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.
as written by the authors arXiv:2608.13041v1
From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $$10^2$$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.
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.