  The increasing need for scaling up quantum computers operating in the
microwave domain calls for advanced approaches for control electronics. To this
end, integration of components at cryogenic temperatures hosting also the
quantum devices seems tempting. However, this comes with the limitations of
ultra-low power dissipation accompanied by stringent signal-quality
requirements to implement quantum-coherent operations. Here, we present a
device and a technique to provide coherent continuous-wave microwave emission.
We experimentally verify that its operation characteristics accurately follow
our introduced theory based on a perturbative treatment of the capacitively
shunted Josephson junction as a gain element. From phase noise measurements, we
evaluate that the infidelity of typical quantum gate operations owing to this
cryogenic source is less than 0.1$\%$ up to 10-ms evolution times, which is
well below the infidelity caused by dephasing of the state-of-the-art
superconducting qubits. Our device provides a coherent tone of 25 pW,
corresponding to the total power needed in simultaneous control of thousands of
qubits. Thus, together with future cryogenic amplitude and phase modulation
techniques, our results may open pathways for scalable cryogenic control
systems for quantum processors.
