Quantum Algorithm for Simulating a Driven Dissipative 3-site Hubbard Ring

Much research has been done concerning the simulation of closed quantum systems on near term quantum computers. Considerably less focus has been given to the simulation of open quantum systems, despite their importance as realistic models of real world systems. We consider the simulation of a three site Hubbard model driven by an electric field, connected to a Fermionic bath. This is the simplest model capable of stabilizing a non-zero steady state current with the added benefit that the fermionic bath admits an analytic solution in the non-interacting limit. We simulate this model classically using a master equation approach and provide an implementation for simulating it on a quantum computer. Even this simple model shows rich steady state behavior and offers a promising approach for simulating a variety of time dependent, driven, dissipative, open quantum systems.