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I'm referring to "They allow the running of some algorithms that normal computers can't physically run."

I understood this as, it's impossible to run some algorithms on a traditional computer. You can run Shor's algorithm on a Turing machine, albeit requiring a simulation of qbits. You can run it in javascript and in your browser if you like.

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True, you can simulate the qbits, so the more precise statement would be they can execute some algorithms in a way that classical computers cannot and this gives them superior efficiency in some situations.

You're right. I should have specified that they can run certain algorithms with a runtime complexity impossible on a classical computer.

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