[理论室报告] Efficient Representation of Quantum Many-body States with Deep Neural Networks
IIIS, Tsinghua University
The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Various variational approaches have been proposed to give efficient representation of quantum many-body states under certain configurations. Recently, a connection has been made between quantum many-body states and the neural network representation. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to popularity of the deep learning methods. Here, we give a rigorous proof that a deep neural network (deep Boltzmann machine) can efficiently represent most physical states, including those generated from dynamics or ground states of complicated Hamiltonians, while a shallow network through a restricted Boltzmann machine, using complexity theory in computer science, cannot efficiently represent those states even without constraint on network architecture. Then we discuss briefly how to train a deep Boltzmann machine. Since related research establish a connection between neural network and quantum many-body physics, we discuss the possibility to introduce physics concepts into machine learning community.
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