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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.03177 |
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| _version_ | 1866914178323709952 |
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| author | Mello, Antonio Francesco Collura, Mario Stoudenmire, E. Miles Levy, Ryan |
| author_facet | Mello, Antonio Francesco Collura, Mario Stoudenmire, E. Miles Levy, Ryan |
| contents | We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magic of the Well: assessing quantum resources of fluid dynamics data Mello, Antonio Francesco Collura, Mario Stoudenmire, E. Miles Levy, Ryan Quantum Physics Fluid Dynamics We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics. |
| title | Magic of the Well: assessing quantum resources of fluid dynamics data |
| topic | Quantum Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2512.03177 |