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1

It turns out the issue with this circuit was in the use of the reset operator in conjunction with entanglement and superposition. In the oracle code I submitted, I use a Toffoli gate several times, which creates an entanglement between both input qubits and the output qubit. Since the input qubits are in superposition, that superposition state then "spreads" ...


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If you implement an oracle for Grover's algorithm that sometimes gives unhelpful answers, you can, as you suggest, rerun and remeasure. In your example, there are only two incorrect answers $x=0$ and $x=m$. With the way you defined $f(x)$, these would indeed be negated and diffused. Because there are only two bad answers, the impact may be small. However ...


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I think you've simplified the problem too much. The way your question is framed it sounds like you expect a square-root speedup of a small problem, which doesn't seem that impressive. In actuality there may be a Grover-style speedup not of $O(\sqrt{X Y})$ but of $O(\sqrt{2^X 2^Y})$. Let's set up the problem, and see what is to be solved. Let's let your ...


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Given the oracle you have provided, the search is indeed pointless. However, that oracle misses the point of Grover's algorithm because searching for a card in a deck of cards is not an unstructured search because, as you stated, you already know the order. Ergo, your search is structured. The reason this oracle is used is that it demonstrates how Grover's ...


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