I'm glad there are people who understand these things. I hope some day when the field of quantum computing congeals a bit more us mere mortals can begin to understand it as well.
If you are just looking for the theoretical basics , this youtube series [1] is a good place to start.
While I do find these videos approachable, they are fairly math heavy. Most of the lectures I've seen explain things at a level that almost anyone can get something out of, and you don't miss out if you skip over the stuff that is beyond you.
For most of the talks, the math involved is only algebra and vectors. Although, the vectors are represented using bra-ket notation which may throw you off.
[1]http://www.youtube.com/user/mnielsencourses?feature=watch
http://michaelnielsen.org/blog/quantum-computing-for-the-det...
The main thing that's needed to follow along is familiarity and comfort with basic linear algebra.
Its very exciting when something comes along that seems genuinely magic. Its working and I haven't the faintest idea of how. I love magic!
- Different hardware. This boils down to different gates/primitive operations, ala [1]. There are currently lots of different proposed methods of how to build the hardware, but I don't know that much about how the physical circuits in a traditional computer work, either.
- Different algorithms. See e.g. Shor's [2]. I think there are only one or two others that have been proven to be more efficiently solvable by quantum means, so a lot more work needs to be done in this area.
The field is in its extreme infancy, and I think it will always be more challenging to program quantum computers by a fairly wide margin.