Neural-network quantum states
Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim A. Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini · Cambridge University Press eBooks · 2025
In this chapter, we review the growing field of research aiming to represent quantum states with machine learning models, known as neural quantum states. We introduce the key ideas and methods and review results about the capacity of such representations. We discuss in details many applications of neural quantum states, including but not limited to finding the ground state of a quantum system, solving its time evolution equation, quantum tomography, open quantum system dynamics and steady-state solution, and quantum chemistry. Finally, we discuss the challenges to be solved to fully unleash the potential of neural quantum states.