论文标题
k王：有效控制量子多体动力学的Krylov子空间方法
K-GRAPE: A Krylov Subspace approach for the efficient control of quantum many-body dynamics
论文作者
论文摘要
梯度上升脉冲工程（葡萄）是一种著名的控制算法，其收敛速度出色，这是由于用于控制功能的零件构成ansatz，可提供廉价的客观梯度。但是，量子动力学的精确模拟涉及的计算工作迅速成为限制大型系统控制的瓶颈。在本文中，我们提出了一种修改的葡萄版本，该版本使用Krylov近似值有效地处理高维状态空间。即使任意控制任务所需的参数数量与系统的维度线性缩放，但我们还是找到了恒定的基本计算工作（每个参数的努力）。由于葡萄的基本努力是超季度的，因此这种速度使我们能够达到远远超出范围的尺寸。 K葡萄算法的性能在范式XXZ旋转链模型中进行了基准测试。
The Gradient Ascent Pulse Engineering (GRAPE) is a celebrated control algorithm with excellent converging rates, owing to a piece-wise-constant ansatz for the control function that allows for cheap objective gradients. However, the computational effort involved in the exact simulation of quantum dynamics quickly becomes a bottleneck limiting the control of large systems. In this paper, we propose a modified version of GRAPE that uses Krylov approximations to deal efficiently with high-dimensional state spaces. Even though the number of parameters required by an arbitrary control task scales linearly with the dimension of the system, we find a constant elementary computational effort (the effort per parameter). Since the elementary effort of GRAPE is super-quadratic, this speed up allows us to reach dimensions far beyond. The performance of the K-GRAPE algorithm is benchmarked in the paradigmatic XXZ spin-chain model.
