The Qin's population is about six million, it produces three millions soldier. Everyman is a soldier, it is integrate part economy, political, and military force. The mass production in manufacturing weapon equal to today standard. The water engineering is one best for it's time. Highway stress across mountain top and cliff, it is engineering wonder for it's time. Why are Qin army so successful, it have to do hard work ethic. The key is best technology, economy, and military. The is WHY, the SEAL OF QIN is MANDATE OF HEAVEN, whoever hold seal is rightful ruler China. It is not the Seal of Qin that is important but rather it is knowledge, it is the Mandate of Tao.
I agree with MHW that the per centage of population that can be placed under arms is much much less, due to sheer logistics. Even among the male draftees, the majority would have to be porters and transportation gang, not actual fighting men in arms.
I have my doubts regarding the supposed Qin economic success. It was a proto- totalitarian state, with the government trying to manage the minutia of people's lives. Of all the totalitarian/fascist states that we have more reliable records of, there has never been an economic success story (or success in any other terms except for in extremely short-run military goals). All the 20th century experiments to duplicate the Qin grain-and-war economic model failed despite much more advanced communication and propaganda technologies 2000+ years later, and failed miserably in very short order. Sure, one may marvel at the Qin gallery roads, canal and straight-way to the north the same way that one might marvel at the Autobahn built by the Nazis in the 1930's; however, let's not forget, not a single VW had been sold to a German consumer until after WWII. The government sponsored factory was simply too inefficient to make them affordable like Ford and GM could despite the supposed German efficiency. Consequently, there simply weren't enough Germans who had cars to run on the Autobahn until long after WWII. In other words, even the much vaunted Autobahn built in the 1930's was a waste of resources.
I'm still of the opinion that Qin was an economic basket case, thanks to all the government intervention. The people of Qin lived off looting the other states. The cheaper looted goods arriving in Qin further bankrupted what producers there had been in Qin (just like in Roman time, and to a degree today's US domestic manufacturing being destroyed by cheap imports). More or more Qin peons had to resort to government jobs (the military being the primary one) in order to make a living. This is a rather common motif for ancient civilizations, just like the "war-like" tribes on northwest fridge of Indian subcontinent and Arabia, they were not economic or technologically advanced (except for in specific very effective weapon when they did succeed militarily for a short time) at the time of conquest.
So, did the Chinese unification experience prove that eventually the more barbaric totalitarian regime wins in the end? Not really. Unlike a computer game that ends after you paint the entire map your own color, real life goes on after "unification." The Qin "unification" of China proved to be an utter disaster for all the people in various states of modern day China; it was a disaster for the people of Qin, who supposedly labored for 130+ years after ShangYang's reforms in order to achieve the ultimate goal, slaughtering and dying in the millions in the process, only to have the new universal regime overthrown after only 13 years, then the slaughtering of hundreds of thousands of more Qin people by the invading armies from elsewhere. What kind of success is that? It too was a disaster for the Qin royal household/lineage, which lasted over 600 years before "unification" only to be utterly eradicated to the last man a decade and half later. What about the bureaucratic intriguers who were the real driving force behind the "I'm the king of the world" enterprise? In that regard it too was a disaster, for ShangYang, LuBuWei, LiSi and ZhaoGao.
That is the intellectual framework we need to understand. The 130+year endeavor by Qin to conquer all other states was not a success story, but an utter disaster for all involved.
As to why Qin Army had disproportional battlefield success vis others, there are several reasons:
1. The most important is Geography. Like Howard and others mentioned earlier, Qin is naturally easy to defend to begin with due to the mountain passes being the only access route from the east. All major Chinese rivers running from west to east tremendously helped Qin army invading the other states down-stream.
The 10-year "unification war" by YingZhen in the 232-222BC was re-fought between LiuBang and XiangYu a mere two decades later (another reason why Qin "unification" was not at all the end of the "game"). Once again, the party who controlled the northwest fulcrum won the fight, largely due to logistics.
2. Bad operational decisions on the part of the other six states, most importantly Chu, Zhao and Qi. Part of the reasons behind those bad decisions was also related to logistics. For example, Zhao at Changping changing over from LianPo's defense to ZhaoKuo's offense was the desire to shorten the war and avoid the insurmountable difficulty of getting food to feed the garrison. Wang Jian's final success against Chu was once again because Chu disbanded large parts of its army to simplify logistics.
3. Qin may have been the first to master Sarissa. This is a new theory on my part. What we see at the QSHD tomb, there were phalanx armed with Sarissa (very very long spear, measuring 17-23ft, 6-7meters). It's the same weapon that Alexander used to conquer the "known world." Massed chariots became completely obsolete if your opponent had well trained phalanx wielding Sarissa, as amply proved by Alexander's success against numerically far superior Persian army. Yet, QSHD tomb also had chariot array . . . which means Qin's opponents did not have well trained Sarissa phalanx. Massed chariots became obsolete in the West immediately after Phillip and Alexander's Sarissa arrays showed up (with adequate flank protection by combined arms of course). Massed chariots became obsolete in China at the end of the Warring State period. Alexander showed up in Afghanistan in the 310'sBC. Qin may well have been the first Chinese state to acquire that technology and put to good use. That may well explain SiMa Qian's "strange formations" at ChangPing, that was able to drive through and divide Zhao's supposedly 400k army with a mere 20k soldiers. May also explain why LianPo's initial combats with Qin in the open were disasterously unfavorable to Zhao and had to abandon open field combat altogether and withdraw into forts behind high walls. Also explains why ZhaoKuo's "paper manuever" using formation head counts fell apart when put into practice in the field; the Sarissa phalanx would sweep much larger infantry arrays and chariot arrays from the field, just like Alexander's did.
Sarissa was not just a longer spear. It was two metal tipped spears made with hard wood, and joined together in the middle with a bronze lock mechanism. When the two parts are joined together, it's much much longer than any single-stick spear. A constant problem with pikemen/pole-arm formation (as late as late mid-ages) is that troops on manuever in the field would shorten the sticks to make their own lives easier, because most war casualties before th 20th century were not from actual combat but from disease, exhaustion, starvation, etc.. So cutting short the stick would help the individual soldier's survival; that is, until real battle is joined, then during the "pushing of pikes" the side with the shorter sticks came out, well, literally holding the short end of the stick, so to speak. Phillip (Alexander's father) invented Sarissa to solve this problem, and it proved a tremendous success (so long as the flanks are covered). The first 4-5 ranks pointing forward could push over anyone not similarly armed; the rear ranks holding the Sarissa upward not only could deflect incoming arrows/bolts but also obscure enemy observation of friendly reserve deployment behind the lines. It's the special formation that conquered the western world under Alexander, and may well have been a major factor in Qin's battlefield success in 260BC and beyond.