a Hamiltonian are difficult due to the intricacies of quantum systems, involving numbers of equations and parameters that grow exponentially with the number of qubits. To mitigate these shortcomings, in this paper, we introduce an innovative and effective procedure integrating a physics-informed neural network (PINN) with a freezing mechanism to learn the Hamiltonian parameters efficiently. Although PINN and experimental data alone would become impractical as $N$ increases, the mechanism we introduce freezes the interactions of most of the qubits, leaving just a qubit subsystem to be analyzed by the PINN method. Determination of all physical parameters is accomplished by analyzing the system by parts until completion. We validated the efficacy of our method using simulation data obtained from the IBM quantum computer to obtain the training data and we found that a PINN can learn the two-qubit parameters with high accuracy, achieving a median error of less than $0.1%$ for systems of up to four qubits. We have successfully combined the PINN analysis of two qubits with the freezing mechanism in the case of a four-qubit system.