Fig. 1: Schematic for the quantum simulation of fluid dynamics.

The initial flow field (exemplified pictorially by a spiral vortex) discretized on a uniform grid in (a) is encoded by the multi-component wave function in (b), followed by state preparation. c Sketch of device topology. Qubits (circles) are arranged in a square lattice and connected through tunable couplers (bars). The ten qubits used here are labeled by Q₁–Q₅ (blue) and Q₆–Q₁₀ (green), encoding the wave function in the x- and y-directions, respectively. d Sketch of the quantum circuit for simulating the 2D unsteady flows. The Hamiltonian simulation is realized by transforming a flow state into the momentum space with quantum Fourier transforms \({\widehat{{{{\rm{QFT}}}}}}_{x}\) and \({\widehat{{{{\rm{QFT}}}}}}_{y}\), applying unitary evolutions \({e}^{-i{\hat{k}}_{x}^{2}t/2}\) and \({e}^{-i{\hat{k}}_{y}^{2}t/2}\), and finally transforming the state back to the coordinate space. The circuit is further compiled with native gate sets (arbitrary single-qubit gates and two-qubit CZ gate) before the experimental execution. e At a given time t, the flow field is extracted by measuring a specific set of Pauli strings.