Description
A variational approach based on Neural Quantum States (NQS) [1, 2] is proposed to simulate the real-time dynamics of bright solitons in the one-dimensional Gross-Pitaevskii Equation (GPE). This framework enables the effective simulation of the system's time evolution by updating the neural network parameters according to the variational equations of motion [3]. This approach offers a flexible alternative to traditional solvers, as it does not rely on a fixed spatial grid or rigid boundary conditions. The developed tool successfully captures the complex dynamics of various solitonic interaction and collision scenarios, providing a robust method that can be validated against established benchmarks to assess accuracy and stability. This work explores the capacity of NQS to represent complex interference patterns and phase shifts, highlighting the potential of neural-variational methods for simulating non-linear quantum phenomena where standard techniques face scaling limitations.
[1] G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science 355(6325), 602 (2017), doi:10.1126/science.aag2302.
[2] A. Romero-Ros, J. Rozalén Sarmiento and A. Rios, Quantum Dynamics with Time-Dependent Neural Quantum States, SciPost Phys. Proc. (2025).
[3] A. Sinibaldi, C. Giuliani, G. Carleo and F. Vicentini, Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution, Quantum 7, 1131 (2023), doi:10.22331/q-2023-10-10-1131.