  Parity measurement is a central tool to many quantum information processing
tasks. In this Letter, we propose a method to directly measure two- and
four-qubit parity with low overhead in hard- and software, while remaining
robust to experimental imperfections. Our scheme relies on dispersive
qubit-cavity coupling and photon counting that is sensitive only to intensity;
both ingredients are widely realized in many different quantum computing
modalities. For a leading technology in quantum computing, superconducting
integrated circuits, we analyze the measurement contrast and the back action of
the scheme and show that this measurement comes close enough to an ideal parity
measurement to be applicable to quantum error correction.
