  Developing compact, low-dissipation, cryogenic-compatible microwave
electronics is essential for scaling up low-temperature quantum computing
systems. In this paper, we demonstrate an ultra-compact microwave directional
forward coupler based on high-impedance slow-wave superconducting-nanowire
transmission lines. The coupling section of the fabricated device has a
footprint of $416\,\mathrm{\mu m^2}$. At 4.753 GHz, the input signal couples
equally to the through port and forward-coupling port (50:50) at
$-6.7\,\mathrm{dB}$ with $-13.5\,\mathrm{dB}$ isolation. The coupling ratio can
be controlled with DC bias current or temperature by exploiting the dependence
of the kinetic inductance on these quantities. The material and
fabrication-process are suitable for direct integration with superconducting
circuits, providing a practical solution to the signal distribution bottlenecks
in developing large-scale quantum computers.
