Whenever a reliable, first-principles understanding of a many-body quantum mechanical problem is required, Monte Carlo methods are needed. Indeed, putting aside uncontrolled approximations based on mean-field or perturbative approaches, numerical methods are the most dependable tools, and in the quantum many-body problem this means using quantum Monte Carlo (QMC) techniques, if exact answers are required. For these reasons, QMC has been in use for decades in a variety of fields, ranging from quantum chemistry to atomic, condensed matter and nuclear physics, as well as in Lattice QCD.

Gathering experts from all those areas, the INT program "Advances in quantum Monte Carlo techniques for non-relativistic many-body systems" aimed to understand the level of progress that has been reached in recent years. In particular, the program addressed the definition of a standard problem to gauge the efficiency and efficacy of the large number of flavors of QMC that exist in the literature. This includes lattice (with and without improved actions) as well as continuum formulations; zero and finite temperature; and strategies to deal with the infamous sign problem. Participants (over 50 of them) attended talks in the morning, followed by dynamic discussion sessions in the afternoon. The variety of areas involved provided remarkable points of contact to compare and contrast the use of the algorithms and machines, as well the challenges faced by each field. Among the participants there were experts in the various areas at all levels, including junior faculty, postdocs and graduate students. This allowed the participants to have an exceptional perspective on what is known to work, what has been tried in the past, what challenges remain unaddressed, and what new out-of-the-ordinary ideas are being tested. In addition to the latest technical advances, a number of talks focused on the latest applications, such as QMC for the chiral effective field theory of nuclear interactions, or quantum gases in optical lattices.

This program contributed to enhance among the participants the sense of a "quantum Monte Carlo community" that operates over a wide range of different sub-fields in physics, but that can make use of the common technical language to promote cross-fertilization both in terms of advancing the algorithms, and of better understanding phenomenological aspects by looking at them from different perspectives. Most participants expressed the need of repeating similar experiences in the next years.

The friendly and supportive environment provided by INT helped the researchers to establish a number of new connections and new projects that will contribute to further strengthen the use ad applications of Quantum Monte Carlo methods across physics and chemistry in the near future