Regarding the specific case of the linked question: the reason I personally voted to close was that it contains more than one question, i.e. it's too broad. Now, the current vote reason appears to be "needs more clarity" instead. I don't remember if I also chose that reason (it appears so as there are only three votes on "needs more clarity"), but if I did it was by mistake and I meant to click the "too broad" one.
The underlying reason why I think these should be closed is that multiple questions asked under a relatively generic title have very low reusability. If someone in the future will be interested in knowing, say, why "the quantum algorithm for order-finding is just the phase estimation algorithm applied to the unitary operator $U|y⟩≡|xy\pmod N⟩$", it's not going to be easy finding the answer from this question.
The solution is simple in these cases, break down the post into its elementary components, asking those in separate questions.
I see closing a question as a way to prevent poor-quality questions, off-topic questions, or duplicate questions from wasting people's valuable time, and wasting space in the unanswered queue. But this question has an answered question, and it's certainly not off-topic, and it's above this site's average standard for quality.
I mostly agree with these reasons, but I'd say the fundamental reason, underlying as special cases the ones you mention, is whether it is useful to have the question/thread in the site. And by "useful" I mean useful for someone else in the future. In other words, is it adding information to the corpus of knowledge stored in the site? If the way the question is stated makes it hard to ever find it again, then, in my opinion, it should be closed, fixed (broken down into multiple ones or clarified), and then eventually reopened.
Of course, the ideal solution would be to just go ahead and edit the question to make it better, but one does not always have the time or energy to do it.
Likewise, I agree that this (Explanation of NOT gate in Hadamard basis) was not the highest-quality question, but the user is being lambasted (see the comment!) for needing "more details or clarity" when the two questions at the end are extremely simple and do not need even one more word of explanation: see my answer to the question.
Well for starters, I just learnt a new word here, so that's nice. Lambasted sounds great.
Regarding the comment, it might be a bit harsh, yes, but I don't see it as that problematic. It's not insulting the OP or anything, just stating very directly the facts of the matter.
The question itself should be closed imo (and I actually voted to close it just now), because (1) we strongly discourage "explain to me the statement in this screenshot" kinds of questions, and (2) it is asking more than one question.
I do understand that sometimes close-voting is used (by some people, not me) to encourage users to improve their question if someone feels there's not enough detail or there needs more focus, but now there's an answer already, which someone spent a large amount of time on, so we probably do not want the question to change substantially anymore, as this would cause the author of the answer to have to go back and change their already perfectly good answer, or if they don't do that then their answer would no longer be valid, which would be very unfortunate.
Eh, this is tricky I think.
On the one hand, one cannot judge the worth of a question from its answers (modulo a few exceptions I'd say). The main reason being that if the questions ought to be modified before being a good fit, they should not have been answered in the first place in that form. In other words, you should have not answered that question at all. If you wanted to answer it because you think that would add valuable information, that's fine, but that should then come together with editing the question to make it better. Note that in other sites (e.g. physics.SE) they also directly delete answers to homework questions, for similar reasons.
I'm sorry, but the amount of effort spent to write an answer is completely beside the point here. Nevertheless, it is easily salvaged by editing the question to make it worth reopening.
If you want to close questions like this, recommend to have "poor quality question" listed as a custom close reason, but don't abuse the "needs details/clarity" option for questions that are crystal clear.
I'll admit I don't quite appreciate the difference between these two close reasons.
We have only a handful of active close voters, and to retain them I think we have to think a bit about our close-vote practices, which also means thinking about why exactly we close vote? I know the answer might seem trivial at first, since the "close vote reasons" are listed right there when you vote to close, but people have different thresholds at which they believe one of those reasons should be put into play, so I want to solicitate the community and start some discussion on the topic to learn more about what people here think.
Regarding retaining the active close voters. This might be a flowed personal impression of mine, but I feel like the more active close voters in SE sites tend to be on the harsh side when it comes to decide how to VTC. Probably for the simple reason that when you see a lot of poor quality questions it becomes hard to give the benefit of the doubt or think too much about every single one.
As stated before, the fundamental meter I use to decide whether I think a question should stay or not is that of reusability. Is it adding new information? Is there a chance it's going to be useful to someone else in the future? And of course, is it on-topic in this particular site? This is also probably why I put so much focus on the title of questions as well. A poor title severely hinders the usefulness of a question, and can make good answers go to waste.
people have different thresholds at which they believe one of those reasons should be put into play
This is certainly true, but I'm not sure it's an avoidable problem. It is the case in any site of the network, and the bigger the site grows the more this can become evident.
We can say whatever we want here, but it ultimately doesn't really matter. People with enough rep will be entitled to vote to close as they see fit (modulo exceptional circumstances I guess). There might be a small number of people following meta that might change their views on the matter, so in the case of this particular site right now, this discussion might have an effect, but in the long term it probably won't.