How do quantum computing work over classic computing of representing data?

I don't fully understand it but I have a background in electronics and some idea about quantum mechanics. What it amounts to is setting up a quantum state that physically represents a system and some aspect of that  system is something you want to know.

So this is just an analogy but it tries to point out the idea of something moving into one final state rather than performing a series of tests. Say you have a complex maze with a minimal distance path from one side to the other and you want to find that path. 

One way would be to make a digital model of the maze and systematically try each turn based on a repeating algorithm. Then eventually you would stumble on the path that makes it through. 

Another way would be to make a physical model of the maze. You would then pour water in one side and wait until it stabilized and water came out the the other side at a steady rate. At this point all you have to do is follow the path of maximum water flow from in to out.

The point being that the model inherently has a physical behaviour that usefully mirrors the thing you want to know. 

One difference between the analogy and QC is that in QC the final state isn't guaranteed to be a solution (as I understand it). But it will preferentially collapse into a solution, so if the test is run repeatedly you will eventually see the distribution of preferred and not so preferred outcomes.