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Many-body physics is one very well suited field for testing quantumalgorithms and for finding working heuristics on present quantum computers. Wehave investigated the non-equilibrium dynamics of one- and two-electronsystems, which are coupled to an environment that introduces decoherence anddissipation. In our approach, the electronic system is represented in theframework of a two-site Hubbard model while the environment is modelled by aspin bath. To simulate the non-equilibrium population probabilities of thedifferent states on a quantum computer we have encoded the electronic statesand 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 systeminteracts with ancilla qubits representing the bath in thermal equilibrium. Wehave specifically studied spin baths leading to both, unital and non-unitaldynamics of the electronic system and have found that electron correlationsclearly enhance the electron transfer rates in the latter case. For short timeperiods, the simulation on the quantum computer is found to be in very goodagreement with the exact results if error mitigation methods are applied. Ourmethod to simulate also non-unitary time-evolution on a quantum computer can bewell extended to simulate electronic systems in correlated spin baths as wellas in bosonic and fermionic baths.

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