I could imagine that the simplest approach would be not to use year-quarter as dimension else using n expressions (for each bar one) because it decoupled the periods from each other. Defining the current and previous one within appropriate set statements is rather simple - but in regard to the relationship of the data the current ones doesn't belong to the previous ones and revers and therefore they couldn't be compared directly.
UI alternatives may be to wrap the comparing logic within (n) aggr() to implement there approaches which ignore/overwrite the relationship with set statements like {1} and/or using interrecord-functions like above() to connect different periods with each other. Depending on real scenario such method could become quite complex.
Personally I would tend to transfer the essential part of the logic into the data-model by using The As-Of Table - Qlik Community - 1466130 or creating (n) flags containing the offset between the sales in day/month/quarters and/or between the sales and today and maybe some kind of clustering/scoring of these flags.
I forgot to say that the end user should be able to filter by product/product category and any other filters in the UI. Then it can't be pre calculated in the script.
using Product as an example. If they select product A, do you want to know if the customer purchased that particular product as a new customer this quarter vs last or any product?
