A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods
Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/4/580 |
| _version_ | 1827745178918584320 |
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| author | Corey Jason Trahan Mark Loveland Noah Davis Elizabeth Ellison |
| author_facet | Corey Jason Trahan Mark Loveland Noah Davis Elizabeth Ellison |
| author_sort | Corey Jason Trahan |
| collection | DOAJ |
| description | Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations. |
| first_indexed | 2024-03-11T05:03:26Z |
| format | Article |
| id | doaj.art-bf71ad227be74b3ea819846fee8a675e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T05:03:26Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bf71ad227be74b3ea819846fee8a675e2023-11-17T19:08:04ZengMDPI AGEntropy1099-43002023-03-0125458010.3390/e25040580A Variational Quantum Linear Solver Application to Discrete Finite-Element MethodsCorey Jason Trahan0Mark Loveland1Noah Davis2Elizabeth Ellison3Information and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USAInformation and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USAApplied Research Laboratories, The University of Texas at Austin, Austin, TX 78713, USAInformation and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USAFinite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.https://www.mdpi.com/1099-4300/25/4/580quantum computingquantum variational algorithmfinite-element methodsPoisson equationheat equationquantum algorithms |
| spellingShingle | Corey Jason Trahan Mark Loveland Noah Davis Elizabeth Ellison A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods Entropy quantum computing quantum variational algorithm finite-element methods Poisson equation heat equation quantum algorithms |
| title | A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods |
| title_full | A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods |
| title_fullStr | A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods |
| title_full_unstemmed | A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods |
| title_short | A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods |
| title_sort | variational quantum linear solver application to discrete finite element methods |
| topic | quantum computing quantum variational algorithm finite-element methods Poisson equation heat equation quantum algorithms |
| url | https://www.mdpi.com/1099-4300/25/4/580 |
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