A quantum advection-diffusion solver using the quantum singular value transform
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911442953830400 |
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| author | Helle, Gard Olav Benacchio, Tommaso Ousager, Anna Bomme Andersen, Jørgen Ellegaard |
| author_facet | Helle, Gard Olav Benacchio, Tommaso Ousager, Anna Bomme Andersen, Jørgen Ellegaard |
| contents | We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantum advection-diffusion solver using the quantum singular value transform Helle, Gard Olav Benacchio, Tommaso Ousager, Anna Bomme Andersen, Jørgen Ellegaard Quantum Physics We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks. |
| title | A quantum advection-diffusion solver using the quantum singular value transform |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.22163 |