A method to calculate effective Hamiltonians in quantum information

Effective Hamiltonian method is widely used in quantum information. We introduce a method to calculate effective Hamiltonians and give two examples in quantum information to demonstrate the method. We also give a relation between the effective Hamiltonian in the Shrödinger picture and the corresponding effective Hamiltonian in the interaction picture. Finally, we present a relation between our effective Hamiltonian method and the James-Jerke method which is currently used by many authors to calculate effective Hamiltonians in quantum information science.