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Is it possible to translate the above circuit into an equivalent one where the number of interaction gates with the first qubit is 1?

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Yes, it is possible.

First, let's recall the bridge-gate, which is

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Then now, using this fact, we have that

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is equivalent to

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which can be simplified to

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Therefore,

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  • $\begingroup$ Thanks a lot! Do you think it might be generalizable to any 3-qubit circuit? $\endgroup$ May 14 at 17:27

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