Hamiltonian of Homonucleus Molecules for NMR Quantum Computing

We derive the Hamiltonian in the rotating frame for NMR quantum computing with homonucleus molecules as its computational resource. The Hamiltonian thus obtained is different from conventional Hamiltonians that appear in literature. It is shown that control pulses designed for heteronucleus spins can be translated to pulses for homonucleus spins by simply replacing hard pulses by soft pulses with properly chosen pulse width. To demonstrate the validity of our Hamiltonian, we conducted several experiments employing cytosine as a homonucleus molecule. All the experimental results demonstrate that our Hamiltonian accurately describes the dynamics of the spins, while the conventional Hamiltonian fails. Finally we use our Hamiltonian for precise control of field inhomogeneity compensation with a pair of $\pi$-pulses.