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The salesman problem is where a computer has to calculate the most efficient route for a man to take between x number of cities. Whilst a classical computer has to go through every single step and then select the most efficient one, I have read that a quantum computer can do every single step simultaneously and then from that find the most efficient one.

Does that mean that the superposition of a qubit allows for it to solve a problem where there are a near infinite number of cities, all in one step? What are the implication of this if it is true? Surely there would be almost no time required to solve any problem.

Furthermore how is this superposition utilised? What is the point of having a superposition if it will collapse when we measure it anyway?

Thank you very much for your time. I understand that some of my knowledge may be wrong, I just hope that you have the patience to deal with me.