One of the most interesting trends in higher education over the last few years is the rise of China and the relative decline of the USA.
Winston Churchill said the empires of the future will be empires of the mind. If that is so then this century will very likely be the age of Chinese hegemony. Chinese science is advancing faster than that of the USA on all or nearly all fronts. Unless we count things like critical race theory or queer studies.
This is something that should show up in the global rankings if we track them over at least a few years. So, here is a comparison of the top two universities in the two countries according to indicators of research output and research quality over a decade.
Unfortunately, most international rankings are not very helpful in this respect. Few of the current ones provide data for a decade or more. QS and THE have seen frequent changes in methodology and THE's citation indicator although charmingly amusing is not useful unless you think that Aswan University, Anglia Ruskin University and the University of Peradeniya are world beaters for research impact. Two helpful rankings here are Shanghai Academic Ranking of World Universities (ARWU), and Leiden Ranking.
Let's compare the comparative performance of Tsinghua University and Harvard in the Shanghai Ranking's indicator of research output, papers over a one year period, excluding arts and humanities. The published scores are derived from the square roots of the raw data with the top scorer getting a score of 100.
In 2009 Harvard's score was 100 while that for Tsinghua was 55.8. In 2019 it was 100 for Harvard and 79.5 for Tsinghua. So the gap is closing 2.37 points every year. At that rate it would take about nine years for Tsinghua to catch up so look out for 2028.
Of course, this is quantity not quality so take a look at another indicator, Highly Cited Researchers. This is a moderately gamable metric and I suspect that Shanghai might have to abandon it one day but it captures the willingness and ability of universities to sponsor research of a high quality. In 2009 Tsinghua's score was zero compared to Harvard's 100. In 2019 it is 37.4. If everything continues at the same rate Tsinghua will overtake Harvard in another 17 years.
Looking at the default indicator in Leiden Ranking, total publications, in 2007-10 Tsinghua was 35% of Harvard and in 2014-17 56%. Working from that Tsinghua would achieve parity in 2029-33, in the rankings published in 2035.
Looking at a measure of research quality, publications in the top 10% of journals, Tsinghua was 15% of Harvard in 2007-10 and 34% in 2014-17. From that, Tsinghua should reach parity in 2038-42. in the rankings published in 2044, assuming Leiden is still following its current methodology.
So it looks like Tsinghua will reach parity in research output in a decade or a decade or a decade and a half and high quality research in a decade and a half or two decades and a half.