They are, of course, weakly correlated. If the US government dropped one million dollars cash into everyone's yard via helicopter, we would probably have some inflation.
But contrary to sibling poster, economists have known for many decades that it is only a weak correlation and plenty of other forces are at work. The weak inflation resulting from QE was predicted by mainstream economics and does not come as any surprise. This is nothing specific to the US economy - Japan and the EU are similar real-world examples if you don't care for the economics and the modeling.
Japan is a fine example actually - 15 years later, Japan is, as expected, still not seeing some kind of phantom, invisible-hand "correction" causing massive inflation.