A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations

• URL: http://arxiv.org/abs/2509.08807v1
• Date: Wed, 10 Sep 2025 17:40:19 GMT
• Title: A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations
• Authors: Xi-Ning Zhuang, Zhao-Yun Chen, Ming-Yang Tan, Jiaxuan Zhang, Chuang-Chao Ye, Tian-Hao Wei, Teng-Yang Ma, Cheng Xue, Huan-Yu Liu, Qing-Song Li, Tai-Ping Sun, Xiao-Fan Xu, Yun-Jie Wang, Yu-Chun Wu, Guo-Ping Guo,
• Abstract summary: Solving the Navier-Stokes equations (NSE) has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity.<n>Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation.<n>This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing.
• Score: 6.682280935861855
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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