  In this work we present and analyze two tensor network-based influence
functional approaches for simulating the real-time dynamics of quantum impurity
models such as the Anderson model. Via comparison with recent numerically exact
simulations, we show that such methods accurately capture the long-time
non-equilibrium quench dynamics. The two parameters that must be controlled in
these tensor network influence functional approaches are a time discretization
(Trotter) error and a bond dimension (tensor network truncation) error. We show
that the actual numerical uncertainties are controlled by an intricate
interplay of these two approximations which we demonstrate in different
regimes. Our work opens the door to using these tensor network influence
functional methods as general impurity solvers.
