mlsanityData to 14 Oct 2026

Continuous-variable neural-network quantum states and the quantum rotor model

arXiv 2107.07105 ↗First posted 15 Jul 2021quant-ph cond-mat.dis-nn cs.LGcited by 2

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Abstract (arXiv)

We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 6 of its 37 references that are in the map. First posted on arXiv 15 Jul 2021.

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6 of 37 references.

References · 6

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  3. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 200
  4. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 28
  5. 2017Equivalence of restricted Boltzmann machines and tensor network statescited by 27
  6. 2020Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum statescited by 15

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Citing papers per year: 2022: 2.

2 papers.

  1. 2022Numerical and geometrical aspects of flow-based variational quantum Monte Carlocited by 1
  2. 2022Estimating truncation effects of quantum bosonic systems using sampling algorithmscited by 0

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