  In this paper, we present a Hamiltonian identification method for a closed
quantum system whose time trace observables are measured with colored
measurement noise. The dynamics of the quantum system are described by a
Liouville equation which can be converted to a coherence vector representation.
Since the measurement process is disturbed by classical colored noise, we
introduce an augmented system model to describe the total dynamics, where the
classical colored noise is parameterized. Based on the augmented system model
as well as the measurement data, we can find a realization of the quantum
system with unknown parameters by employing an Eigenstate Realization
Algorithm. The unknown parameters can be identified using a
transfer-function-based technique. An example of a two-qubit system with
colored measurement noise is demonstrated to verify the effectiveness of our
method.
