ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation

• URL: http://arxiv.org/abs/2304.01996v3
• Date: Tue, 16 Apr 2024 17:55:48 GMT
• Title: ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation
• Authors: Zhuo Chen, Laker Newhouse, Eddie Chen, Di Luo, Marin Soljačić,
• Abstract summary: We develop a novel architecture, Autoregressive NeuralNet, which bridges tensor networks and autoregressive neural networks. We show that Autoregressive NeuralNet parameterizes normalized wavefunctions, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.
• Score: 5.283885355422517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• CTRQNets & LQNets: Continuous Time Recurrent and Liquid Quantum Neural Networks [76.53016529061821]
  Liquid Quantum Neural Network (LQNet) and Continuous Time Recurrent Quantum Neural Network (CTRQNet) developed. LQNet and CTRQNet achieve accuracy increases as high as 40% on CIFAR 10 through binary classification.
  arXiv  Detail & Related papers  (2024-08-28T00:56:03Z)
• Quantum Neural Network for Quantum Neural Computing [0.0]
  We propose a new quantum neural network model for quantum neural computing. Our model circumvents the problem that the state-space size grows exponentially with the number of neurons. We benchmark our model for handwritten digit recognition and other nonlinear classification tasks.
  arXiv  Detail & Related papers  (2023-05-15T11:16:47Z)
• Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superposition [16.1356415877484]
  We introduce quantum hypernetworks as a mechanism to train binary neural networks on quantum computers. We show that our approach effectively finds optimal parameters, hyperparameters and architectural choices with high probability on classification problems. Our unified approach provides an immense scope for other applications in the field of machine learning.
  arXiv  Detail & Related papers  (2023-01-19T20:06:48Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Quantum Neural Networks -- Computational Field Theory and Dynamics [0.0]
  A formalization of quantum artificial neural networks as dynamical systems is developed. The implications for quantum computer science, quantum complexity research, quantum technologies and neuroscience are also addressed.
  arXiv  Detail & Related papers  (2022-03-19T10:37:23Z)
• Scaling of neural-network quantum states for time evolution [0.0]
  We benchmark the variational power of different shallow and deep neural autoregressive quantum states to simulate global dynamics of a non-integrable quantum Ising chain. We find that the number of parameters required to represent the quantum state at a given accuracy increases exponentially in time.
  arXiv  Detail & Related papers  (2021-04-21T18:00:07Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Quantum neural networks with deep residual learning [29.929891641757273]
  In this paper, a novel quantum neural network with deep residual learning (ResQNN) is proposed. Our ResQNN is able to learn an unknown unitary and get remarkable performance.
  arXiv  Detail & Related papers  (2020-12-14T18:11:07Z)
• Quantum Deformed Neural Networks [83.71196337378022]
  We develop a new quantum neural network layer designed to run efficiently on a quantum computer. It can be simulated on a classical computer when restricted in the way it entangles input states.
  arXiv  Detail & Related papers  (2020-10-21T09:46:12Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.