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

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