Quantum algorithms for solving a drift-diffusion equation: A complexity analysis
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908593144463360 |
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| author | Devereux, Ellen Datta, Animesh |
| author_facet | Devereux, Ellen Datta, Animesh |
| contents | We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalization via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum algorithms for solving a drift-diffusion equation: A complexity analysis Devereux, Ellen Datta, Animesh Quantum Physics We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalization via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer. |
| title | Quantum algorithms for solving a drift-diffusion equation: A complexity analysis |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.21221 |