Solving the quantum many-body problem with artificial neural networks

By Giuseppe Carleo, Matthias Troyer. 2016

2,329 citations recorded by the source corpus.

Machine learning and quantum physics 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. Science, this issue p. 602; see also p. 580 A machine-learning approach sets a computational benchmark for a prototypical two-dimensional problem. 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.

Subfields: Atomic and Molecular Physics, and Optics

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Citations in the corpus

Learning to predict the cosmological structure formation (2018, background): “This new paradigm is also significantly impacting a variety of domains in the sciences, from biology (24, 25) to chemistry (26, 27) and physics (28, 29).”
Quantum machine learning (2016, neutral): “As quantum physics offers certain enhancements in the storage and processing of information, a clear research track is to develop and tailor these quantum methods to apply to problems when facing ‘big data’ sets [14, 15, 18–20, 48, 49, 54–59].”
Reinforcement Learning in Different Phases of Quantum Control (2017, background): “ML has recently been applied successfully to several problems in equilibrium condensed matter physics [46,47], turbulent dynamics [48,49], and experimental design [50,51], and here we demonstrate that reinforcement learning (RL) provides deep insights into nonequilibrium quantum dynamics [52–57].”
Unsupervised Generative Modeling Using Matrix Product States (2017, background): “” Various Ansätze have been developed to express quantum states, such as the variational Monte Carlo [15], the tensor network (TN) states, and recently artificial neural networks [16].”
Spectral Inference Networks: Unifying Deep and Spectral Learning (2018, methodology): “Typically the class of function approximator is tailored to the system, but neural networks have been used for calculating ground states (Carleo & Troyer, 2017) and excited states (Choo et al., 2018).”
All-optical neural network with nonlinear activation functions (2019, background): “ANNs also show great potential in scientiﬁc researches [3–6], especially in discovering new materials [7], classifying phases of matter [8, 9], representing variational wave functions [10], accelerating Monte Carlo simulations [11, 12], etc.”
Neural-network quantum state tomography (2017, background): “9,14,15 20 Given these favorable properties, RBM-based quantum states are natural candidates for QST of low and high-dimensional many-body systems.”