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Are Quantum States Exponentially-Long Vectors?
Scott Aaronson, University of Waterloo
Some computer scientists argue that quantum computing is an extravagant model, since it involves manipulating exponentially-large objects in unit time. But of course, classical probability distributions are also exponentially-large objects, and no one objects to those. So, are quantum states "more similar" to 2^n-bit strings or to distributions over n-bit strings? That seems like a vague question, but I'll show you some nontrivial results that strongly suggest an answer to it.
