Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation
When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/62 |
| _version_ | 1827626154856546304 |
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| author | Yuanye Zhu |
| author_facet | Yuanye Zhu |
| author_sort | Yuanye Zhu |
| collection | DOAJ |
| description | When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d’Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm. |
| first_indexed | 2024-03-09T12:49:49Z |
| format | Article |
| id | doaj.art-3ce2edba67e043c28581591020653e82 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T12:49:49Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3ce2edba67e043c28581591020653e822023-11-30T22:07:41ZengMDPI AGEntropy1099-43002022-12-012516210.3390/e25010062Quantum-Solving Algorithm for d’Alembert Solutions of the Wave EquationYuanye Zhu0Center on Frontiers of Computing Studies and School of Computer Science, Peking University, Beijing 100871, ChinaWhen faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d’Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm.https://www.mdpi.com/1099-4300/25/1/62quantum algorithmquantum computationquantum information |
| spellingShingle | Yuanye Zhu Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation Entropy quantum algorithm quantum computation quantum information |
| title | Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation |
| title_full | Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation |
| title_fullStr | Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation |
| title_full_unstemmed | Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation |
| title_short | Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation |
| title_sort | quantum solving algorithm for d alembert solutions of the wave equation |
| topic | quantum algorithm quantum computation quantum information |
| url | https://www.mdpi.com/1099-4300/25/1/62 |
| work_keys_str_mv | AT yuanyezhu quantumsolvingalgorithmfordalembertsolutionsofthewaveequation |