  The realization of on-chip quantum gates between photons and solid-state
spins is a key building block for quantum-information processors, enabling,
e.g., distributed quantum computing, where remote quantum registers are
interconnected by flying photons. Self-assembled quantum dots integrated in
nanostructures are one of the most promising systems for such an endeavor
thanks to their near-unity photon-emitter coupling and fast spontaneous
emission rate. Here we demonstrate an on-chip entangling gate between an
incoming photon and a stationary quantum-dot spin qubit. The gate is based on
sequential scattering of a time-bin encoded photon with a waveguide-embedded
quantum dot and operates on sub-microsecond timescale; two orders of magnitude
faster than other platforms. Heralding on detection of a reflected photon
renders the gate fidelity fully immune to spectral wandering of the emitter.
These results represent a major step in realizing a quantum node capable of
both photonic entanglement generation and on-chip quantum logic, as demanded in
quantum networks and quantum repeaters.
