Quick Ascensions give you Hero Souls without needing to ascend so that you can immediately buy or upgrade Ancients. The number 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)
As of patch 1.0e10, Quick Ascensions are no longer useful at the beginning of a transcendence due to the flat DPS boost from Phandoryss. They are however useful before zone 1000000 in ascensions where it would take a significant amount of time to get back to where you were. As of patch 1.0e11, after zone 1000000, quick ascensions no longer increase in Hero Souls. The best place to use quick ascensions as of the current patch is to wait until zone 250k, which is around Xavira's third upgrade, then use quick ascensions every time you fail to kill a boss. Note it costs around 3.3k Rubies to quick ascend from zone 250k to 1 mil. Once you reach zone 1 million, ascend when you fail to kill a boss and follow the timelapse calculator.