If you had a better knowledge of history you would realise that China does not need to "overtake" the US in turbofan technology. All it needs is an engine that provides power in the range 170KN+ for J-20 to be a serious air superiority fighter but be "reliable enough". Since the J-20 is a twin engine fighter each turbofan does not need to be as reliable as engines like the F100 in the F-16 as the fighter can always land on one engine if the other one fails. What is important is reaching the thrust levels while achieving a decent level of reliability.
China's engine designers openly admit that it could be 2040 till they reach US levels of turbofan technology. As long as the J-20 has good avionics and a good airframe, the inability to design an engine as reliable as the US will matter little. After all, did the AL-31 in the SU-27 reach the level of the F-100 in the F-15? No it did not but the Su-27 was not considered an inferior fighter as it could deliver the same levels of thrust as the F-15 and hence it had better maneuverability due to a better airframe.