  Fast and accurate measurement is a highly desirable, if not vital, feature of
quantum computing architectures. In this work we investigate the usefulness of
adaptive measurements in improving the speed and accuracy of qubit measurement.
We examine a particular class of quantum computing architectures, ones based on
qubits coupled to well controlled harmonic oscillator modes (reminiscent of
cavity-QED), where adaptive schemes for measurement are particularly
appropriate. In such architectures, qubit measurement is equivalent to phase
discrimination for a mode of the electromagnetic field, and we examine adaptive
techniques for doing this. In the final section we present a concrete example
of applying adaptive measurement to the particularly well-developed circuit-QED
architecture.
