A quantum turbuloscope: unlocking end-to-end quantum simulation of turbulence

Abstract

Multiscale organization is a hallmark of complex natural systems, spanning climate dynamics, biological morphogenesis, and fluid turbulence. While quantum computing promises exponential speedups for solving the evolution equations governing these fields, this potential is fundamentally hindered by the quantum state preparation bottleneck, the prohibitive cost of loading classical complex data into quantum states. Here, we overcome this barrier by introducing a physics-informed, three-stage geometric encoding method "turbuloscope", which efficiently generates complex turbulent fields. Rather than brute-force data loading, our approach acts as a kaleidoscope, leveraging the intrinsic structures of turbulence. We capture scale-invariant self-similarity via a hyperplane approximation in high-dimensional feature space, and utilize the Hopf fibration to map quantum observables directly onto vortex tubes, the fundamental building blocks of fluid turbulence. Remarkably, the algorithm requires no ancillary qubits, utilizes a linear-depth quantum circuit, and scales logarithmically with the Reynolds number, an exponential speedup compared to classical methods. We demonstrate the power of this method by generating an instantaneous turbulent field at a high Reynolds number of 35,000 across over one billion grid points using only 30 qubits, reproducing Kolmogorov's 5/3 energy spectrum, tangled vortex structures, and strong intermittency. This asymptotically optimal approach not only signals a near-term pathway to practical quantum advantage in fluid dynamics, but establishes a scalable foundation for the quantum simulation of broad multiscale systems.