Solving Fluid Dynamics Equations with Differentiable Quantum Circuits

Differentiable quantum circuits (DQCs) are the hybrid quantum-classical alternative to Physics-Informed Neural Networks (PINNs). The latter ones have been introduced from the machine learning community to avoid the curse of dimensionality in mesh-based computational fluid dynamics (CFD) solvers, and allow for seamless inclusion of information from available data. The adoption of quantum circuits is motivated by enabling access to highly expressive feature maps, which might be key in capturing intricate solutions to selected fluid dynamics problems. In this work, we discuss the potential of DQCs and its recent extensions to address paradigmatic CFD use cases.