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Quantum computers are poised to revolutionize the simulation ofquantum-mechanical systems in physics and chemistry. Current quantum computersexecute their algorithms imperfectly, due to uncorrected noise, gate errors,and decoherence. This severely limits the size and scope of protocols which canbe run on near-term quantum hardware. Much research has been focused onbuilding more robust hardware to address this issue, however the advantages ofmore robust algorithms remains largely unexplored. Here we show that algorithmsfor solving the driven-dissipative many-body problem, among the hardestproblems in quantum mechanics, are inherently robust against errors. We find itis possible to solve dissipative problems requiring deep circuits on currentquantum devices due to the contractive nature of their time evolution maps. Wesimulate one thousand steps of time evolution for the non-interacting limit ofthe infinite driven-dissipative Hubbard model, calculate the current throughthe system and prepare a thermal state of the atomic limit of the Hubbardmodel. These problems were solved using circuits containing up to two thousandentangling gates on quantum computers made available by IBM, showing no signsof decreasing fidelity at long times. Our results demonstrate that algorithmsfor simulating dissipative problems are able to far out-perform similarlycomplex non-dissipative algorithms on noisy hardware. Our two algorithmicprimitives are the basic building blocks of many condensed-matter-physicssystems, and we anticipate their demonstrated robustness to hold whengeneralized to solve the full many-body driven-dissipative quantum problem.Building upon the algorithms presented here may prove to be the most promisingapproach to tackle important, classically intractable problems on quantumcomputers before error correction is available.

Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers