Bi-Lipschitz Ansatz for Anti-Symmetric Functions
This addresses a specific bottleneck in quantum simulation methods, offering a potentially more stable and quantifiable approach for approximating anti-symmetric functions.
The authors tackled the problem of approximating anti-symmetric functions for quantum many-body simulations by proposing a new universal ansatz that is bi-Lipschitz, enabling quantitative approximation results for Lipschitz continuous anti-symmetric functions and showing preliminary experimental evidence of improved performance.
Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating 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.