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Is there such a quantum oracle that makes the oracle corresponding to the function sigmoid? That is: ${{U}_{f}}|\psi \rangle =\text{sigmoid}(|\psi \rangle )$, where $\text{sigmoid}=\frac{{{e}^{x}}}{\sum\limits_{i=0}^{{{2}^{n}}-1}{{{e}^{i}}}}$ What is the essence of the oracle?

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  • $\begingroup$ I'm not sure about what you mean by "that makes the oracle corresponding to the function sigmoid". Can you elaborate on that? What would like to have as inputs, and what would be the desired outputs? $\endgroup$ Apr 7, 2022 at 11:49

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I have considered your question before, and I am pessimistic about the possibility. Considering the definition of the one-qubit state $|0\rangle$ or $|1\rangle$ in the Bloch sphere, such an oracle can be interpreted as some sort of trending to the nearest axis. However, if you, change the subject from "the closest axis" to "a specific axis", this looks quite like the initial state preparation.

If you really want to further investigate such an oracle, maybe instead of a deterministic method, a probabilistic approach is more reasonable. Otherwise, you can artificially generate a truth table and employ a neural network to do the labor. But I will never promise the success of the upper two directions.

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  • $\begingroup$ But multiple qubits are less likely to be represented by a Bloch sphere. We have no way of knowing the Bloch sphere representation of a multi-qubit in an entangled state. $\endgroup$ Apr 7, 2022 at 12:13

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