One of the most challenging problems in modern theoretical physics is the so-called many-body problem. Typical many-body systems are composed of a large number of strongly interacting particles. Few such systems are amenable to exact mathematical treatment and numerical techniques are needed to make progress. However, since the resources required to specify a generic many-body quantum state depend exponentially on the number of particles in the system (more precisely, on the number of degrees of freedom), even today's best supercomputers lack sufficient power to exactly encode such states (they can handle only relatively small systems, with less than 45 particles). As we shall see, recent applications of machine learning techniques (artificial neural networks in particular) have been shown to provide highly efficient representations of such complex states, making their overwhelming complexity computationally tractable.

Engineers have modelled the interactions between subatomic components of a complex molecule using a quantum computer, making a significant leap forward in our modelling of chemical reactions. The simulations were carried out by IBM on superconducting hardware, and this milestone just pushed into new territory for what can be achieved using quantum computing. The molecule in question was beryllium hydride – or BeH2. It's not the fanciest molecule in town, but there's still a lot going on between those two hydrogens and single beryllium for a computer to figure out. Molecular simulations aren't revolutionary on their own – classical computers are capable of some pretty detailed models that can involve far more than three atoms.

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.