  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.
