Curator's Take
This research represents a significant breakthrough in quantum fluid dynamics simulation by developing the first quantum algorithm that can handle the full complexity of the Navier-Stokes equations, including pressure, dissipation, and vorticity effects that previous quantum approaches have struggled to address. The team's clever workaround using Hamilton-Jacobi formulation and tensor-network Carleman embedding could unlock quantum advantages for computational fluid dynamics, a field that consumes enormous classical computing resources across industries from aerospace to weather prediction. While the current demonstration focuses on moderate Reynolds numbers, this foundational work opens the door to quantum simulations of turbulent flows that are computationally intractable on classical machines. The approach builds on largely overlooked 1985 theoretical work, showing how revisiting fundamental physics with modern quantum computing techniques can yield unexpected algorithmic innovations.
— Mark Eatherly
Summary
The search for quantum-like wave formulations of the Navier-Stokes (Schrödinger-Navier-Stokes, SNS for short) equations describing classical dissipative fluids has met with increasing attention in the recent years, due to the large portfolio of potential applications in science and engineering. A SNS formulation of classical fluids was first presented in a largely un-noticed paper by Dietrich and Vautherin back in 1985(Journal de Physique). In this paper, we revisit this specific SNS approach and assess its viability for quantum implementations based on Carleman embedding/linearization techniques. Specifically, we i) Clarify in full mathematical detail why the SNS dissipator presents a steep challenge for quantum computers and propose a way out strategy based on the Hamilton-Jacobi (HJ) formulation of fluid dynamics; ii) Develop a corresponding quantum algorithm using a new technique based on a tensor-network representation of Carleman embedding of the HJ equations (CHJ) which permits substantial memory savings; iii) Emulate the CHJ quantum algorithm on a classical computer and analyse its convergence and accuracy for the specific case of Kolmogorov-like flows at moderate Reynolds numbers. To the best of our knowledge, this is the first quantum algorithm based on a quantum-like wave formulation of the genuine Navier-Stokes equations, including pressure, dissipation and vorticity.