Ever since  Peter Shor  exploited quantum mechanics to show the possibility of writing an algorithm to crack an erstwhile intractable problem of factorizing two large numbers, there has been a furry of public interest regarding this new technology.  Quantum computing, if successful, will develop new engines capable of performing calculations and simulations that are deemed presently infeasible on our computers.

If you surf around, you should be able to get many articles on the subject.  I have done a tiny search and I have gathered together some of the more interesting sites that I think you might be interested.  These sites usually do not demand an in-depth knowledge of quantum mechanics.

Overviews
 
     A very short overview by Elmer Smalling
     Notes on quantum computing by R.F. Werner (Technical University of Braunschweig)
     A pretty good one by  Dana Mackenzie (Nanothinc) or another one by  Matias Castro
     Simon Bone's Hitchhiker's  Guide to Quantum Computing
        Another funny one by  someone from a galaxy far away.
     An FAQ by  RSA Security Company on QC.
     A fairly comprehensive one by  Amit Gulaya
     For more information:  a  summary from IRO group, University of Montreal.

More Readings:
          Charles Bennett: Quantum Information and Computation, Physics Today, 48 (October
          1995), pp. 24-30.
          Seth Lloyd: Quantum-Mechanical Computers, Scientific American, 273 (October 1995), pp.
          44-50.
          David DiVincenzo: Quantum Computation, Science, 270 (13 October 1995), pp. 255-261.

Imagine using classical computing to simulate quantum computing!
Bernhard Ömer has written a C++ class library for the simulation of a quantum computer.
He has also written a short  report  on the topic.
 

What about Quantum Hardware?

Here is one on the Ion Trap...

     An overview on Ion Trap from  Los Alamos
     Other Experiments on quantum computation at  Los Alamos
     Ion trap experiments at  NIST Boulder, Colorado