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Convergence to the fixed-node limit in deep variational Monte Carlo.

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Deep neural networks in variational quantum Monte Carlo (QMC) improve accuracy by overcoming basis set limitations and reaching the fixed-node limit. Larger networks yield more accurate variational energies, enhancing QMC

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Machine Learning

Background:

  • Variational quantum Monte Carlo (QMC) is a powerful ab initio method for solving the electronic Schrödinger equation.
  • The accuracy of variational QMC is often limited by the flexibility of trial wavefunctions (Ansätze).
  • Deep neural networks offer a promising new avenue for constructing highly flexible Ansätze in QMC.

Purpose of the Study:

  • To analyze the convergence behavior of deep neural network Ansätze in variational QMC.
  • To understand how increasing network size impacts the approach to the fixed-node limit.
  • To benchmark the performance of deep variational QMC against traditional methods.

Main Methods:

  • Investigated deep neural network Ansätze (PauliNet, FermiNet) within variational QMC.
  • Analyzed the impact of network size on achieving the mean-field complete-basis-set limit.
  • Performed hyperparameter scans for deep Jastrow factors in LiH and H4 systems.
  • Benchmarked mean-field and many-body Ansätze for H2O, including Slater-Jastrow and Slater-Jastrow-backflow variations.

Main Results:

  • Deep neural networks successfully overcome small basis set limitations, reaching the mean-field complete-basis-set limit.
  • Sufficiently large deep neural network Ansätze achieve variational energies at the fixed-node limit for electron correlation.
  • Deep variational QMC significantly improved the recovery of fixed-node correlation energy compared to previous methods.
  • A single-determinant Slater-Jastrow-backflow Ansatz demonstrated the ability to overcome fixed-node limitations.

Conclusions:

  • Deep neural networks provide a pathway to highly accurate variational QMC calculations, approaching the accuracy of diffusion QMC.
  • The flexibility of deep Ansätze allows for overcoming limitations of traditional trial wavefunctions.
  • This work provides insights into the convergence of deep variational QMC and guides future neural network architecture development.