Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena

• URL: http://arxiv.org/abs/2411.14931v1
• Date: Fri, 22 Nov 2024 13:39:49 GMT
• Title: Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• Authors: Sergio Bengoechea, Paul Over, Dieter Jaksch, Thomas Rung,
• Abstract summary: 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.
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• Abstract: 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 $\textit{polylog}$ complexity in the number of qubits of the quantum circuits involved. Remaining challenges refer to the implicit construction of upwind schemes.

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