What technologies did the Han and Qin Dynasties invent and were known for?

The Qin and Han were early dynasties of a unified China.
The Qin dynasty ruled briefly, from just 221-206 BCE, but was important because it was
the dynasty that first unified China. It had a rather authoritarian rule, and its
harshness was part of the reason for its downfall and replacement with the Han dynasty.
Among its other achievements, the Qin dynasty standardized measurements and invented the
crossbow. But I think the answer you’re looking for is that the Qin dynasty’s signature
accomplishment was the completion of the Great Wall to fortify, secure, and define its
borders. It’s an accomplishment we still associate with China
today.

The Han dynasty (206 BCE-220 CE) was a period of
advancement in thought and culture in ancient China. Developments were made in
iron-working and in methods of agriculture and engineering. But the most significant
advance was the invention of paper for writing by Cai Lun in about 105 CE, although
there is some evidence that paper was used earlier than that. Early paper was made from
plant fibers and old rags. It was used for wrapping things as much as anything. But of
course, given the importance of writing and the importance ancient China placed on
preserving its history and other texts, the adoption of paper for writing is the most
important achievement of this early period.

Note that China
has a long history as a continuous civilization and a number of other key advances were
made here. Gunpowder especially came from China (although much later than the Han
or Qin) and has influenced the history of the world, perhaps more than any other
invention.