It all depends on where the money generated by quantitative easing ends up. In Japan, the money borrowed by the government has found its way back into the pockets of the Japanese people in the form of social security and interest on their savings. Money in consumer bank accounts stimulates demand, stimulating the production of goods and services, increasing supply; and when supply and demand rise together, prices remain stable.
However, what we didn't know before he did it, Ben Bernanke lent the money to the banksters and let them park it at the Fed to earn a spread on that money created just for those banksters to do just that rather than lending it out to Main Street and possibly overheating the economy (causing higher inflation). Ben, of course, has rightly pointed out that the Fed's legal mandate did not include the Fed giving money directly to Main Street. Also of course, during the height of the hyperactivity to address the crash, the US government could have, and should have, changed that mandate. If it had, and if the right investments had been made, the US would not now be in this long depression about to dip again if they don't act and act correctly very soon.