Everybody knows Cong "StrifeCro" Shu -- the winner of many Hearthstone championships and a great streamer. Here you can see his version of the Quest Mage that relies on Alexstraza and Arcane Giants instead of the more typical Exodia Mage with Antonidas.
The strategy is the same in both cases: you need to play six spells that didn’t start in your deck. When the right time comes you play two Giants, then the next turn you set your opponent’s health to 15 and hit it for another 16 for a lethal sweep.
The great advantage of this deck is that you may not even need to finish the Quest to win the matchup. You also don’t need as many cards to set up the lethal as with Exodia Mage. But there is also a drawback -- if your opponent suddenly plays a lot of taunts just before you decide to play Open the Waygate, it can actually prevent you from winning.