Identification of quantum closed systems via the quantum process tomography

The dynamics of an unknown closed quantum system can be characterized by a Hamiltonian. We discuss the identification of this Hamiltonian from quantum process tomography data at several time points for systems with a time-independent Hamiltonian. Quantum process tomography (QPT) yields a set of unitary operators and allows us to convert the identification problem into an estimation problem for the eigenfrequencies of the system. Spectral decomposition of Hermitian and unitary operators shows that process tomography needs to be performed at least at two different time points and the identifiability of the Hamiltonian depends on the choice of these points. Sufficient conditions on the timing to ensure complete identifiability of the Hamiltonian are presented under the assumption that unitary matrices obtained from QPT are exact without numerical errors.