Quantitative easing (QE) is essentially a large-scale form of open market operations, in which the Fed buys large amounts of treasury bills of all maturities (ranging from 1-month to 30-year) and mortgage-backed securities from commercial banks. By doing so, they are crediting these depository institutions with large amounts of electronic money. Thus, wouldn't there be a large expansion of the supply of federal funds in the federal funds market as a result of QE? And hence, wouldn't the federal funds rate keep on decreasing, even below zero, as the Fed's massive "QE infinity" programme continues?
At the time of writing this answer, the Federal Reserve pays 0.1% on reserves: link to Fed webpage.
Banks have no incentive to lend Fed Funds at rates below 0.1%, as they can keep the excess reserves and earn a higher rate of interest.
Interest rates are largely set by price signals made by central banks, not quantities.