Water in a river changes its path as it flows around a stone: some streams press against the surface, others detach and swirl downstream. A classical computer simulates such flows by dividing the fluid into millions of tiny parcels and tracking each one. A quantum computer could do the same by storing the probabilities for all parcels in a single quantum state, but until now it has not been able to correctly describe what happens right at the wall.

Researchers from Peking University proposed writing the probabilities of all possible particle velocities at all grid nodes into the diagonal of a density matrix. This is like an orchestra score, where each row corresponds to a velocity and each column to a point in space. Then the streaming step, where particles hop to neighboring nodes, becomes a simple shuffling of rows and columns that can be performed on a quantum computer without losing information.

For walls, they introduced an extra step before streaming: if a particle is heading toward a wall, its component swaps with the reflected component at the adjacent boundary point. After that, the usual streaming automatically returns the particle to the fluid, and the no-slip condition is satisfied by itself. This trick works for walls of any shape, whether it is a straight pipe, a curved airfoil, or letters on a building facade.

The method was tested on three types of flows. For a decaying channel flow, the error decreased as the grid resolution increased. For flow over a backward-facing step, the length of the recirculation zone differed from the classical simulation by 10–17 percent depending on the flow speed. For flow around a cylinder, the error was 12–17 percent. Finally, they simulated flow around the letters 'PKU' on a grid of more than a million nodes, and vortices appeared in the gaps between the letters, just as in a real experiment. This shows that a quantum computer can handle complex geometries.