  Photon detectors are an elementary tool to measure electromagnetic waves at
the quantum limit and are heavily demanded in the emerging quantum technologies
such as communication, sensing, and computing. Of particular interest is a
quantum non-demolition (QND) type detector, which projects the quantum state of
a photonic mode onto the photon-number basis without affecting the temporal or
spatial properties. This is in stark contrast to conventional photon detectors
which absorb a photon to trigger a `click' and thus inevitably destroy the
photon. The long-sought QND detection of a flying photon was recently
demonstrated in the optical domain using a single atom in a cavity. However,
the counterpart for microwaves has been elusive despite the recent progress in
microwave quantum optics using superconducting circuits. Here, we implement a
deterministic entangling gate between a superconducting qubit and a propagating
microwave pulse mode reflected by a cavity containing the qubit. Using the
entanglement and the high-fidelity qubit readout, we demonstrate a QND
detection of a single photon with the quantum efficiency of 0.84, the photon
survival probability of 0.87, and the dark-count probability of 0.0147. Our
scheme can be a building block for quantum networks connecting distant qubit
modules as well as a microwave photon counting device for multiple-photon
signals.
