  We describe how to perform fast quantum limited read-out of a solid state
qubit biased at its degeneracy point. The method is based on homodyne detection
of the phase of a microwave signal reflected by a slow oscillator coupled to
the qubit. Analyzing the whole quantum read-out process, we find that the
detection is indeed quantum limited and that this limit may be reached even
using a resonance circuit with a low quality factor, thus enabling the use of
short measurement pulses. As an example, we discuss in detail the read-out of a
Cooper-pair box capacitively coupled to a lumped element LC-oscillator.
Furthermore, we give formulas for the backaction while not measuring, and
discuss optimal parameters for a realistic design capable of fast (~50 ns)
single-shot read-out.
