2024/11/22 by Sergio Bengoechea, Bengoechea, Sergio, Paul Over +5 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Model Reduction and Neural Networks #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2411.14931
openalex publication_date 2024/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in combination with different engineering boundary conditions. Topics covered include the encoding of band matrices, as in the consideration of non-constant material properties and upwind-biased first- and higher-order approximations, widely used in engineering Computational Fluid Dynamics, by the use of a mask function. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a polylog scaling of the number of quantum gates with the number of qubits. Remaining challenges refer to the implicit construction of upwind schemes and the identification of an appropriate parameterization strategy of the quantum ansatz.