Abstract: Machine-learning-based approaches, routinely adopted in cutting-edge industrial applications, are being increasingly adopted to study fundamental problems in science. Many-body physics is very much at the forefront of these exciting developments, given its intrinsic "big-data" nature. In this seminar I will present selected applications to the quantum realm.
First, I will discuss how a systematic, and controlled machine learning of the many-body wave-function can be realized. This goal is achieved by a variational representation of quantum states based on artificial neural networks [1].
I will then discuss recent applications in diverse domains, focusing on prototypical open problems in many-body quantum physics.
I will especially focus on the problem of accurately describing interacting fermions, in Condensed Matter [2], Chemistry [3], and Nuclear Matter [4] — where these approaches have significantly improved over previous variational descriptions.

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[1] Carleo and Troyer, Science 355, 602 (2017)
[3] Moreno et al., PNAS 119, e2122059119 (2022)
[4] Hermann et al., Nat. Chemistry 12, 891 (2020)
[5] Adams et al., Phys. Rev. Lett. 127, 022502 (2021)