  We present a superconducting circuit consisting of a flux qubit and a
single-charge transistor serving as a detector. As flux and charge are
conjugate, the transistor can detect states of the qubit close to the flux
degeneracy point, when the eigenstates are quantum superpositions of fluxes.
The coupling has a flip-flop symmetry conserving the total number of
excitations, and so the measurement outcome results in the absence or presence
of an incoherent tunneling cycle. We evaluate the performance of a practical
device and show that it is an attractive tool for measuring at the degeneracy
point.
