Quantum system identification is a prerequisite for any technology in quantum engineering in order to build reliable devices for quantum computation, quantum cryptography, or quantum metrology. In particular, characterization of the many-body qubit Hamiltonians is essential in the quest of building a scalable quantum information processor. Also, the development of system identification techniques is expected to have impact in diverse fields, such as structural determination of a complex molecule, biosensing and studying magnetism at the nanoscale.

Recent progress in quantum metrology assisted by single quantum probe has demonstrated the ability to achieve precise estimation of a few unknown parameters. These advances now open experimental opportunities for multiple parameter estimation, while offering the advantage of nanoscale probing and coherent coupling of complex quantum systems.

In this talk, I discuss the estimation of the Hamiltonian parameters and the dimension of the finite-size Hilbert space assisted by a single quantum probe coupled to the target many-body qubit system. I focus on the idea of identifiability by employing realization theory in the classical linear system theory. For the parameter estimation, I also demonstrate the application of the Groebner bases for the determination of the Hamiltonian identifiability and also demonstrate a possible control protocol to achieve the identifiability in the one-dimensional spin chain system. For the dimension estimation, I demonstrate an exact dimension estimation of a finite-size Hilbert space, which can be given from the model order of the system when the system is minimal (controllable and observable). Also I introduce some possible open problems related to the quantum system identification problem.