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DTSTAMP:20210402T160557Z
LOCATION:Track 7
DTSTART;TZID=America/New_York:20201111T163000
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UID:submissions.supercomputing.org_SC20_sess199_ws_dls107@linklings.com
SUMMARY:Vandermonde Wave Function Ansatz for Improved Variational Monte Ca
 rlo
DESCRIPTION:Workshop\n\nVandermonde Wave Function Ansatz for Improved Vari
 ational Monte Carlo\n\nAcevedo, Curry, Leroux, Joshi, Malaya\n\nSolutions 
 to the Schrödinger equation can be used to predict the electronic structur
 e of molecules and materials and therefore infer their complex physical an
 d chemical properties. Variational Quantum Monte Carlo (VMC) is a techniqu
 e that can be used to solve the weak form of the Schrödinger equation. App
 lying VMC to systems with N electrons involves evaluating the determinant 
 of an N x N matrix. The evaluation of this determinant scales as N^3 and i
 s the main computational cost in the VMC process. In this work we investig
 ate an alternative VMC technique based on the Vandermonde determinant. The
  Vandermonde determinant is a product of pairwise differences and so evalu
 ating it scales as N^2. Therefore, our approach reduces the computational 
 cost by a factor of N. \n\nWe implemented VMC using the new low cost appro
 ach in PyTorch and compared its use in approximating the ground state ener
 gy of various quantum systems against existing techniques, starting with t
 he one-dimensional particle in a box and moving on to more complicated ato
 mic systems with multiple particles. We also implemented the Vandermonde d
 eterminant as a part of PauliNet, a deep-learning architecture for VMC. Wh
 ile the new method is computationally efficient and obtains a reasonable a
 pproximation for wavefunctions of atomic systems, it does not reach the ac
 curacy of the Hartree-Fock method that relies on the Slater determinant. W
 e observed that while the use of neural networks in VMC can result in high
 ly accurate solutions, further new approaches are needed to best balance c
 omputational cost with accuracy.\n\nRegistration Category: Workshop Reg Pa
 ss
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