Fast Extrapolation of Open Quantum System Dynamics via Machine-Learned Time-Dependent Density Functionals

Simulating open quantum systems requires capturing the influence of an extended bath on a subspace. When modelling open systems with a discretized impurity model coupled to a bath, two key challenges arise: (1) representing the bath’s influence with minimal modes while preserving accuracy, and (2) simulating dynamics efficiently over long timescales in an exponentially large system–bath Hilbert space. We address these using tensor network simulation [1] and introduce a machine-learned time-dependent density functional framework to address scaling bottlenecks, particularly bond-dimension growth. By training a Gaussian Process-based functional on short-time evolution data, we show how to extract a density-history-dependent exchange-correlation potential in the site-orbital basis. This enables accurate extrapolation of the dynamical behaviour even in strongly correlated regimes.

We demonstrate this for single- and double-impurity Anderson models, showing accurate reproduction and extrapolation of quench dynamics beyond the training window. This approach mitigates long-time complexity growth in tensor networks and can be adapted to quantum computing, offering a scalable tool for open quantum system dynamics with applications in dynamical mean-field theory [2] and quantum device modelling.

[1] L P Lindoy, D Rodrigo-Albert, Y Rath, I Rungger. pyTTN: An Open Source Toolbox for Open and Closed System Quantum Dynamics Simulations Using Tree Tensor Networks. arXiv:2503.15460 (2025)

[2] F Jamet, L P Lindoy, et al. Anderson impurity solver integrating tensor network methods with quantum computing. APL Quantum 2, 016121 (2025)