Potential energy of proton transfer. The systems are (a) in vacuum and (b) in the aqueous system; the nucleotide base pairs are (1) DNA: A=T, (2) DNA: \(C\equiv G\) \(\), (3) RNA : \(C\equiv G\) , (4) RNA: A=U, and (5) RNA: G=U. T1, T2, and T3 indicate the transfer process for protons H1, H2, and H3, respectively. All proton transfer potential surfaces contain an asymmetric double-well. \(\Delta\)GD ( \(\Delta\)GA) is the barrier height from the donor state (the acceptor state) to the barrier top and it is much larger than the thermal energy kBT at room temperature. When the residue pairs are in aqueous solution, it is explicitly shown that \(\Delta\)GD ( \(\Delta\)GA) is increased. Under such high energy barriers, there is a distinct separation between the donor state and the acceptor state, where the donor (acceptor) state can be defined as either \(|0\rangle\) (\(|1\rangle\)) or \(|1\rangle\) (\(|0\rangle\)) \(\). In Appendix, Eq.(A3) shows the superposition of the two states \(|0\rangle\) and \(|1\rangle\) , and then the qubit state can be obtained.