It's difficult to rank ancient empires, however, you cannot take the estimate of the world population by one scholar and mix it with estimates of a particular empire by another without adjustment. That is the problem with the random figures given for the Achaemenid empire. You cannot take a baseless high figure of 50 million and mix it with the low count given by McEvdy and Jones, then take McEvdy and Jone's figure of world population, which only assumed a 17 million people for the Achaemenid Empire, without at least adding another 30 million to it, making the world population at least over 130 million rather than 116 million (the source of which I have not being able to locate).And as noted by others, also the estimates of the population of the ancient Empires vary a lot [I mean academic estimates].
These two aspects make similar comparisons not that meaningful. As usual, to make a chart, we need the certainty of a good level of approximation. And statistically, when it comes the time to make the chart, a difference of just a 10% in the estimates of the world population can change the position of this or that Empire. Just consider the very different estimates about world population in 1st century CE and the estimates about the Roman Empire …
Furthermore, the figure of 50 million did not come from any exhaustive professional demographic estimate, but from generic introductory history books and journals written by non-historians (the citation page is now taken down from wikipedia, so I don't know why people are still circulating the figure). The figure is even more unlikely when you consider that even as late as 1900, the population of the region outside of Pakistan which constituted the entire Persian Empire was just over 50 million, broken down as follows:
Iran: 10 million
Iraq: 2 milion
Turkey: 12 million
Egypt: 10 million
Armenia: 1.3 million
Afghanistan: 3.6 million
Persian Central Asia: 7 million
With clear population growth (doubling or more) in places like Egypt, Central Asia, Afghanistan, and Iran where we have actual Roman era statistics, rough Han figures, and middle age census. It is absurd to think the region had the same population in 500 BC as 1900 and much greater in 500 BC than it was in the first century and in the late middle ages.
Both the Han and Roman Empire probably ranges in estimate from below 1/4 - just over 1/3, if we adopt Durand and McEvdy and Jones high end and low end estimates respectively. It's unlikely however, that either surpassed the Qing in total percentage even if we assume a lower world population given by McEvdy and Jones.
I would say the only state where a range of plausible academic estimates allows it to potentially surpass the Qing in total world population percentage count is the mid-8th century Tang, if the higher figure of 90 million is used (and there are a number of historians which accept it based on actual primary records such as the Yuanhe Junxiantuzhi, which showed that hidden households in the Tang might have been as large as those on the census).