Experiments I'd Like To See, Part 1

I am selfish. Sometimes when I work on a research problem, I do it in the hope that it will actually turn into something which, you know, will be done experimentally. I know, I know, I should be more of a pure theorist and not hope for salvation validation from reality, but hey we can’t all be perfect. So, here is an experiment I’d like to see done: I would think it would be within the regime of what is doable in a few physical implementations of quantum computers now.