  Integrated photonics provides a route both to miniaturize quantum key
distribution (QKD) devices and to enhance their performance. A key element for
achieving discrete-variable QKD is a single-photon detector. It is highly
desirable to integrate detectors onto a photonic chip to enable the realization
of practical and scalable quantum networks. We realize an integrated
heterogeneous superconducting-silicon-photonic chip. Harnessing the unique
high-speed feature of our optical waveguide-integrated superconducting
detector, we perform the first optimal Bell-state measurement (BSM) of time-bin
encoded qubits generated from two independent lasers. The optimal BSM enables
an increased key rate of measurement-device-independent QKD, which is immune to
all attacks against the detection system, and hence provides the basis for a
QKD network with untrusted relays. Together with the time-multiplexed
technique, we have enhanced the sifted key rate by almost one order of
magnitude. With a 125 MHz clock rate, we obtain a secure key rate of 6.166 kbps
over 24.0 dB loss, which is comparable to the state-of-the-art MDI-QKD
experimental results with GHz clock rate. Combined with integrated QKD
transmitters, a scalable, chip-based and cost-effective QKD network should
become realizable in the near future.
