Quantum Random Feature Method for Solving Partial Differential Equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909832633647104 |
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| author | Hu, Junpeng Jin, Shi Liu, Nana Zhang, Lei |
| author_facet | Hu, Junpeng Jin, Shi Liu, Nana Zhang, Lei |
| contents | Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks present a mesh-free alternative to solve partial differential equations (PDEs), their accuracy is difficult to achieve since one needs to solve a high-dimensional non-convex optimization problem using the stochastic gradient descent method and its variants, the convergence of which is difficult to prove and cannot be guaranteed. The classical random feature method (RFM) effectively merges advantages from both classical numerical analysis and neural network based techniques, achieving spectral accuracy and a natural adaptability to complex geometries. In this work, we introduce a quantum random feature method (QRFM) that leverages quantum computing to accelerate the classical RFM framework. Our method constructs PDE solutions using quantum-generated random features and enforces the governing equations via a collocation approach. A complexity analysis demonstrates that this hybrid quantum-classical algorithm can achieve a quadratic speedup over the classical RFM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Random Feature Method for Solving Partial Differential Equations Hu, Junpeng Jin, Shi Liu, Nana Zhang, Lei Quantum Physics Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks present a mesh-free alternative to solve partial differential equations (PDEs), their accuracy is difficult to achieve since one needs to solve a high-dimensional non-convex optimization problem using the stochastic gradient descent method and its variants, the convergence of which is difficult to prove and cannot be guaranteed. The classical random feature method (RFM) effectively merges advantages from both classical numerical analysis and neural network based techniques, achieving spectral accuracy and a natural adaptability to complex geometries. In this work, we introduce a quantum random feature method (QRFM) that leverages quantum computing to accelerate the classical RFM framework. Our method constructs PDE solutions using quantum-generated random features and enforces the governing equations via a collocation approach. A complexity analysis demonstrates that this hybrid quantum-classical algorithm can achieve a quadratic speedup over the classical RFM. |
| title | Quantum Random Feature Method for Solving Partial Differential Equations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.07945 |