Quantum simulation of Burgers flow: Nonlinear transformation and direct evaluation of statistical quantities

F. Uchida, K. Miyamoto, S. Yamazaki, K. Fujisawa, N. Yoshida · 2024 · arXiv

| 编号 QC034 | 主题 量子 PDE 求解 | 链接 arXiv:2412.17206 |

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。

Fault-tolerant quantum computing is a promising technology to solve linear partial differential equa tions that are classically demanding to integrate. It is still challenging to solve nonlinear equations in fluid dynamics, such as the Burgers equation, using quantum computers. We propose a novel quantum algorithm to solve the Burgers equation. With the Cole–Hopf transformation that maps the fluid velocity field u to a new field ψ, we apply a sequence of quantum gates to solve the resulting linear equation and obtain the quantum state |ψ⟩ that encodes the solution ψ. We also propose an efficient way to extract stochastic properties of u, namely the multi-point functions of u, from the quantum state of |ψ⟩. Our algorithm offers an exponential advantage over the classical finite difference method in terms of the number of spatial grids when a perturbativity condition in the information-extracting step is met.

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