The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory

• URL: http://arxiv.org/abs/2507.05303v1
• Date: Mon, 07 Jul 2025 06:46:11 GMT
• Title: The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory
• Authors: Guojun Huang, Kai Zhou,
• Abstract summary: We establish a theoretical connection between complex-valued neural networks (CVNNs) and fermionic quantum field theory (QFT)<n>CVNNs equipped with tensor-valued weights intrinsically generate fermionic quantum fields.<n>It extends NN-QFT beyond bosonic theories and opens avenues for encoding fermionic symmetries into machine learning models.
• Score: 4.674525304427816
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we establish a theoretical connection between complex-valued neural networks (CVNNs) and fermionic quantum field theory (QFT), bridging a fundamental gap in the emerging framework of neural network quantum field theory (NN-QFT). While prior NN-QFT works have linked real-valued architectures to bosonic fields, we demonstrate that CVNNs equipped with tensor-valued weights intrinsically generate fermionic quantum fields. By promoting hidden-to-output weights to Clifford algebra-valued tensors, we induce anticommutation relations essential for fermionic statistics. Through analytical study of the generating functional, we obtain the exact quantum state in the infinite-width limit, revealing that the parameters between the input layer and the last hidden layer correspond to the eigenvalues of the quantum system, and the tensor weighting parameters in the hidden-to-output layer map to dynamical fermionic fields. The continuum limit reproduces free fermion correlators, with diagrammatic expansions confirming anticommutation. The work provides the first explicit mapping from neural architectures to fermionic QFT at the level of correlation functions and generating functional. It extends NN-QFT beyond bosonic theories and opens avenues for encoding fermionic symmetries into machine learning models, with potential applications in quantum simulation and lattice field theory.

Related papers

• Quantum Recurrent Embedding Neural Network [11.54075064463256]
  We propose a quantum recurrent embedding neural network (QRENN) inspired by fast-track information pathways in ResNet.<n>We provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus.<n>Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning.
  arXiv  Detail & Related papers  (2025-06-16T07:50:31Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Emergence of global receptive fields capturing multipartite quantum correlations [0.565473932498362]
  In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations. We show that monitoring the neural network weight space while learning quantum statistics allows to develop physical intuition about complex multipartite patterns. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns.
  arXiv  Detail & Related papers  (2024-08-23T12:45:40Z)
• Neural-network quantum states for ultra-cold Fermi gases [49.725105678823915]
  This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.
  arXiv  Detail & Related papers  (2023-05-15T17:46:09Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Power and limitations of single-qubit native quantum neural networks [5.526775342940154]
  Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. We formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks.
  arXiv  Detail & Related papers  (2022-05-16T17:58:27Z)
• The role of coherence theory in attractor quantum neural networks [0.0]
  We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that aQNNs are associated to non-coherence-generating quantum channels.
  arXiv  Detail & Related papers  (2021-12-20T21:26:22Z)
• 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)
• 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.