Machine Learning Application for Quantum System States Fitting

In current research work the application of machine learning methods for predicting the states of quantum systems is considered. The task was to reconstruct the dynamics of the system from a set of experimental data using the Hamiltonian learning method. To achieve this goal, a modern technique for solving neural differential equations was used: Neural ODE. To solve this problem, a simulator was created to generate experimental data. Further, on this dataset, training was carried out and the parameters of the Hamiltonian were selected. Using the Hamiltonian, it was possible to predict the state of a quantum system at an arbitrary moment in time. The experiments were carried out on one-qubit models and a multi-qubit model of the Ising spin chain. During the experiments, the limits of applicability of the algorithm were investigated, as well as the achieved quality.