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Is the correct analogy that in a computer, the implementation of a function is some sequence of gates. Yes, that's almost always what an oracle will be. The oracle could be some physical object that you are trying to analyze. For example, the computation could look like "pass these carefully polarized photons through the rock sample and check what ...

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I am answering my own question as I found an answer. The answer is affirmative, that the standard phase oracle made of CNOT gates and an ancilla qubit can be replaced by Z and I gates by discarding the ancilla. The oracle ($U_f$) in the BZ alogorithm follows: |x\rangle|b\rangle \stackrel{U_{f}}{\rightarrow}|x\rangle|y \oplus f(x)\rangle \equiv|x\rangle|b \...

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I think the output is the same of what you are suggesting but the function has changed.The Oracle is described as a function $f:\{0,1\}^n→ \{0,1\}$ which is no longer the case when you replace the CNOT gates by Z gates. I don't any applications for this algorithm but I can tell you why quantum is advantageous for solving the problem of the oracle. This can ...

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