Machine learning wavefunction

Kaitlin McCardle

Mandira Dey, Debashree Ghosh

ABSTRACT The exact solution of strongly correlated systems is a computationally demanding problem, scaling exponentially with system size. Over the decades, several approximate methods have been developed to address this scaling problem. Among these, matrix product state (MPS) has emerged as physically intuitive and polynomially scaling. Methods such as density matrix renormalization group (DMRG), time evolution block decimation (TEBD), etc., use the underlying MPS wavefunction ansatz to optimize it variationally. MPS can also be utilized as a machine learning model to select the most important electronic configurations, as employed in selected configuration interactions. This work uses machine learning (ML) optimization of MPS wavefunctions to eliminate the need for multiple diagonalizations during the optimization process. We compare the performance of the machine‐learned MPS‐assisted selected configuration interaction approach, often mentioned as a classifier, to the machine‐learned MPS wavefunction ansatz itself. While showing the viability of the machine‐learned MPS ansatz, it is observed that within ML, MPS is best used as a selected configuration interaction.

Rei Sakuma, Y. Iiyama, Lento Nagano +2 more

Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes low-resolution (low plane-wave energy cutoff) one-particle molecular wavefunctions in plane-wave basis as input and generates high-resolution (high plane-wave energy cutoff) wavefunctions in fictitious one-dimensional systems, and study the performance of different learning models. We show that the trained models can generate wavefunctions having higher fidelity values with respect to the ground-truth wavefunctions than a simple linear interpolation, and the results can be improved both qualitatively and quantitatively by including data-dependent information in the ansatz. On the other hand, the accuracy of the current approach deteriorates for wavefunctions calculated in electronic configurations not included in the training dataset. We also discuss the generalization of this approach to many-body electron wavefunctions.

George Chapline

Gennadiy N Burlak

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.

Michael Brooks