  The ability to nondestructively detect the presence of a single, traveling
photon has been a long-standing goal in optics, with applications in quantum
information and measurement. Realising such a detector is complicated by the
fact that photon-photon interactions are typically very weak. At microwave
frequencies, very strong effective photon-photon interactions in a waveguide
have recently been demonstrated. Here we show how this type of interaction can
be used to realize a quantum nondemolition measurement of a single propagating
microwave photon. The scheme we propose uses a chain of solid-state 3-level
systems (transmons), cascaded through circulators which suppress photon
backscattering. Our theoretical analysis shows that microwave-photon detection
with fidelity around 90% can be realized with existing technologies.
