When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.
The authors of the new study found a workaround. They encoded the fluid flow as a set of parameters in a quantum circuit, then let the computer adjust those parameters to match real physics. This is a hybrid approach: part of the computation runs on a classical computer, part on a quantum one. For the first time, they were able to track how the flow evolves over time on a quantum processor, including regimes with a Reynolds number around 100—which is already noticeable turbulence.
To cope with the noise of quantum hardware, the physicists used a trick: they ran the same circuit with different levels of noise and then extrapolated the result to the 'ideal' zero-noise case. This allowed them to execute deep quantum circuits with hundreds of entangled operations — more than such devices usually handle. As a result, they managed to reconstruct the evolution of the field over several time steps, despite the processor's imperfections.
The result is the first experimental demonstration of nonlinear dynamics on a quantum computer. Previously, quantum simulations were limited to linear problems like molecular vibrations. Now the path is open to calculating turbulence, shock waves, and other phenomena where classical methods hit computational walls.
The Burgers equation, which the authors solved, first appeared in 1939 in a paper on turbulence, and later found applications in cosmology: it describes how voids and galaxy clusters form in the universe.