A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations
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arXiv
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| Autori principali: | , , , , , , , , , , , , , , |
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| Natura: | Preprint |
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2025
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| _version_ | 1866914031509438464 |
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| author | Zhuang, Xi-Ning Chen, Zhao-Yun Tan, Ming-Yang Zhang, Jiaxuan Ye, Chuang-Chao Wei, Tian-Hao Ma, Teng-Yang Xue, Cheng Liu, Huan-Yu Li, Qing-Song Sun, Tai-Ping Xu, Xiao-Fan Wang, Yun-Jie Wu, Yu-Chun Guo, Guo-Ping |
| author_facet | Zhuang, Xi-Ning Chen, Zhao-Yun Tan, Ming-Yang Zhang, Jiaxuan Ye, Chuang-Chao Wei, Tian-Hao Ma, Teng-Yang Xue, Cheng Liu, Huan-Yu Li, Qing-Song Sun, Tai-Ping Xu, Xiao-Fan Wang, Yun-Jie Wu, Yu-Chun Guo, Guo-Ping |
| contents | The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations Zhuang, Xi-Ning Chen, Zhao-Yun Tan, Ming-Yang Zhang, Jiaxuan Ye, Chuang-Chao Wei, Tian-Hao Ma, Teng-Yang Xue, Cheng Liu, Huan-Yu Li, Qing-Song Sun, Tai-Ping Xu, Xiao-Fan Wang, Yun-Jie Wu, Yu-Chun Guo, Guo-Ping Quantum Physics Numerical Analysis Computational Physics Fluid Dynamics The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing. |
| title | A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations |
| topic | Quantum Physics Numerical Analysis Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2509.08807 |