AI 中文总结
该研究扩展了卡尔曼嵌入量子算法求解弗拉索夫-泊松方程的收敛范围，通过傅里叶-厄米特展开建立收敛性，明确收敛对碰撞频率的要求，并指出量子算法复杂度与输出类型相关。
AI 中文摘要
我们扩展了用于求解动力学等离子体物理中弗拉索夫-泊松方程的卡尔曼嵌入量子算法的收敛范围。采用移位相空间分布函数的傅里叶-厄米特展开，结合解析与数值下界，为物理上合理的碰撞频率建立了收敛性。我们还表明，对于一大类基函数，卡尔曼嵌入的弗拉索夫-泊松系统的收敛性要求碰撞频率强度随速度分辨率提高而增大。量子算法的复杂度在很大程度上取决于我们是寻求时间平均输出还是时间分辨输出。
英文摘要
We extend the regime of convergence of Carleman-embedded quantum algorithms that solve the Vlasov-Poisson equations from kinetic plasma physics. We establish convergence, using both analytical and numerical lower bounds, for physically reasonable collision frequencies using a Fourier-Hermite expansion of the shifted phase-space distribution function. We also show that for a large class of basis functions, the convergence of the Carleman-embedded Vlasov-Poisson system requires increasing collision frequency strength with velocity resolution. The complexity of the quantum algorithm depends strongly on whether we seek time-averaged or -resolved outputs.
Comments11 pages, 2 figures
