Tensor-Programmable Quantum Circuits for Solving Differential Equations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918457955581952 |
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| author | Siegl, Pia Reese, Greta Sophie Hashizume, Tomohiro van Hülst, Nis-Luca Jaksch, Dieter |
| author_facet | Siegl, Pia Reese, Greta Sophie Hashizume, Tomohiro van Hülst, Nis-Luca Jaksch, Dieter |
| contents | We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor-Programmable Quantum Circuits for Solving Differential Equations Siegl, Pia Reese, Greta Sophie Hashizume, Tomohiro van Hülst, Nis-Luca Jaksch, Dieter Quantum Physics We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts. |
| title | Tensor-Programmable Quantum Circuits for Solving Differential Equations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.04425 |