SciPost Physics Core

SciPost Phys. Core 4, 001 (2021) · published 2 February 2021

• doi: 10.21468/SciPostPhysCore.4.1.001
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Abstract

In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferromagnetic Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack of a detailed comparison of the expressiveness of these increasingly popular, variational ans\"atze.

• Felser et al., Quantum-inspired machine learning on high-energy physics data
  npj Quantum Inf 7, 111 (2021) [Crossref]
• Pei et al., Neural-Network Quantum States for Spin-1 Systems: Spin-Basis and Parameterization Effects on Compactness of Representations
  Entropy 23, 879 (2021) [Crossref]
• Mendes-Santos et al., Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity
  PRX Quantum 2, 030332 (2021) [Crossref]
• Lami et al., Matrix product states with backflow correlations
  Phys. Rev. B 106, L081111 (2022) [Crossref]
• Rieser et al., Tensor networks for quantum machine learning
  Proc. R. Soc. A. 479, 20230218 (2023) [Crossref]
• Zhang et al., Ground state search by local and sequential updates of neural network quantum states
  Phys. Rev. B 107, 165149 (2023) [Crossref]