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In the charge qubit, the charge on the island acts as a control parameter. The gate charge is normalized by the charge of a Cooper pair ( nG ＝ CG・VG / 2e ), the effect of the gate voltage VG is originated in such a control parameter.
For the charge qubit, the charging energy Wc ＝ e＾2 / 2 ( Cj ＋ Cg ) is much larger than the Josephson coupling energy Wj .
A convenient basis is formed by the charge states, it’s parameterized by the number of Cooper pairs n on the island.
In this basis, the Hamiltonian ( 4 ) can be written as follows.
H ＝ n Σ ｛ 4Wc（n − nG）＾2 |n〉〈n| ＋ 1/2 Wj ( |n〉〈n＋1| ＋ |n＋1〉〈n| )｝
( 6 )
