Vlasov方程的量子算法
Quantum Algorithm for the Vlasov Equation
摘要：
描述经典等离子体物理的弗拉索夫-麦克斯韦方程组，即使在功能强大的计算机上进行数值模拟，也是极具挑战性的。通过线性化和假设一个麦克斯韦背景分布函数，我们将Vlasov-Maxwell系统转化为一个哈密顿模拟问题。然后针对静电朗道阻尼的极限情形，设计并验证了一种适用于未来纠错通用量子计算机的量子算法。虽然经典模拟的成本，规模为$\mathcal{O}(N_v t)$的速度网格与$N_v$网格点和模拟时间$t$，我们的量子算法规模为$\mathcal{O}(\text{polylog}(N_v) t/δ)$，其中$δ$是测量误差，和较弱的缩放已被丢弃。扩展，包括电磁学和更高的维度，进行了讨论。量子计算机可以有效地处理高分辨率的六维相空间网格，但提取准确结果的$1/δ$成本因素仍然是一个困难。这篇论文提供了一种在量子计算机上实现高效等离子体模拟的可能性。
英文摘要：
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution function, we convert the Vlasov-Maxwell system into a Hamiltonian simulation problem. Then for the limiting case of electrostatic Landau damping, we design and verify a quantum algorithm, appropriate for a future error-corrected universal quantum computer. While the classical simulation has costs that scale as $\mathcal{O}(N_v t)$ for a velocity grid with $N_v$ grid points and simulation time $t$, our quantum algorithm scales as $\mathcal{O}(\text{polylog}(N_v) t/δ)$ where $δ$ is the measurement error, and weaker scalings have been dropped. Extensions, including electromagnetics and higher dimensions, are discussed. A quantum computer could efficiently handle a high-resolution, six-dimensional phase-space grid, but the $1/δ$ cost factor to extract an accurate result remains a difficulty. This paper provides insight into the possibility of someday achieving efficient plasma simulation on a quantum computer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
