Simulating unsteady fluid flows on a superconducting quantum processor

TL;DR

This paper demonstrates the digital simulation of unsteady fluid flows using a superconducting quantum processor, showcasing high fidelity quantum encoding and evolution of flow states, and highlighting potential for simulating complex fluid dynamics.

Contribution

It presents the first experimental quantum simulation of unsteady fluid flows on a superconducting quantum processor, using Hamiltonian simulation of the Schrödinger equation for fluid dynamics.

Findings

Achieved median gate fidelities of 99.97% and 99.67%.

Successfully simulated 2D compressible diverging flow and decaying vortex.

Captured temporal evolution and spatial flow features with moderate noise.

Abstract

Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital for practical applications, emerges as a good candidate for showing quantum utility. Here, we report an experiment on the digital simulation of unsteady flows, which consists of quantum encoding, evolution, and detection of flow states, with a superconducting quantum processor. The quantum algorithm is based on the Hamiltonian simulation using the hydrodynamic formulation of the Schr\"odinger equation. With the median fidelities of 99.97% and 99.67% for parallel single- and two-qubit gates respectively, we simulate the dynamics of a two-dimensional (2D) compressible diverging flow and a 2D decaying vortex with ten qubits. The experimental results well capture the temporal evolution of averaged density and momentum profiles, and qualitatively reproduce spatial flow fields with moderate noises. This work demonstrates the potential of quantum computing in simulating more complex flows, such as turbulence, for practical applications.