Q-Carbon Is Harder (and Brighter) Than Diamond

Not at all true.

In this case, it could be a phosphorescence or fluorescence process (the NYT says fluorescence), initiated by ambient light.

I skimmed both scholarly publications on this material but didn't find any mention of optical properties. I would ordinarily guess that any optical emission would involve an internal defect site (as happens with other optically-active diamond structures), but I'm thinking that's not a good guess given the synthesis process and overall quality of the monocrystalline product. A better guess might be some sort of "deep trap" emission involving surface defects.