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Quantum Information Geometry and Boltzmann Machines

  • Dimitri Marinelli (Romanian Institute of Science and Technology - RIST, Romania)
A3 01 (Sophus-Lie room)

Abstract

The Stochastic Reconfiguration algorithm has been recently proposed to efficiently train Neural-Network Quantum States, i.e., Restricted Boltzmann Machines (RBMs) with complex parameters built to simulate the ground state of a quantum many-body problem. The SR algorithm is not only a convenient algorithm for the training these RBMs, but it is also theoretically justified once a non-Euclidean manifold structure, based on Quantum Information Geometry, is defined over the search space associated to a RBM. I will show that the gradient descent optimization algorithm used for the many-body problem is the quantum generalization of the Riemannian natural gradient introduced by Amari. Moreover, I will compare the geometry of the Neural-Network Quantum States with the one of the Quantum Boltzmann Machine.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail