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 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.

An efficient state estimation model, neural network estimation (NNE), empowered by machine learning techniques, is presented for full quantum state tomography (FQST). A parameterized function based on neural network is applied to map the measurement outcomes to the estimated quantum states. Parameters are updated with supervised learning procedures. From the computational complexity perspective our algorithm is the most efficient one among existing state estimation algorithms for full quantum state tomography. We perform numerical tests to prove both the accuracy and scalability of our model.

Rocchetto, Andrea, Grant, Edward, Strelchuk, Sergii, Carleo, Giuseppe, Severini, Simone

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a new representation of states based on variational autoencoders. Variational autoencoders are a type of generative model in the form of a neural network. We probe the power of this representation by encoding probability distributions associated with states from different classes. Our simulations show that deep networks give a better representation for states that are hard to sample from, while providing no benefit for random states. This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in first generation quantum hardware.

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.