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The loss of amorphous hydrogenated silicon nitride (a-SiN$_{x}$:H) ismeasured at 30 mK and 5 GHz using a superconducting LC resonator down toenergies where a single-photon is stored, and analyzed with an independenttwo-level system (TLS) defect model. Each a-SiN$_{x}$:H film was deposited withdifferent concentrations of hydrogen impurities. We find that quantum-regimedielectric loss tangent $\tan\delta_{0}$ in a-SiN$_{x}$:H is stronglycorrelated with N-H impurities, including NH$_{2}$. By slightly reducing $x$ weare able to reduce $\tan\delta_0$ by approximately a factor of 50, where thebest films show $\tan\delta_0$ $\simeq$ 3 $\times$ 10$^{-5}$.

Reducing quantum-regime dielectric loss of silicon nitride for superconducting quantum circuits