Solving Navier–Stokes fluid equations with Quantum Computing

Flow through a convergent-divergent (de Laval) nozzle.

Researchers have presented a quantum algorithm for solving the Navier–Stokes equations.

There is great interest in using quantum computers to efficiently simulate a quantum system’s dynamics as existing classical computers cannot do this. Little attention, however, has been given to quantum simulation of a classical nonlinear continuum system such as a viscous fluid even though this too is hard for classical computers.

Such fluids obey the Navier–Stokes nonlinear partial differential equations, whose solution is essential to the aerospace industry, weather forecasting, plasma magneto-hydrodynamics, and astrophysics.

They tested the algorithm by using it to find the steady-state inviscid, compressible flow through a convergent-divergent nozzle when a shockwave is (is not) present.

They found excellent agreement between numerical simulation results and the exact solution, including shockwave capture when present. Finally, they compared the algorithm’s computational cost to deterministic and random classical algorithms and showed that a significant speed-up is possible.

This work points to a large new application area for quantum computing with substantial economic impact, including the trillion-dollar aerospace industry, weather-forecasting, and engineered-plasma technologies.

The study has been published in npj Nature Quantum Information.