Evaluation of the spectrum of a quantum system using machine learning based on incomplete information about the wavefunctions

We propose an effective approach to rapid estimation of the energy spectrum of quantum systems with the use of machine learning (ML) algorithm. In the ML approach (back propagation), the wavefunction data known from experiments is interpreted as the attributes class (input data), while the spectrum of quantum numbers establishes the label class (output data). To evaluate this approach, we employ two exactly solvable models with the random modulated wavefunction amplitude. The random factor allows modeling the incompleteness of information about the state of quantum system. The trial wave functions fed into the neural network, with the goal of making prediction about the spectrum of quantum numbers. We found that in such configuration, the training process occurs with rapid convergence if the number of analyzed quantum states is not too large. The two qubits entanglement is studied as well. The accuracy of the test prediction (after training) reached 98 percent. Considered ML approach opens up important perspectives to plane the quantum measurements and optimal monitoring of complex quantum objects.