  A central problem in quantum mechanics involves solving the Electronic
Schrodinger Equation for a molecule or material. The Variational Monte Carlo
approach to this problem approximates a particular variational objective via
sampling, and then optimizes this approximated objective over a chosen
parameterized family of wavefunctions, known as the ansatz. Recently neural
networks have been used as the ansatz, with accompanying success. However,
sampling from such wavefunctions has required the use of a Markov Chain Monte
Carlo approach, which is inherently inefficient. In this work, we propose a
solution to this problem via an ansatz which is cheap to sample from, yet
satisfies the requisite quantum mechanical properties. We prove that a
normalizing flow using the following two essential ingredients satisfies our
requirements: (a) a base distribution which is constructed from Determinantal
Point Processes; (b) flow layers which are equivariant to a particular subgroup
of the permutation group. We then show how to construct both continuous and
discrete normalizing flows which satisfy the requisite equivariance. We further
demonstrate the manner in which the non-smooth nature ("cusps") of the
wavefunction may be captured, and how the framework may be generalized to
provide induction across multiple molecules. The resulting theoretical
framework entails an efficient approach to solving the Electronic Schrodinger
Equation.
