In the quantum information science, quantum simulation is one of the new field which imitate other quantum mechanical behavior by using well known quantum computer.
In this study, we simulated the energy exchanging interaction $a^{\dagger}ㆍb + aㆍb^{\dagger}$ between two qubits by NMR quantum computer. To simulate the exchanging interaction, we mapped the simulating Hamiltonian to NMR quantum computer`s Hamiltonian and then we were prepared the effective pure state to survey how final state is changed as the interaction time goes longer. Effective Hamiltonian in a NMR quantum computer was implemented on the effective pure state by using several NMR pulses. we were focused on the initial state $|10\rangle$, because the exchanging interaction gave the same density matrix in the states of $|00\rangle$ and $|11\rangle$. The tomography of the final density matrix was shown the same result of theoretical expectation that the elements of $|01\rangle$ and $|10\rangle$ was oscillated respectively as interaction time increased during the period π.