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.
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.
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.