>>7616193That is extremely difficult to explain without a lot of math.
The best explanation I can give is that quantum computers can be in many states simultaneously. This does NOT mean it can compute every single possibility "in parallel", because in the end it will collapse into just one randomly-picked answer.
However, these possible states all interfere with each other, and if you're clever you can set things up so that states with a property you want interfere constructively and become more likely, and ones that don't interfere destructively and become less likely.
For instance, here's how this lets you solve prime factoring problems unusually fast:
http://www.scottaaronson.com/blog/?p=208 
