Simulation of the Hubbard Model as an Open Quantum system on Near-term Quantum Computers

Open quantum systems are everywhere in real life, whether it is systems exposed to temperature, electric field, or anything that causes dissipation and/or driving. I will be describing a couple of such systems that we have run on quantum hardware [1], which turns out to be an excellent platform for such simulations, being inherently robust against quantum hardware errors even with deep circuits. We give two examples: 1) we simulate one thousand steps of time evolution for the non-interacting limit of the infinite driven-dissipative Hubbard model and calculate the current through the system; and 2) we prepare a thermal state of the atomic limit of the Hubbard model in a magnetic field. These problems were solved using circuits containing up to two thousand entangling gates on quantum computers made available by IBM, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating dissipative problems are able to far out-perform similarly complex non-dissipative algorithms on noisy hardware. Our two examples are the basic building blocks of many condensed matter physics systems, and we anticipate their demonstrated robustness to hold with increasing complexity of driven-dissipative problems.