Abstract: Predicting the ground-state properties of quantum many-body systems using classical computers is, in the most general case, an intractable computational problem. Also predicting the output of gate-based quantum computers is computationally prohibitive for classical computers. However, it was recently shown that classical machine-learning algorithms trained on databases of solved instances can predict ground-state properties with rigorous accuracy guarantees.

In this talk, I will discuss the use of deep neural networks — trained via supervised learning — to predict the ground-state properties of disordered quantum systems, as well as the output expectation values of random quantum circuits. Special attention is devoted to the scalability property. This allows us training neural networks on (computationally accessible) small systems, to predict properties of (computationally challenging) larger systems with more particles or more qubits. If time permits, I will also briefly discuss the development of energy-density functionals for density functional theory via deep neural networks with tailored architectures.

References

P. Mujal, À. Martínez Miguel, A. Polls, B. Juliá-Díaz, S. Pilati, Supervised learning of few dirty bosons with variable particle number, SciPost Physics 10, 073 (2021).

S. Cantori, D. Vitali, S. Pilati, Supervised learning of random quantum circuits via scalable neural networks, arXiv:2206.10348 (2022).

E. Costa, G. Scriva, R. Fazio, S. Pilati, Deep learning density functionals for gradient descent optimization, arXiv:2205.08367 (2022).