According to Guns, Germs, and Steel, why did politically united China lose its technological advantage to the formerly backward and politically fragmented Europe?
The answer to this can be found in the Epilogue. There, Diamond tells us that the very fact that China was united while Europe was fragmented gave Europe an advantage over time.
Because Europe was fragmented, there was competition between various states. If one state refused to go exploring (to send Columbus out, for example) another would try it to see if it could gain an advantage over its neighbors. China had no such rivals. If China wanted to stop exploring, there was no other rival power to try exploring. This meant that various sorts of technologies or ideas could be rejected by China. In contrast, one European country or another would surely embrace every possible idea or technology.
In short, China was able to rest on its laurels while European countries had to fight constantly to get ahead of one another. This caused China to lose its lead to those countries.