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

Scalable two- and four-qubit parity measurement with a threshold photon counter