  We perform a detailed analysis of how an amplified interferometer can be used
to enhance the quality of a dispersive qubit measurement, such as one performed
on a superconducting transmon qubit, using homodyne detection on an amplified
microwave signal. Our modeling makes a realistic assessment of what is possible
in current circuit-QED experiments; in particular, we take into account the
frequency-dependence of the qubit-induced phase shift for short microwaves
pulses. We compare the possible signal-to-noise ratios obtainable with
(single-mode) SU(1,1) interferometers with the current coherent measurement and
find a considerable reduction in measurement error probability in an
experimentally-accessible range of parameters.
