Waveflow: boundary-conditioned normalizing flows applied to fermionic wavefunctions
This work addresses the problem of scalable and expressive wavefunction ansätze for many-body electronic structures in quantum chemistry, representing an incremental improvement over existing methods.
The authors tackled the limited expressiveness of Slater determinants in fermionic wavefunction ansätze by introducing Waveflow, a framework using boundary-conditioned normalizing flows to impose antisymmetry, and applied it to a one-dimensional many-electron system, achieving effective resolution of topological mismatches and learning of the ground-state wavefunction.
An efficient and expressive wavefunction ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wavefunction ansätze, this construction can result in limited expressiveness when the targeted wavefunction is highly complex. In this work, we introduce Waveflow, an innovative framework for learning many-body fermionic wavefunctions using boundary-conditioned normalizing flows. Instead of relying on Slater determinants, Waveflow imposes antisymmetry by defining the fundamental domain of the wavefunction and applying necessary boundary conditions. A key challenge in using normalizing flows for this purpose is addressing the topological mismatch between the prior and target distributions. We propose using O-spline priors and I-spline bijections to handle this mismatch, which allows for flexibility in the node number of the distribution while automatically maintaining its square-normalization property. We apply Waveflow to a one-dimensional many-electron system, where we variationally minimize the system's energy using variational quantum Monte Carlo (VQMC). Our experiments demonstrate that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wavefunction.