  Recently, a new theory of superconductivity has been put forward that
attributes the origin of superconductivity to the appearance of a non-trivial
Berry connection from many-electron wave functions.
  This theory reproduces the major results of the BCS theory with conserving
the particle number, and predicts the single-electron supercurrent tunneling
across the Josephson junction with keeping the correct Josephson relation. We
re-examine the quantization of superconducting qubit circuits by taking into
account the above development, and show that the dynamical variables used in
the standard theory, the flux nodes relating to the voltage, should be replaced
by those relating to the electromagnetic vector potential. The fact that the
Josephson junction tunneling allows the single-electron supercurrent tunneling
is the reason for the existence of excited single electrons in superconducting
qubits with Josephson junctions. We predict that it will be avoided by
weakening the coupling between two superconductors in the Josephson junction.
