An end-to-end quantum algorithm for nonlinear fluid dynamics with bounded quantum advantage

D. Jennings, K. Korzekwa, M. Lostaglio, R. Ashworth, E. Marsili, S. Rolston · 2025 · arXiv

| 编号 QC032 | 主题 量子 PDE 求解 | 链接 arXiv:2512.03758 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Computational fluid dynamics (CFD) is a cornerstone of classical scientific comput ing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum algorithms for CFD have almost exclusively been based on the Carleman embedding method, used to encode nonlinearities on a quantum computer. In this work, we begin by showing that these proposals suffer from a range of severe bottlenecks that negate conjectured quantum advantages: lack of convergence of the Carleman method, prohibitive time stepping requirements, unfavorable condition number scaling, and inefficient data extraction. With these roadblocks clearly identified, we develop a novel algorithm for the incompressible lattice Boltzmann equation that circumvents these obstacles, and then provide a detailed analysis of our algorithm, including all potential sources of algorith mic complexity, as well as gate count estimates. We find that for an end-to-end problem, a modest quantum advantage may be preserved for selected observables in the high error-tolerance regime. We lower bound the Reynolds number scaling of our quantum algorithm in dimension D at Kolmogorov microscale resolution with $O({\mathrm{Re}}^{\frac{3}{4}(1+\frac{D}{2})}\times q_M)$ where $q_M$ is a multiplicative overhead for data extraction with $q_M=O({\mathrm{Re}}^{\frac{3}{8}})$ for the drag force. This upper bounds the scaling improvement over classical algorithms by $\mathcal{O}({\mathrm{Re}}^{\frac{3D}{8}\cdot })$ ). However, our numerical investigations suggest a lower speedup, with a scaling estimate of $O({\mathrm{Re}}^{1.936}\times q_M)$ for $D=2$ Our results give robust evidence that small, but nontrivial, quantum advantages can be achieved in the context of CFD, and motivate the need for additional rigorous end-to-end quantum algorithm development.

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