Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model
  Simulated on IBM Quantum Computers
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. To simulate the non-equilibrium population probabilities of the
different states on a 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 very good
agreement with the exact results if error mitigation methods are applied. Our
method to simulate also non-unitary time-evolution on a quantum computer can be
well extended to simulate electronic systems in correlated spin baths as well
as in bosonic and fermionic baths.
Sabine Tornow Wolfgang Gehrke Udo Helmbrecht