Bi-Lipschitz Ansatz for Anti-Symmetric Functions

The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with respect to a naturally defined metric. As a result, we are able to obtain quantitative approximation results for approximation of Lipschitz continuous antisymmetric functions. Moreover, we provide preliminary experimental evidence to the improved performance of this ansatz for learning antisymmetric functions. The search for an ansatz for quantum many-body wave functions dates back to the early days of quantum mechanics [Sla29], and has been a central task in quantum chemistry [SO96]. In recent years, it has received renewed excitement primarily due to the advances of neural network-based ansatz.