The quantum yield depends on your method of preperation and the geometry of GQD. Also it will depend on the standard you use for the calulation of the quantum yield.
First things is the preparation method you are adopting for the highly fluorescent QDs. Secondly, go for pH studies and temperature studies for the better yield at optimized molar ratios.
Third the most important is the measuring method for the QY you are adopting, as other researchers mentioned above.
Consider the solvent nature of your standards and your sample while calculating QY. However you can follow the following paper for measuring QY it is quite simple but is little lengthy, it provides good measurement method with less mistakes.
As far as I know, The functionalisation of QDs has a major role in enhancing the quantum yield. During the synthesis of QDs a certain ligand is added (e.g. TOPO), so the yield should be cleaned several times to remove the excess of ligand, and then a ligand exchange should be performed to play with the surface chemistry of QDs by choosing a good ligand (e.g. amines). after doing the ligand exchange you can measure the fluorescence if there is a sort of luminescence in the spectrum then you can say that the QDs are not well passivated. Overall, consider the functionality of the surface and try to maintain a well passivation to it.
I believe you can enhance the QY% if you passivate their surface with a polymer such as PEG or PEI and also if you have your GQDs in a medium when they might quench that would be a reason for the low QY%. Also the pH is very important factor due to protonation and deprotonation processes at the edges.
Manila, i am also synthesis Graphene Quantum Dots (GQDs) very difficult, Yes, Low Yield, Purification, Filtration very difficult and Low Yield few mg only, few synthesis method to GQDs. it may be try precursor materials taken more.