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Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers

Over, Paul; Bengoechea, Sergio; Rung, Thomas; Clerici, Francesco; Scandurra, Leonardo; De Villiers, Eugene; Jaksch, Dieter

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    <subfield code="a">&lt;p&gt;The data refers to a variational quantum algorithm experiments solving initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results are complemented by classical finite difference results, which have been taken for comparison in the underlying document (&lt;a href="https://doi.org/10.48550/arXiv.2402.18619"&gt;arXiv.2402.18619&lt;/a&gt;). For a more detailed understanding, a reduced MATLAB code example of original VQCFD code is available within the repository.&lt;/p&gt;</subfield>
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    <subfield code="a">The current work have received funding from the European Union's Horizon Europe research and innovation program (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10) under grant agreement No. 101080085 QCFD.</subfield>
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Publication date:
February 28, 2024
DOI:
10.25592/uhhfdm.17336

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Keyword(s):
Computational Fluid Dynamics Variational Quantum Algorithms Quantum Computing Boundary Conditions
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Referenced by:
10.1016/j.compfluid.2024.106508
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Creative Commons Attribution 4.0 International

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Version v3 10.25592/uhhfdm.17336 Feb 28, 2024
Version 2 10.25592/uhhfdm.14152 Feb 28, 2024
Version 1 10.25592/uhhfdm.14124 Feb 28, 2024
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