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

摘要

We propose an effective approach for rapid estimation of the energy spectrum of quantum systems with the use of the machine learning (ML) algorithm. In the ML approach (backpropagation), the wavefunction data obtained from experiments are interpreted as the attribute 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 are fed into the neural network, with the goal of making prediction about the spectrum of quantum numbers. We found that in such a configuration, the training process occurs with rapid convergence if the number of analyzed quantum states is not too large. The two qubit entanglement is studied as well. The accuracy of the test prediction (after training) reached 98%. It is considered that the ML approach opens up important perspectives to plane the quantum measurements and optimal monitoring of complex quantum objects.