  We construct an ensemble of two-dimensional nonintegrable quantum circuits
that are chaotic but have a conserved particle current, and thus a finite Drude
weight. The long-wavelength hydrodynamics of such systems is given by the
incompressible Navier-Stokes equations. By analyzing circuit-to-circuit
fluctuations in the ensemble we argue that these are negligible, so the
circuit-averaged value of transport coefficients like the viscosity is also (in
the long-time limit) the value in a typical circuit. The circuit-averaged
transport coefficients can be mapped onto a classical irreversible Markov
process. Therefore, remarkably, our construction allows us to efficiently
compute the viscosity of a family of strongly interacting chaotic
two-dimensional quantum systems.
