  Quantum Hamiltonian identification is important for characterizing the
dynamics of quantum systems, calibrating quantum devices and achieving precise
quantum control. In this paper, an effective two-step optimization (TSO)
quantum Hamiltonian identification algorithm is developed within the framework
of quantum process tomography. In the identification method, different probe
states are inputted into quantum systems and the output states are estimated
using the quantum state tomography protocol via linear regression estimation.
The time-independent system Hamiltonian is reconstructed based on the
experimental data for the output states. The Hamiltonian identification method
has computational complexity O(d^6) where d is the dimension of the system
Hamiltonian. An error upper bound O(d^3/N^(1/2))$ is also established, where N
is the resource number for the tomography of each output state, and several
numerical examples demonstrate the effectiveness of the proposed TSO
Hamiltonian identification method.
