Learning Solutions to the Schrödinger equation with Neural-Network Quantum States

The theoretical description of several complex quantum phenomena fundamentally relies on many-particle wave functions and our ability to represent and manipulate them. Variational methods in quantum mechanics aim at compact descriptions of many-body wave functions in terms of parameterised ansatz states, and are at present living exciting transformative developments informed by ideas developed in machine learning. In this presentation I will discuss variational representations of quantum states based on artificial neural networks [1] and their use in approximately solving the Schrödinger equation. I will further highlight the general representation properties of such states, the crucial role of physical symmetries, as well as the connection with other known representations based on tensor networks [2]. Finally, I will discuss how some classic ideas in machine learning, such as the Natural Gradient, are being used and re-purposed in quantum computing applications [3].

[1] Carleo and Troyer, Science 365, 602 (2017)
[2] Sharir, Shashua, and Carleo, arXiv:2103.10293 (2021)
[3] Stokes, Izaac, Killoran, and Carleo, Quantum 4, 269 (2020)