  State-of-the-art machine learning techniques promise to become a powerful
tool in statistical mechanics via their capacity to distinguish different
phases of matter in an automated way. Here we demonstrate that convolutional
neural networks (CNN) can be optimized for quantum many-fermion systems such
that they correctly identify and locate quantum phase transitions in such
systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample
the many-fermion system, we show that the Green's function (but not the
auxiliary field) holds sufficient information to allow for the distinction of
different fermionic phases via a CNN. We demonstrate that this QMC + machine
learning approach works even for systems exhibiting a severe fermion sign
problem where conventional approaches to extract information from the Green's
function, e.g.~in the form of equal-time correlation functions, fail. We expect
that this capacity of hierarchical machine learning techniques to circumvent
the fermion sign problem will drive novel insights into some of the most
fundamental problems in statistical physics.
