Quick Ascensions give you Hero Souls without needing to ascend so that you can immediately buy or upgrade Ancients. The amount of souls depends on your game progress, starting at 7 if you are in a new game, or several hundred if you've been playing a while. The amount resets once you transcend. Buying one will also add 1 ascension to your total, seen in the stats tab.
Quick Ascensions are available in the Ruby Shop for 50 Rubies.
The formula for QA is the following:
(((BaseTPReward + BasePrimalReward × PonyboyMutliplier)) × PrimalChance
BaseTPReward = 20 × (((1 + TP) ^ (UncappedBosses + 1) - 1) / TP)
BasePrimalReward = Sum from 1 to TotalBosses: ((boss + 4) / 5) ^ 1.3
Bosses = Floor((CapZone-100)/5)
It's a good idea to buy a Quick Ascension immediately after you transcend. The bonuses that come with Outsiders apply to Ancients, so if you don't immediately ascend then you'll be waiting a long time to take advantage of the Transcendence.