Quantum Solver Using Singular Value Decomposition for Computational Fluid Dynamics

Conference · Thu Jan 01 00:00:00 EST 2026

DOI:https://doi.org/10.2514/6.2026-1934· OSTI ID:3016992

Gottiparthi, Kalyan ^[1]; Lu, Chao ^[1]; Gopalakrishnan Meena, Murali ^[1]; Chaudhary, Manu ^[2]; El-Araby, Esam ^[3]

---

1. ORNL
2. Illinois State University
3. University of Kansas

Numerical solutions for fluid flow problems are challenging and have been focus of Computational Fluid Dynamics (CFD) research for past several decades. The advent of quantum computing promises exponential speedup in comparison to existing classical methods and alleviate computational constraints posed by CFD problems. Although solutions for most problems of interest in fluid dynamics using quantum computing are distant, recent advances in algorithms, software and hardware provide a path towards realizing this goal. Quantum linear solver algorithms (QLSA) such as Harrow–Hassidim–Lloyd (HHL) and Variational Quantum Linear Solver (VQLS) have been successfully implemented to solve for canonical problems such as Hele-Shaw flow. However, these algorithms still suffer to scale and address problems with ill-conditioned Jacobians. In the current paper, we alleviate these restrictions with a new quantum solver based on Singular Value Decomposition (SVD) and simulate flow past a 2D cylinder. The fidelity of the SVD based quantum solver in predicting the flow past 2D cylinder is computed along with an assessment of errors. Classical and quantum solutions for the flow are compared for different resolutions. Finally, we discuss variation in the solutions based on number of shots used.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 3016992
• Resource Type: Conference paper/presentation
• Conference Information: American Institute of Aeronautics and Astronautics (AIAA) SciTech 2026 Forum - Orlando, Florida, United States of America - 1/12/2026-1/16/2026
• Country of Publication: United States
• Language: English