Optimal sampling of dynamical large deviations via matrix product states

The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute relevant leading eigenvalues and eigenvectors accurately. However, efficient generation corresponding rare trajectories a harder task. Here we show how exploit MPS approximation dominant eigenvector implement an sampling scheme which closely resembles optimal (so-called "Doob") dynamics realises events. We demonstrate our approach on three well-studied lattice models, Fredrickson-Andersen East kinetically constrained models (KCMs), symmetric simple exclusion process (SSEP). discuss generalise higher dimensions.