How are companies chosen for the Nasdaq-100 index? I'm having difficulty finding out. Is it a rules-based system?
...
Well, I just asked Bard (it does seem smarter than me):

May I humbly (yet with great emphasis) suggest nobody ever post information from a generative AI?
In this case the key point--it's the 100 largest non-financial firms on Nasdaq--is pretty much correct.
(they only kick you out after you fall below rank 105).
But, let's be very clear about this, the fact that it's correct is purely a coincidence. It's a bullshit machine which happens to be right, or close, sometimes.

In this case the response is a muddled mix of things about the Nasdaq 100 and the Nasdaq 100 Equal Weight indexes.
The index constituents are chosen only annually for both, a pretty important point it doesn't mention.
The equal weight is rebalanced quarterly.
The non-equal-weight index is NOT cap weighted. It's the one that is a popular benchmark, not the equal weight index that I presume you asked about, which is very niche.

Eligibility is open to non US firms and ADRs, but only if they have US listed options.

Let's make a consensus note not ever to post generative AI text on any subject.
It will be hard enough to avoid in the years to come, so there is no need to pollute our own swimming pool as well.
If its poetry ever gets to be any good, we can consider an exception for that.

Separately---
Just be aware that QQQ has outperformed QQQE on price by @30% over the last 5 years - with significantly more volatility, of course.

The Nasdaq 100 Equal Weight index (e.g., QQQE) can be thought of as a very good tracker of a certain style of company, without material company specific risk.
The "normal" (broken cap weight) is best thought of as the same thing, plus or minus a huge random number based on the company-specific fortunes of a handful of very large firms.
The random number has been kind in some recent years, which has recently caused the result you mention.
But--
* One should not attempt to extrapolate that result. The gap will just be more random numbers.
Bearing in mind that the very largest cap firms are historically on average underperformers over time, the dice are arguably slightly weighted against QQQ in the long run.
* If you have informed opinions on the fortunes of those few very big firms, buy or short those, don't use QQQ.
* If you don't have informed opinions on those few firms, don't use QQQ.

Jim