This article proposes a Variational Quantum Algorithm (VQA) 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 consideration of non-constant material properties and upwind-biased first- and higher-order approximations, widely used in engineering Computational Fluid Dynamics (CFD), by the use of a mask function. The framework is able to convert band matrices arising from Partial Differential Equations (PDEs) discretized on structured grids into quantum gates, thus contributing to the development of a modular library for quantum computing translations of CFD procedures. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a polylog complexity in the number of qubits of the quantum circuits involved. Remaining challenges refer to the implicit construction of upwind schemes.
Cite as BibTeX
@misc{bengoechea2024variationalquantumalgorithmsgeneralized,
title={Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena},
author={Sergio Bengoechea and Paul Over and Dieter Jaksch and Thomas Rung},
year={2024},
eprint={2411.14931},
archivePrefix={arXiv},
primaryClass={quant-ph},
url={https://arxiv.org/abs/2411.14931},
}