Efficient method for quantum impurity problems out of equilibrium

We introduce an efficient method to simulate dynamics of interacting quantum impurity coupled non-interacting fermionic reservoirs. Viewing the as open system, we describe reservoirs by their Feynman-Vernon influence functionals (IF). The IF are represented matrix-product states in temporal domain, which enables computation for arbitrary interactions. apply our study quenches and transport Anderson model, including highly non-equilibrium setups, find favorable performance compared state-of-the-art methods. computational resources required accurate scale polynomially with evolution time, indicating that a broad class out-of-equilibrium problems efficiently solvable. This approach will provide new insights into dynamical properties mesoscopic devices correlated materials.