Machine learning ground-state energies and many-body wave function

          @misc{ pirsa_PIRSA:19070011,
            doi = {10.48660/19070011},
            url = {https://pirsa.org/19070011},
            author = {Pilati, Sebastiano},
            keywords = {Condensed Matter},
            language = {en},
            title = {Machine learning ground-state energies and many-body wave function},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {jul},
            note = {PIRSA:19070011 see, \url{https://pirsa.org}}
          }
          

Abstract

In the first part of this presentation, I will present supervised machine-learning studies of the low-lying energy levels of disordered quantum systems. We address single-particle continuous-space models that describe cold-atoms in speckle disorder, and also 1D quantum Ising glasses. Our results show that a sufficiently deep feed-forward neural network (NN) can be trained to accurately predict low-lying energy levels. Considering the long-term prospect of using cold-atoms quantum simulator to train neural networks to solve computationally intractable problems, we consider the effect of random noise in the training data, finding that the NN model is remarkably resilient. We explore the use of convolutional NN to build scalable models and to accelerate the training process via transfer learning. In the second part, I will discuss how generative stochastic NN, specifically, restricted and unrestricted Boltzmann machines, can be used as variational Ansatz for the ground-state many-body wave functions. In particular, we show how to employ them to boost the efficiency of projective quantum Monte Carlo (QMC) simulations, and how to automatically train them within the projective QMC simulation itself. SP, P. Pieri, Scientific Reports 9, 5613 (2019) E. M. Inack, G. Santoro, L. Dell’Anna, SP, Physical Review B 98, 235145 (2018)