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The idea I'm looking for is to go from (a) to (b) or (c). Any help?

For example: Hadamard Test

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    $\begingroup$ What are you looking to do? Are you looking to go from (a) to (b) or (c)? What do you mean by "remove a control from a quantum circuit."? The ancilla qubit $\vert 0\rangle_{\mathrm{anc}}$ controls operation of the other gates. Can you clarify your question? $\endgroup$ – Mark S 2 days ago
  • $\begingroup$ Hi @Mark, I'm looking to go from (a) to (b). What I am pursuing is to get an equivalent circuit from (a), for example, to (b) without the not control the $|0 >_{anc}$. So basically, I am looking for a way to remove the control gate on any circuit. $\endgroup$ – Parfait Atchadé 2 days ago
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It looks like the first circuit is a hadamard test. So if you are looking to calculate the expectation value without the use of a control or ancilla then I recommend reading through this post.

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  • $\begingroup$ Many thanks, @thespaceman. The answer you give me is VQE, but I'm looking for anything else. What I am pursuing is to see get an equivalent circuit, for example, to the Hadamard Test without the not control. So basically, I am looking for a way to remove the control gate on any circuit. $\endgroup$ – Parfait Atchadé 2 days ago
  • $\begingroup$ I think you need to add some details to your question. I don't think what you are specifically asking for is possible. $\endgroup$ – thespaceman yesterday

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