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by miles7
1181 days ago
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Your comment is helpful to us to see what are some common misunderstandings about what we are saying in our paper versus not saying. It could be some problems with our writing. For example, we state all of the things you said above explicitly in the paper and wrestle with them in quite a few places. Also there is a whole second half of the paper that addresses precisely the question of "what if we have an instance that we can't classically simulate? i.e. scales as 2^n?". Your comments don't address that part of the paper. The first half of the paper, about opening up the oracle is written by definition for people who don't know it, as is the case in any article. Personally knowing about something but which is not published is not a valid or helpful criticism of a published work (or preprint). On the other hand we could not find any publications talking about opening the oracle in the context of attempting to simulate it nor discussing entanglement barriers in the oracle (other than giving unhelpfully general worst-case bounds). The one exception is the following paper by Chamon and Mucciolo https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.10.... If you know of some publications you could point us to, we'd be happy to incorporate them into a later draft of the article and cite them. |
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"There are many cases where it's already known one doesn't need Grover's algorithm, such as if a problem already has a polynomial-time solution. We have now identified a new set of cases where one doesn't need Grover's, which is where the oracle can be simulated only once by a tensor network (or log(N) times in a "closed" simulation".
So the point of that part of the article is to further delineate when Grover's algorithm is actually needed or not needed. It only applies to real-life problems where one must actually know the circuit.