Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena

Fuente: arXiv
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Main Authors: Bengoechea, Sergio, Over, Paul, Jaksch, Dieter, Rung, Thomas
Format: Preprint
Published: 2024
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author Bengoechea, Sergio
Over, Paul
Jaksch, Dieter
Rung, Thomas
author_facet Bengoechea, Sergio
Over, Paul
Jaksch, Dieter
Rung, Thomas
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14931
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
Bengoechea, Sergio
Over, Paul
Jaksch, Dieter
Rung, Thomas
Quantum Physics
Fluid Dynamics
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.
title Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
topic Quantum Physics
Fluid Dynamics
url https://arxiv.org/abs/2411.14931