论文标题
一种量子启发的方法，用于求解Vlasov-Poisson方程
A quantum-inspired method for solving the Vlasov-Poisson equations
论文作者
论文摘要
由于高分辨率要求和相对于维度的计算成本的指数缩放，使用VLASOV方程的无碰撞（或弱碰撞）等离子体的动力学模拟通常是不可行的。最近，有人提出，矩阵乘积状态（MPS）方法是一种量子启发但经典的算法，可以使用指数加速求解部分微分方程，前提是该解决方案可以被压缩并有效地表示为在某些可耐受性误差阈值中的MPS。在这项工作中，我们探讨了MPS方法在1D1V中求解Vlasov-Poisson方程的实用性，并发现线性和非线性动力学的重要特征（例如阻尼或生长速率和饱和振幅）可以在重大压缩溶液的同时捕获。此外，通过比较分布函数的不同映射到MPS上的性能，我们在求解Vlasov-Poisson方程的情况下开发了MPS表示及其行为的直觉，这将有助于将这些方法扩展到更高的尺寸问题。
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as an MPS within some tolerable error threshold. In this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations in 1D1V, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher dimensional problems.
