AI 中文总结
研究针对弱非线性等离子体物理问题，结合等离子体自由能、分层块编码协议及信息提取子程序等关键要素构建端到端量子算法，可估计时空平均动能，相比传统方法节省指数级内存并超二次加速，为量子模拟建立了非线性等离子体基准。
AI 中文摘要
非线性动力学等离子体模拟是高维的且对经典计算要求很高，而量子算法面临不同瓶颈。本文提出一种针对弱非线性动力学等离子体模型的端到端量子算法并给出严格收敛保证。该系统描述了具有绝热电子、动力学离子、德拜屏蔽和克鲁克弛豫的三维电子 - 离子等离子体。经傅里叶 - 厄米截断后动力学简化为高维二次常微分方程。为解决量子瓶颈，结合三个关键要素：用等离子体自由能确定李雅普诺夫变换使卡尔曼线性嵌入在弱非线性区域内按截断阶指数收敛；开发用于密集矩阵的分层块编码协议利用场的空间衰减避免稀疏访问编码的多项式开销；引入信息提取子程序利用全卡尔曼历史状态中编码的非线性分量改进线性可观测量估计。构建量子算法估计时空平均动能，相对于傅里叶 - 厄米谱求解器，节省指数级内存并实现时间上的超二次改进，为量子模拟建立了可控的非线性等离子体基准。
英文摘要
Nonlinear kinetic plasma simulation is high-dimensional and classically demanding, while quantum algorithms face different bottlenecks: embedding nonlinear dynamics into a linear computation, loading dense field-interaction data, and efficiently extracting information. We present an end-to-end quantum algorithm, with rigorous convergence guarantees, for a weakly nonlinear kinetic plasma model. The system describes a 3D electron-ion plasma with adiabatic electrons, kinetic ions, Debye screening, and Krook relaxation. After Fourier-Hermite truncation, the dynamics reduces to a high-dimensional quadratic ordinary differential equation. To tackle quantum bottlenecks we combine three key ingredients. First, we use a plasma free energy to identify a Lyapunov transform under which a Carleman linear embedding converges exponentially in the truncation order within a certified weakly nonlinear regime. Second, we develop a hierarchical block-encoding protocol for dense matrices, exploiting the spatial decay of the field to avoid polynomial overhead from sparse access encodings. Third, we introduce a subroutine for information extraction that exploits nonlinear components encoded in the full Carleman history state to improve the estimation of linear observables. We construct a quantum algorithm to estimate the spacetime-averaged kinetic energy using $\widetilde{O}\!\left( N_F N_H^{1/2} \operatorname{polylog}\!\left(\frac{T}ε\right)\frac{1}ε\right)$ gates and $\widetilde{O}\!\left(\log\!\left(N_F N_H^{1/2}T\right)\log\!\left(\frac{1}ε\right)\right)$ qubits, where $N_F$ and $N_H$ are the Fourier and Hermite cutoffs. Relative to a Fourier-Hermite spectral solver, this yields exponential memory savings and superquadratic improvements in time. Together, these results establish a controlled nonlinear plasma benchmark for quantum simulation.
Comments70 pages, 4 figures
