Neural-Network Quantum States, String-Bond States, and Chiral Topological States

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

doi:10.1103/physrevx.8.011006

Cited by 267 publications

(274 citation statements)

References 94 publications

(133 reference statements)

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“…ZAJ and LW are of equal contribution to this work. We acknowledge Dong-Ling Deng for discussions during his visiting at USTC, we also acknowledge I. Glasser for bringing our attentions to the works [63][64][65], where special case of local quasi-product state is given (the local cluster states are of MPS form or more general tensor network form). ZAJ acknowledges Zhenghan Wang and the math department of UCSB for hospitality.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Entanglement area law for shallow and deep quantum neural network states

Jia

et al. 2020

New J. Phys.

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A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.

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Section: Acknowledgmentsmentioning

confidence: 99%

Entanglement area law for shallow and deep quantum neural network states

Jia

et al. 2020

New J. Phys.

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“…We note that there are also several studies trying to combine the respective advantages of a tensor network and a neural network to give a more powerful representation of the quantum many‐body states …”

Section: Artificial Neural Network Ansatz For Quantum Many‐body Systemmentioning

confidence: 99%

Quantum Neural Network States: A Brief Review of Methods and Applications

et al. 2019

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One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

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“…At the theoretical level, there is a mapping between deep learning and the renormalization group [15], which in turn connects holography and deep learning [16,17], and also allows to design networks from the perspective of quantum entanglement [18]. In turn, neural networks can represent quantum states [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Machine learning by unitary tensor network of hierarchical tree structure

et al. 2019

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The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and flexibilities. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multi-scale entanglement renormalization ansatz. This approach introduces mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states are defined, which encode classes of images into quantum many-body states. We study the quantum features of the TN states, including quantum entanglement and fidelity. We find these quantities could be properties that characterize the image classes, as well as the machine learning tasks.

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Neural-Network Quantum States, String-Bond States, and Chiral Topological States

Cited by 267 publications

References 94 publications

Entanglement area law for shallow and deep quantum neural network states

Entanglement area law for shallow and deep quantum neural network states

Quantum Neural Network States: A Brief Review of Methods and Applications

Machine learning by unitary tensor network of hierarchical tree structure

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