Quantum framework for parameterizing partial differential equations via diagonal block-encoding
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908859265712128 |
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| author | Yano, Hiroshi Sato, Yuki |
| author_facet | Yano, Hiroshi Sato, Yuki |
| contents | We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal matrices, or diagonal block-encodings, can be used to represent spatially varying coefficients with structured, potentially complicated profiles. This encoding enables efficient quantum simulation of forward PDEs and extends naturally to parameter-dependent settings. Such simulations are a key primitive for quantum algorithms for PDE-constrained optimization, where the goal is to identify optimal design parameters. We illustrate the framework numerically through forward simulation and parameter design for the two-dimensional wave equation with a Gaussian parameter profile. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum framework for parameterizing partial differential equations via diagonal block-encoding Yano, Hiroshi Sato, Yuki Quantum Physics We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal matrices, or diagonal block-encodings, can be used to represent spatially varying coefficients with structured, potentially complicated profiles. This encoding enables efficient quantum simulation of forward PDEs and extends naturally to parameter-dependent settings. Such simulations are a key primitive for quantum algorithms for PDE-constrained optimization, where the goal is to identify optimal design parameters. We illustrate the framework numerically through forward simulation and parameter design for the two-dimensional wave equation with a Gaussian parameter profile. |
| title | Quantum framework for parameterizing partial differential equations via diagonal block-encoding |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.01358 |