Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model Simulated on the IBM Quantum Computer

Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are coupled to an environment that introduces decoherence and dissipation. In our approach, the electronic system is represented in the framework of a two-site Hubbard model while the environment is modelled by a spin bath. In order to simulate the non-equilibrium population probabilities of the different states on the quantum computer we have encoded the electronic states and environmental degrees of freedom into qubits and ancilla qubits (bath), respectively. The total evolution time was divided into short time intervals, during which the system evolves. After each of these time steps, the system interacts with ancilla qubits representing the bath in thermal equilibrium. We have specifically studied spin baths leading to both, unital and non-unital dynamics of the electronic system and have found that electron correlations clearly enhance the electron transfer rates in the latter case. For short time periods, the simulation on the quantum computer is found to be in good qualitative agreement with the exact results. We also show that slight improvements are already possible with various error mitigation techniques while even significant improvements can be achieved by using the recently implemented single-qubit reset operations. Our method can be well extended to simulate electronic systems in correlated spin baths as well as in bosonic and fermionic baths