  Tensor networks are a powerful tool for many-body ground states with limited
entanglement. These methods can nonetheless fail for certain time-dependent
processes - such as quantum transport or quenches - where entanglement growth
is linear in time. Matrix-product-state decompositions of the resulting
out-of-equilibrium states require a bond dimension that grows exponentially,
imposing a hard limit on simulation timescales. However, in the case of
transport, if the reservoir modes of a closed system are arranged according to
their scattering structure, the entanglement growth can be made logarithmic.
Here, we apply this ansatz to open systems via extended reservoirs that have
explicit relaxation. This enables transport calculations that can access steady
states, time dynamics and noise, and periodic driving (e.g., Floquet states).
We demonstrate the approach by calculating the transport characteristics of an
open, interacting system. These results open a path to scalable and numerically
systematic many-body transport calculations with tensor networks.
