The growing entanglement in scaled-up or time-evolved strongly correlated many-body systems poses a fundamental challenge in an accurate, yet affordable description of their quantum states. In the light of neural-network quantum states (NQS) [1], such an entanglement barrier may be finally overcome. Evidence exists that such ansätze can indeed simulate highly entangled (volume-law) states with only polynomial cost [2,3], thereby achieving a quantum state compression. That being said, there is an apparent mismatch between the entangled states, that each NQS ansatz targets, and the physically or chemically relevant ones [4]. Recent developments in fermionic NQS ansätze [5,6] showed that, despite the validity of the universal approximation theorem, a network agnostic of the indistinguishability of the particles may have a harder time achieving the same accuracy than a network that is physically aware. In this work, we set out to understand the reason behind the compact expression of highly entangled quantum states by a physically aware NQS design, specifically the neural backflow ansatz for fermions [5]. We then incorporate these insights into the construction of a bosonic analogue, where these advantages could be even more pronounced. Applications will then consider vibrational ground and time-evolved states calculations.

[1] Carleo G., Troyer M., Science, 2017, 355, 6325, 602

[2] Deng D.-L., Li X., S. D. Sarma, Phys. Rev. X, 2017, 7, 2, 021021

[3] Levine Y., Sharir. O, et al., Phys. Rev. Lett., 2019, 122, 6, 065301

[4] Passetti G., Hofmann D., et al. Phys. Rev. Lett., 2023, 131, 3, 036502

[5] Liu A.-J., Clark, B. K., Phys. Rev. B., 2024, 11, 115137

[6] Zakari, D., Allessandro, S., et al., arXiv preprint, 2023, arXiv:2309.11534