It's notoriously difficult to make sense of Quantum mechanics, and it's equally difficult to calculate the behavior of many quantum systems. That's due in part to the description of a quantum system called its wavefunction. The wavefunction for most single objects is pretty complicated on its own, and adding a second object makes predicting things even harder, since the wavefunction for the entire system becomes a mixture of the two individual ones. The more objects you add, the harder the calculations become. As a result, many-body calculations are usually done through methods that produce an approximation.

The same type of artificial intelligence that mastered the ancient game of Go could help wrestle with the amazing complexity of quantum systems containing billions of particles. Google's AlphaGo artificial neural network made headlines last year when it bested a world champion at Go. After marvelling at this feat, Giuseppe Carleo of ETH Zurich in Switzerland thought it might be possible to build a similar machine-learning tool to crack one of the knottiest problems in quantum physics. Now, he has built just such a neural network – which could turn out to be a game changer in understanding quantum systems. Go is far more complex than chess, in that the number of possible positions on a Go board could exceed the number of atoms in the universe.

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.

Elucidating the behavior of quantum interacting systems of many particles remains one of the biggest challenges in physics. Traditional numerical methods often work well, but some of the most interesting problems leave them stumped. Carleo and Troyer harnessed the power of machine learning to develop a variational approach to the quantum many-body problem (see the Perspective by Hush). The method performed at least as well as state-of-the-art approaches, setting a benchmark for a prototypical two-dimensional problem. With further development, it may well prove a valuable piece in the quantum toolbox.

The groundwork for machine learning was laid down in the middle of last century. When your bank calls to ask about a suspiciously large purchase made on your credit card at a strange time, it's unlikely that a kindly member of staff has personally been combing through your account. Instead, it's more likely that a machine has learned what sort of behaviours to associate with criminal activity – and that it's spotted something unexpected on your statement. Silently and efficiently, the bank's computer has been using algorithms to watch over your account for signs of theft. Monitoring credit cards in this way is an example of "machine learning" – the process by which a computer system, trained on a given set of examples, develops the ability to perform a task flexibly and autonomously.