It seems absolutely bizarre that counterfactual computation -- using information that is counter to what must have actually happened -- could find an answer without running the entire quantum computer. But the nature of quantum interrogation makes this amazing feat possible.

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I think in principle it can be built. In practice maybe.

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In a sense, it is the possibility that the algorithm could run which prevents the algorithm from running. That is at the heart of quantum interrogation schemes, and to my mind, quantum mechanics doesn't get any more mysterious than this.

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