Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Q47: Machine Learning for Quantum Matter IFocus Recordings Available

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Sponsoring Units: DCOMP GDS DMP Chair: Anna Dawid, University of Warsaw Room: McCormick Place W470B 
Wednesday, March 16, 2022 3:00PM  3:36PM 
Q47.00001: Highly accurate potential energy surfaces with deep quantum Monte Carlo Invited Speaker: Frank Noe The combination of deep learning with variational Monte Carlo offers a promising new direction to compute properties of quantum systems with high accuracy and acceptable computational complexity without having to specifically taylor the method to the specific molecule or material. Building on the PauliNet deep quantum Monte Carlo architecture we present new approaches and results on using fermionic networks to solve quantum chemical systems with high accuracy. 
Wednesday, March 16, 2022 3:36PM  4:12PM 
Q47.00002: Artificial neural networks for quantum manybody problems Invited Speaker: Yusuke Nomura It is a great challenge to accurately represent quantum manybody states. In this talk, we will show that Boltzmann machines used in machine learning can be useful for analyzing quantum manybody problems. 
Wednesday, March 16, 2022 4:12PM  4:24PM Withdrawn 
Q47.00003: Abinitio solutions to the manybody Schödinger Equation with Deep Neural Networks James Spencer, David Pfau, Aleksander Botev, Gino Cassella, Halvard Sutterud, W Matthew C Foulkes Variational approximations to the manybody Schrödinger equation can provide accurate energies and properties, but the accuracy is determined by the flexibility and representation capacity of the wavefunction form. We demonstrate that deep neural networks with physicallymotivated structures offer a compact and highly accurate wavefunction Ansatz, can be efficiently optimized using variational Monte Carlo, and frequently outperform even diffusion Monte Carlo calculations using conventional wavefunctions. We demonstrate the applicability of our approach on a range of atoms, small molecules and model reactions. 
Wednesday, March 16, 2022 4:24PM  4:36PM 
Q47.00004: Fermionic variational wavefunctions from neuralnetwork constrained hidden states Javier Robledo Moreno, Giuseppe Carleo, Antoine Georges, James Stokes For the variational simulation of fermionic systems in first quantization, trial wavefunctions must be antisymmetric functions of the particle configurations, while being able to capture correlations beyond the singleparticle Slater determinants. This is typically achieved either by considering backflow transformations, or with Jastrowlike projection factors. Despite the recent success of neuralnetwork based parametrizations, the strong coupling limit remains to be a challenging regime. 
Wednesday, March 16, 2022 4:36PM  4:48PM 
Q47.00005: Bosonic Neural Quantum States in Continuous Space Gabriel M Pescia Neural quantum states (NQS) have been shown to be a powerful tool in the computation of groundstates for several quantum mechanical manybody systems. 
Wednesday, March 16, 2022 4:48PM  5:00PM 
Q47.00006: Determinantfree fermionic wave function using feedforward neural networks Koji Inui, Yasuyuki Kato, Yukitoshi Motome In recent years, there has been a remarkable increase in research on approximating manybody wave functions by neural networks. It is, however, still challenging to find the ground state of fermionic manybody systems due to the complex sign structure arising from the anticommutation relation between fermions. The sign structure is usually implemented to a variational wave function by the Slater determinant (or Pfaffian), which is a computational bottleneck because of the numerical cost of O(N^{3}) for N particles. We here propose a framework to bypass this bottleneck by explicitly calculating the sign changes associated with particle exchanges in real space and using fully connected neural networks for optimizing the rest parts of the wave function. This reduces the computational cost to O(N^{2}) or less. In addition, we device some numerical tricks for stabilization of the calculations, e.g., a reweighting method in Monte Carlo sampling. We apply our method to the Hubbard model with 6x6 lattice sites and N=10, and find that it achieves a lower energy than the manyvariable variational Monte Carlo calculation. 
Wednesday, March 16, 2022 5:00PM  5:12PM 
Q47.00007: Equivariant Variational Monte Carlo for quantum systems Jannes Nys Variational Monte Carlo algorithms based on sampling basis states in a computational basis often suffer from breaking of SU(2)symmetry when the basis states transform nontrivially under the symmetry group. We propose two ways to solve this issue. On one hand, we construct basis states that transform trivially under the continuous SU(2) symmetry group, and use them as input states of a suitable variational wave function. On the other hand, we move the transformation requirements of SU(2) to the variational wave function, allowing us to use simple basis states as its input. In this way, we reconcile SU(2) symmetry with basis states defined on the local degrees of freedom, allowing us to additionally include lattice symmetries. We show that both constructions lead to accurate variational states on antiferromagnetic and frustrated heisenberg systems in one and two dimensions. 
Wednesday, March 16, 2022 5:12PM  5:24PM 
Q47.00008: Improving Convolutional Neural Network Wave Functions Optimization Douglas G Hendry, Adrian E Feiguin Convolutional neural networks (CNN) have become a staple of modern machine learning research, where they are ideally suited for learning local features with spatial inputs such as images. This has made them an obvious candidate for variational wave functions to represent 2D systems. However, their optimization with state of the art variational Monte Carlo (VMC) methods relies on natural gradient descent, which becomes intractable for a large number of variational parameters. This is due to requiring inverting a matrix whose dimensions scale with the number of parameters. We propose an approximate natural gradient method that minimizes an upper bound on the exact natural gradient descent residual. The method relies on grouping the parameters of the CNN by dependency and inverting submatrices of dimension equal to the number of parameters in that group. We Implement our method on a deep CNN with ResBlock architecture and complex valued parameters. We benchmark our results on the frustrated 2D J1J2 Heisenberg model on the square lattice. 
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