  We study an open quantum system simulation on quantum hardware, which
demonstrates robustness to hardware errors even with deep circuits containing
up to two thousand entangling gates. We simulate two systems of electrons
coupled to an infinite thermal bath: 1) a system of dissipative free electrons
in a driving electric field; and 2) the thermalization of two interacting
electrons in a single orbital in a magnetic field -- the Hubbard atom. These
problems are solved using IBM quantum computers, showing no signs of decreasing
fidelity at long times. Our results demonstrate that algorithms for simulating
open quantum systems are able to far outperform similarly complex
non-dissipative algorithms on noisy hardware. Our two examples show promise
that the driven-dissipative quantum many-body problem can eventually be solved
on quantum computers.
