The other day I was thinking about NP complete problems, then my mind wandered over to quantum computing, then it settled on thinking about electricity. Specifically, the path of least resistance. Traveling salesman problem perhaps?
Contrary to lay belief, electricity does not just follow the path of least resistance. It follows all paths simultaneously with a current that is inversely proportional to the resistance of that path. In other words, the weaker the resistance, the stronger the current.
So I really don't know enough about the subjects to think it through but this is the type of stuff that pops into my head.