to implement the simulations. It grows exponentially with the system size when no or poor guiding wave-functions are utilized. Nevertheless, we demonstrate that when good enough guiding wave-functions are used – in our case we choose artificial neural networks – the computational complexity seems to go from exponential to polynomial in the system size. We advocate for a search of more efficient guiding wave functions since they could determine when PQMC simulations are feasible on classical computers, a question closely related to a provable need or speed-up of a quantum computer.

References:

- E. M. Inack and S. Pilati, Phys. Rev. E 92, 053304 (2015)

- E. M. Inack, G. Giudici, T. Parolini, G. Santoro and S. Pilati, Phys. Rev. A 97, 032307 (2018)

- E. M. Inack, G. Santoro, L. Dell’Anna, and S. Pilati, arXiv:1809.03562v1

discuss applications to different models where we successfully interpreted what was learned by the neural networks. ]]>

**References**

has seen a rapid development driven, in particular, by the remarkable progress

in quantum simulators, which today provide access to dynamics in quantum

matter with an unprecedented control. However, the efficient numerical

simulation of nonequilibrium real-time evolution in isolated quantum matter

still remains a key challenge for current computational methods especially

beyond one spatial dimension. In this talk I will present a versatile and

efficient machine learning inspired approach. I will first introduce the

general idea of encoding quantum many-body wave functions into artificial

neural networks. I will then identify and resolve key challenges for the

simulation of real-time evolution, which previously imposed significant

limitations on the accurate description of large systems and long-time

dynamics. As a concrete example, I will consider the dynamics of the

paradigmatic two-dimensional transverse field Ising model, where we observe

collapse and revival oscillations of ferromagnetic order and demonstrate that

the reached time scales are comparable to or exceed the capabilities of state-

of-the-art tensor network methods. ]]>