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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 SchrÃ¶dinger 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 SchrÃ¶dinger 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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