Quantum computing using molecular electronic and vibrational states

We numerically constructed elementary phase-correct global quantum gates by using molecular electronic and vibrational states to encode two qubits and implement the Deutsch-Jozsa algorithm. The calculations were based on optimal control theory (OCT). The molecular species we chose were Na2 and Li2. The electronic X1Σg+ and A1Σu+ states were taken as two orthonormalized energy levels of the electronic qubit. The vibrational qubits were those involved in these electronic states. The time duration of the optimized pulses with high fidelity was typically 500-900 fs, which reflects the wavepacket dynamics in electronically ground and excited states. When implementing the Deutsch-Jozsa algorithm by combining these elementary gates, we obtained a maximum probability 83.12% for Li2 molecule, which indicates that the electronic-vibrational qubits are worse than the vibrational-vibrational and the vibrational-rotational qubits reported so far.