Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity ( u · ∇ u ) to lattice-Boltzmann nonlinearity ( u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

The pore sizes of shale and other unconventional plays are of the order of tens of nanometers. Based on the fundamental theory of thermodynamics, several studies have indicated that, in such small pores, phase behavior is affected by the capillary pressure and surface forces and is different from that characterized in PVT cells. No experimental evidence of this phenomenon, however, has been presented in the literature. In this study, we apply nanofluidic devices to visualize phase changes of pure alkane and an alkane mixture under nanoconfinement as a means to approach oil/gas phase behaviors in nanoporous rocks. Pure alkane starts vaporizing in the micro-channels first, and then the meniscus flashes into the nanochannels immediately after the complete vaporization of the liquid in the micro-channels. The vaporization of the ternary hydrocarbon mixture, however, is very different from pure alkane. Although the liquid starts to vaporize in the microchannels first, as expected, the meniscus cannot propagate into the nano-channels in a comparable time scale as the pure alkane. The reason is that the liberation of lighter components from the liquid phase to the gas phase in the micro-channels increases the apparent molecular weight of the liquid in the nano-channels, suppressing the bubble point of the remaining fluid. A modified flash calculation procedure that uses the sizes of micro-channels and nano-channels as the characteristic lengths and assumed contact angle can reproduce the vaporization propagation sequence in the experimental observations. Experiments and modeling presented in this paper provide the proof of the concept and promote the understanding of phase behavior in nanoporous unconventional reservoirs.