Normally, the only Quick Combos you have access to are the four preset combos (one comes with the game, the other three are free DLC). However, if you buy the Quick Combo Editor DLC (costs 320 MSP/$3), you can make your own Quick Combos and design them move by move.
This thread in particular is discussing the recently-released Quick Combo Editor Expansion (80 MSP/$1; must have the base QC Editor to purchase), which allows you to design combos down to the frame, as well as do “hit confirms” if I remember correctly (basically, you can program your combo to stop after a specific point if the opponent is blocking; nasty, right?).
Personally, I’m going to get both pieces of DLC as soon as I can, since the expansion basically sounds like it allows you to make tool-assisted combos, which will be insanely useful for discovering new combo possibilities.