Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines.

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ID: 67851
2019
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Abstract
The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground-state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate trial wave function is used to guide the simulation. In the standard approach, this guiding wave function is obtained in a separate simulation that performs a variational minimization. Here we show how to perform PQMC simulations guided by an adaptive wave function based on a restricted Boltzmann machine. This adaptive wave function is optimized along the PQMC simulation via unsupervised machine learning, avoiding the need of a separate variational optimization. As a byproduct, this technique provides an accurate ansatz for the ground-state wave function, which is obtained by minimizing the Kullback-Leibler divergence with respect to the PQMC samples, rather than by minimizing the energy expectation value as in standard variational optimizations. The high accuracy of this self-learning PQMC technique is demonstrated for a paradigmatic sign-problem-free model, namely, the ferromagnetic quantum Ising chain, showing very precise agreement with the predictions of the Jordan-Wigner theory and of loop quantum Monte Carlo simulations performed in the low-temperature limit.
Reference Key
pilati2019selflearningphysical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Pilati, S;Inack, E M;Pieri, P;
Journal physical review e
Year 2019
DOI
10.1103/PhysRevE.100.043301
URL
Keywords
quality improvement medical education problem-based learning competency-based education clinical competences

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