Unified Framework for Fermionic Neural Network Quantum States

Recent research by Zejun Liu and Bryan K. Clark presents a unified approach to understanding fermionic neural network quantum states, specifically focusing on neural network backflow (NNBF) and hidden fermion determinant states (HFDS). The paper, titled "A Unifying View of Fermionic Neural Network Quantum States: From Neural Network Backflow to Hidden Fermion Determinant States," was submitted to arXiv on November 15, 2023, and is available for review.

The authors explore how NNBF wave-functions can be adapted to represent HFDS, which are known for their effectiveness in approximating the ground state of fermionic Hamiltonians. They demonstrate that HFDS can be reformulated within the NNBF framework, highlighting that these wave-functions utilize configuration-dependent single-particle orbitals (SPO) parameterized by a neural network.

One significant finding is that HFDS with a certain number of hidden fermions can be expressed as a NNBF with a determinant Jastrow factor and a restricted low-rank additive correction to the SPO. The research indicates that while determinant Jastrow factors can be removed from NNBF wave-functions, this process complicates the additive SPO correction, increasing its rank.

The study also includes numerical and analytical comparisons of the additive SPO corrections, suggesting that larger wave-functions can span a broader space and yield better energy estimates. The results imply that simpler updates to the SPOs tend to be more effective energetically, reinforcing the preference for the standard NNBF approach over other related methods.

This research contributes to the field of quantum physics by providing insights into the efficiency and expressiveness of neural network-based approaches in quantum state representation, which could have implications for future developments in quantum computing and many-body physics. The full paper can be accessed through arXiv at arXiv:2311.09450.