  In a recent milestone experiment, Google's processor Sycamore heralded the
era of "quantum supremacy" by sampling from the output of (pseudo-)random
circuits. We show that such random circuits provide tailor-made building blocks
for simulating quantum many-body systems on noisy intermediate-scale quantum
(NISQ) devices. Specifically, we propose an algorithm consisting of a random
circuit followed by a trotterized Hamiltonian time evolution to study
hydrodynamics and to extract transport coefficients in the linear response
regime. We numerically demonstrate the algorithm by simulating the buildup of
spatiotemporal correlation functions in one- and two-dimensional quantum spin
systems, where we particularly scrutinize the inevitable impact of errors
present in any realistic implementation. Importantly, we find that the
hydrodynamic scaling of the correlations is highly robust with respect to the
size of the Trotter step, which opens the door to reach nontrivial time scales
with a small number of gates. While errors within the random circuit are shown
to be irrelevant, we furthermore unveil that meaningful results can be obtained
for noisy time evolutions with error rates achievable on near-term hardware.
Our work emphasizes the practical relevance of random circuits on NISQ devices
beyond the abstract sampling task.
