Machine learning has been used to beat a human competitor in a game of Go (1), a game that has long been viewed as the most challenging of board games for artificial intelligence. Research is now under way to investigate whether machine learning can be used to solve long outstanding problems in quantum science. Carleo and Troyer used an artificial neural network to represent the wave function of a quantum many-body system and to make the neural network'learn' what the ground state (or dynamics) of the system is. Their approach is found to perform better than the current state-of-the-art numerical simulation methods.

Machine learning techniques have so far proved to be very promising for the analysis of data in several fields, with many potential applications. However, researchers have found that applying these methods to quantum physics problems is far more challenging due to the exponential complexity of many-body systems. Quantum many-body systems are essentially microscopic structures made up of several interacting particles. While quantum physics studies have focused on the collective behavior of these systems, using machine learning in these investigations has proven to be very difficult. With this in mind, a team of researchers at Harvard University recently developed a quantum circuit-based algorithm inspired by convolutional neural networks (CNNs), a popular machine learning technique that has achieved remarkable results in a variety of fields.

The complexity of interacting quantum many-body systems leads to exceedingly long recurrence times of the initial quantum state for all but the smallest systems. Thus, experimentally, recurrences can only be determined on the level of the accessible observables. Realizing a commensurate spectrum of collective excitations in one-dimensional superfluids, we demonstrate recurrences of coherence and long-range order in an interacting quantum many-body system containing thousands of particles. Our findings will enable the study of the coherent dynamics of large quantum systems even after they have reached a transient thermal-like state.

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.

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.