initially QE may only increase base money supply - as commercial banks reserve balances get credited by the Central Bank if the Central Bank purchases assets from non-bank financial institutions, then broad money increases directly as well, as deposits increase
the US Treasury may also issue more debt to increase the supply of safe assets, thus offsetting the compression shock end result: more safe assets/prime collateral provided to markets. remember that the newly issued treasuries are likely to be rehypothecated several times