Quantum PDE Solvers for CFD

In collaboration with BQP, this project explores the development of quantum algorithms for solving nonlinear partial differential equations relevant to computational fluid dynamics (CFD). High-fidelity fluid simulations are central to aerospace, energy, and engineering applications, but solving nonlinear flow equations at high resolution remains computationally demanding even on modern high-performance computing systems.

The project focuses on constructing quantum circuit frameworks for nonlinear fluid equations, leveraging tensor-network–inspired compression techniques and hybrid simulation strategies. In particular, the work applies Quantum Tensor Network (QTN) methods and Hamiltonian Simulation (HSE) frameworks to represent fluid state evolution efficiently within quantum circuits.

To evaluate feasibility and performance, the WISER team is benchmarking the approach on the Burgers' Equation, a canonical nonlinear PDE widely used as a simplified model for studying turbulence, shock formation, and nonlinear wave propagation. By compressing the effective state space and reducing circuit depth requirements, the project aims to construct quantum algorithms that remain viable on near-term quantum hardware.

WISER Research Fellows: Kudzai Musarandega, Weronika Golletz, Akash Malemath