Data-driven spectral analysis of quantum spin networks with limited access using Hankel dynamic mode decomposition
Data-driven spectral analysis of quantum spin networks with limited access using Hankel dynamic mode decomposition
复制标题
DOI：
10.1109/cdc51059.2022.9993116
复制
发表时间：
2022-12
期刊：
影响因子：
--
通讯作者：
Yuzuru Kato;H. Nakao
中科院分区：
文献类型：
--
作者：
Yuzuru Kato;H. Nakao
动态模式分解（DMD）是一种用于预测和控制复杂动力系统的无方程、数据驱动的方法。最近提出了一种用于数据驱动量子控制的DMD方法，并在单自旋系统中进行了数值模拟，其中可以获得完整的正交规范哈密顿量集的时间序列[1]。在量子自旋网络中，通常很难访问所有的自旋，但实际上只有一小部分自旋是可以访问的。在本文中，我们制定了一个开放的量子系统的Hankel-DMD方法和DMD框架的适用性扩展到量子自旋网络有限的访问。我们表明，汉克尔DMD可以精确地评估本征值和分解的动力学到各自的振荡本征模式从观察到的数据。特别地，它可以揭示在虚轴上具有本征值的自旋网络中的无退相干动力学。
Dynamic mode decomposition (DMD) is an equation-free, data-driven method for the prediction and control of complex dynamical systems. A DMD method for data-driven quantum control was proposed recently and numerically demonstrated in a single spin system where time series of a complete orthonormal set of Hamiltonian is available [1]. In quantum spin networks, it is generally difficult to access all spins but only a small set of spins is practically accessible. In this paper, we formulate a Hankel-DMD method for open quantum systems and extend the applicability of the DMD framework to quantum spin networks with limited access. We demonstrate that Hankel DMD can precisely evaluate the eigenvalues and decompose the dynamics into the respective oscillatory eigenmodes from the observed data. In particular, it can reveal the decoherence-free dynamics in spin networks possessing eigenvalues on the imaginary axis.