A Bayesian machine-learning approach to the quantum many-body problemInvited Talk: George Booth, King's College London*

The quantum many-body problem is a keystone challenge, with developments impacting a huge diversity of fields. At its heart is an exponentially complex space, which naturally lends itself to synergistic developments with the machine learning community. In this presentation, we will consider the problem from a Bayesian perspective, whereby the many-body wavefunction is rigorously and statistically inferred from a set of support states, in a novel form we have denoted the Gaussian Process State. We find that connections from this viewpoint naturally emerge with both tensor networks and neural quantum states. We will show that as well as providing a compact, expressive and systematically improvable approximation, we can also lean more heavily on machine learning ideas of generalization errors and regularization which can be efficiently formulated in this framework, to extend the toolset at hand to treat the challenge of quantum many-body problems.