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.

Glasser, Ivan, Pancotti, Nicola, August, Moritz, Rodriguez, Ivan D., Cirac, J. Ignacio

Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dimensions. In particular we demonstrate that short-range Restricted Boltzmann Machines are Entangled Plaquette States, while fully connected Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of Restricted Boltzmann Machines and their efficiency at representing many-body quantum states. String-Bond States also provide a generic way of enhancing the power of Neural-Network Quantum States and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of Tensor Networks and the efficiency of Neural-Network Quantum States into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional Tensor Networks, we show that Neural-Network Quantum States and their String-Bond States extension can describe a lattice Fractional Quantum Hall state exactly. In addition, we provide numerical evidence that Neural-Network Quantum States can approximate a chiral spin liquid with better accuracy than Entangled Plaquette States and local String-Bond States. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.

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.

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.

Neural networks are behind technologies that are revolutionizing our daily lives, such as face recognition, web searching, and medical diagnosis. These general problem solvers reach their solutions by being adapted or "trained" to capture correlations in real-world data. Having seen the success of neural networks, physicists are asking if the tools might also be useful in areas ranging from high-energy physics to quantum computing [1]. Four research groups now report on using neural network tools to tackle one of the most computationally challenging problems in condensed-matter physics--simulating the behavior of an open many-body quantum system [2–5]. This scenario describes a collection of particles--such as the qubits in a quantum computer--that both interact with each other and exchange energy with their environment.