  The readout process of a superconducting flux-qubit is theoretically analyzed
in terms of the quantum dynamics of a qubit-SQUID coupled system during
measurement. The quantity directly observed by the measurement is the switching
current (Isw) of the dc-SQUID placed around the qubit ring. In order to clarify
the relation between the Isw and the qubit state, we calculated the time
evolution of the density operator of the qubit-SQUID system while increasing
the SQUID bias current until switching events occur and obtained the switching
current distributions. This clarifies what information of the qubit is obtained
by a dc-SQUID switching current measurement under specific conditions, for
example, when the qubit eigenstate is a superposition of two different flux
states.
