Quick Ascensions give you free Hero Souls so 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 up to several hundred if you've been playing a while. The amount resets once you transcend.
Quick Ascensions are available in the Ruby Shop for 50 Rubies.
The formula for QA is the following:
(((BaseTPReward + BasePrimalReward × SolomonMutliplier) + CappedBosses × TPCap) × PrimalChance
BaseTPReward = 20 × (((1 + TP) ^ (UncappedBosses + 1) - 1) / TP)
BasePrimalReward = Sum from 1 to TotalBosses: ((boss + 4) / 5) ^ 1.3
Capped Bosses = Floor((HZE-CapZone)/5) Assuming HZE > CapZone
Uncapped Bosses = Floor((CapZone-100)/5)
TotalBosses =UncappedBosses + CappedBosses
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.