Giuseppe Carleo
In this talk I will discuss recent advances in the numerical simulation of driven and open quantum systems using several variational representations of the many-body quantum state based on artificial neural networks [1]. First, I will consider the case of driven, closed quantum systems and take the case of driven spin ½ Heisenberg systems both in one and two dimensions as a benchmark for both the expressive power and the simulation complexity of quantum dynamics with neural quantum states [2].
I will then discuss extensions of neural-network quantum states to study open quantum systems using representations of the density matrix based on Restricted Boltzmann Machines [3]. I will show how this representation can be used to simulate Lindblad dynamics in two-dimensional dissipative spin systems. Finally, I will present a novel variational representation of the density matrix, based on more expressive deep neural networks and with the important property of being automatically positive definite. I will discuss applications of this new representation for finite-temperature quantum simulation [4].
[2] Hofmann et al, in preparation (2021).
[2] Hartmann and Carleo, PRL 122, 250502 (2019).
[3] Torlai and Melko, PRL 120, 240503 (2018).
[4] Vicentini and Carleo, in preparation (2021).