Raffaele Salioni — Università degli Studi dell'Insubria #
Adaptive quantum dynamics with the time-dependent variational Monte Carlo method #
Describing the dynamics of quantum many-body systems is a formidable problem in contemporary physics. 
Understanding these dynamics is crucial for characterizing non-equilibrium phenomena and for the development of quantum technologies.
The simulation of such systems with variational methods is a promising yet challenging task, especially in regimes where highly expressive ansätze lead to numerical instabilities.
We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method [1] that adaptively controls the expressivity of the variational quantum state during the dynamics.
Our adaptive tVMC (atVMC) [2] approach addresses the ill-conditioned equations of motion arising in overparameterized regimes by selectively evolving only the most relevant parameters at each time step. Relevance is quantified through the local-in-time error (LITE), which measures the deviation between variational and exact evolution, using only quantities already available in standard tVMC simulations.
We benchmark the method on quantum quenches in the one-dimensional transverse-field Ising model using both spin-Jastrow and restricted Boltzmann machine wave functions. The adaptive scheme significantly improves numerical stability and reduces the need for strong regularization, enabling reliable simulations with highly expressive variational ansätze.  


[1] G. Carleo, F. Becca, M. Schiró, and M. Fabrizio, Sci. Rep. 2, 243 (2012).
[2] R. Salioni, R. Martinazzo, D.E. Galli, C. Apostoli, Phys. Rev. B 113, 014408 (2026).