Quantum Computing Without Working in a Quantum Garage?

Over at Computational Complexity, Bill Gasarch asks about some of the things he’s heard about quantum computing:

I have been told quite often that
“You don’t have to understand Quantum Mechanics to work in Quantum Computing.”
Thats a good thing since I’ve also been told
“Nobody really understands Quantum Mechanics.”
I’ve also been told
“You don’t have to have studied Quantum Mechanics to work in Quantum Computing.”
I am skeptical of that.

Which reminds me of story about how I first tried to learn quantum theory. When I was growing up we belonged to a science book club. Most of the books we ordered where the fairly standard popular science kind of books. But there were more technical books available and I had already read a lot of popular science on quantum theory, so I decided that I wanted to get a real textbook on quantum theory.
So I ordered up this textbook and dived right in. Now the first thing this book talks about is the ultraviolet catastrophe and Planck’s solution to this problem (of course this is a made up history: Planck wasn’t trying to solve the ultraviolate catastrophe when he derived his theory of quanta.) And in this problem one of the essential points was that if you took this equation that had a symbol like [tex]$$int $$[/tex] and turned it into a symbol like [tex]$$Sigma$$[/tex], then you could avoid this catastrophe. Now I knew what the latter meant, a sum, but I had no clue what that first symbol was. But I did know a chemistry teacher who had gone to Berkeley, so I thought he would know. So I went and showed him the book, and he said “Oh! That’s an integral symbol.” And then he told me that I would have to learn Calculus to understand what this meant. Really! You have to understand calculus to learn quantum theory. Well that was a setback. (Luckily our local library had a calculus book, which I promptly checked out and learned calculus from. Ah, those were the days. BTW, a math teacher I had in high school claimed he could teach his eight year old calculus.)
Okay, so now you’re saying, “Get to the point Dave!” And certainly most of you might guess that the point I’m trying to make is that you don’t need calculus to learn quantum computing (true) or that you don’t need to know quantum physics to learn quantum computing (note I said “physics” here.). Of course the later is true, you could pick up Nielsen and Chuang and learn quantum computing without ever solving a particle in a box problem in quantum physics. But why would you want to do this? When you really care about learning something, it’s not about what you do or don’t need to begin learning, it’s about trying to grab ahold of as much information and having as much fun as possible. For example, you could turn this question around and ask, “Do you need to have taken a course in computational complexity in order to do quantum computing?” The answer is, I think (no wait, I know from personal experience!), “no.” But why would you not want to learn about P, NP, PP, BPP, EXP, etc. (and the new complexity class MIT. By the way MIT is contained inside of CIT. I have a proof of this, but it doesn’t fit in the margins of this blog.)? So while I think it is certainly true that you could learn quantum computing without taking a course (or learning on your own) in quantum physics, why in the world would you want to do this? Why not learn as much as you can about both “quantum” and about “computing”? This doesn’t guarantee success or anything, but I can guarantee you that it would benefit your soul (and it might even lead to things like physicists designing algorithms where scattering off a tree solves the NAND tree problem.)
(The main point of Bill’s article, of course is to ask whether quantum physicists should learn quantum computing, to which I refer the reader to Scott Aaronson’s answer in the comment section of the post.)