Waveflow: boundary-conditioned normalizing flows applied to fermionic wavefunctions

• URL: http://arxiv.org/abs/2211.14839v3
• Date: Thu, 18 Jul 2024 20:57:51 GMT
• Title: Waveflow: boundary-conditioned normalizing flows applied to fermionic wavefunctions
• Authors: Luca Thiede, Chong Sun, Alán Aspuru-Guzik,
• Abstract summary: We introduce Waveflow, a framework for learning fermionic wavefunctions using boundary-conditioned normalizing flows. We show that Waveflow can effectively resolve topological mismatches and faithfully learn the ground-state wavefunction.
• Score: 3.7135179920970534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 ans\"{a}tze, 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.

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