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. Here we present a quantum algorithm for solving the Navier–Stokes equations. We test 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. We find excellent agreement between numerical simulation results and the exact solution, including shockwave capture when present. Finally, we compare the algorithm’s computational cost to deterministic and random classical algorithms and show that a significant speed-up is possible. Our 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.

使用量子计算机来有效地模拟量子系统的动力学引起了极大的兴趣，因为现有的经典计算机无法做到这一点。但是，对经典非线性连续体系统（例如粘性流体）的量子模拟几乎没有引起注意，即使这对于经典计算机也很困难。这类流体服从Navier-Stokes非线性偏微分方程，该方程的解对航空航天工业，天气预报，等离子磁流体动力学和天体物理学至关重要。在这里，我们提出了一种求解Navier-Stokes方程的量子算法。我们通过使用算法来查找（不）存在冲击波时通过收敛-发散喷嘴的稳态无粘性可压缩流，从而对该算法进行测试。我们发现数值模拟结果与精确解（包括存在时的冲击波捕获）之间有着极好的一致性。最后，我们将算法的计算成本与确定性和随机经典算法进行比较，并表明可以显着提高速度。我们的工作指向具有巨大经济影响的量子计算新的大型应用领域，包括数万亿美元的航空航天工业，天气预报和工程等离子技术。