Geometric quantum encoding of a turbulent field

The chaotic structure of multiscale systems presents a formidable challenge to their quantum encoding. We propose a three-stage hyperspherical encoding method for turbulent fields. This method comprises a symmetry-preserving perturbation of the ground state, a measurement-specific convolution, and a final deconvolution of observables. The latter two stages employ the Hopf fibration to map quantum observables onto vortex tubes, the building blocks of fluid turbulence. Using 27 qubits, we generate an instantaneous turbulent field at a Reynolds number of $\mathit{Re} = 13900$ that reproduces the energy spectrum with Kolmogorov's five-thirds scaling, tangled vortex structures, and strong intermittency. The method only requires $\mathcal{O}(\log_2\mathit{Re})$ qubits, which is asymptotically optimal for turbulent-field encoding. This yields an exponential memory reduction over classical methods, and enables state preparation for large-scale quantum simulation of multiscale systems.