Dynamical Evolution of Superoperator for Hamiltonian Identification and Quantum Dynamical Control

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Estimation of quantum Hamiltonian systems is a pivotal challenge to modern quantum physics and especially plays a key role in quantum control. In the last decade, several methods have been developed for complete characterization of a \'superopertor\', which contains all information about a quantum dynamical process. However, it is not fully understood how the estimated elements of the superoperator could lead to a systematic reconstruction of many-body Hamiltonians parameters generating such dynamics. Moreover, it is often desirable to utilize the relevant information obtained from quantum process estimation experiments for optimal control of a quantum device. In this work, we introduce a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we develop a dynamical equation for the evolution of the superoperator acting on the system. This equation does not presume any Markovian or perturbative assumptions, hence it provides a broad framework for analysis of arbitrary quantum dynamics. As a result, we demonstrate that one can efficiently estimate certain classes of Hamiltonians via application of particular quantum process tomography schemes. We also show that, by appropriate modification in the data analysis techniques, the parameter estimation procedures can be implemented with calibrated faulty state generators and measurement devices. Furthermore, we propose an optimal control theoretic approach for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.