Abstract
Digital quantum computers have the potential to study the dynamics of many-body quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we explore the feasibility of studying steady-state transport in strongly interacting many-body quantum systems on a digital quantum computer. To do so, we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven XXZ spin chain. More specifically, we investigate how the depth of the quantum circuit is affected by how close we want the steady state to be to the one expected from the underlying master equation. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the XXZ spin chains are subject to nonuniform magnetic fields and show that, although the circuit depths required to reach steady states are still prohibitive for today's hardware, few collisions are enough to suggest a strong rectifying power.