Neural-Network Quantum States: Machine-learning the dynamics of many-body quantum systems

by Prof. Filippo Vicentini (Ecole Polytechnique, Paris)

Thursday 15 Jun 2023, 15:00 → 17:00 Europe/Rome

P2A (Dipartimento di Fisica e Astronomia - Edificio Paolotti)

Part he success of Machine Learning owes to the development of neural-networks, variational approximators that can efficiently represent unknown functions living in high-dimensional spaces. Recently, those techniques have been ported to the field of numerical physics and used to approximate inherently high dimensional objects such as the Many-Body Wave-Function [1] or Density-Matrix [2] in an approach generally known as Neural-Network Quantum States (See Ref.3 for a general introduction). This Ab-Initio computational method is not data-driven, and it is therefore much more well behaved than standard machine learning algorithms.

 

In recent years we have proven several connections of this new class of variational ansatz to existing approaches such as tensor networks [4]. Moreover for structured problems such as for the ground state of an Hamiltonian the field has rapidly developed, delivering state-of-the art results for the ground-state properties of several strongly interacting systems, but for the more complex problem of quantum dynamics, NQS have yet to deliver significant improvements over existing methods.

 

In this seminar I will first introduce the basic concepts of the field, discussing how to build reliable, symmetry aware wave-function approximations using Neural Networks. Then, I will devote significant time to discuss recent advances in the treatment of variational dynamics, showing various quenches and concluding with recent developments in the field of Entanglement Phase transitions [5].

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[1] Carleo and Troyer, Science 355, 602 (2017)

[2] F Vicentini, A Biella, N Regnault, C Ciuti, Phys. Rev. Lett 122 (25), 250503

[3] A. Dawid et Al, arXiv:2204.04198 (2022)

[4] D. Wu, R. Rossi, F. Vicentini, G. Carleo, arXiv:2206.12363 (2022)

[5] A. Sinibaldi, C. Giuliani, G. Carleo, F. Vicentini, arXiV: 2305.14294 (2023)