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Science China Physics Mechanics and Astronomy

Neural network representations of quantum many-body states

Ying Zhen Yang, Huaixin Cao, Zhanjun Zhang

Published Jun 20, 2019• 13 citations
Publisher
DOI
10.1007/s11433-018-9407-5

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With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.
Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.