Data-driven spectral analysis of quantum spin networks with limited access using Hankel dynamic mode decomposition

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.