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Suppose I have this quantum XOR circuit; this is a quantum circuit for the classical XOR operation $$\begin{eqnarray*} x_1'= x_1\oplus x_2\oplus x_3\oplus x_4,\\ x_2'=x_2\oplus x_3\oplus x_4\oplus x_5,\\ x_3'=x_3\oplus x_4\oplus x_5\oplus x_6. \end{eqnarray*}$$ Now suppose I had $l$ quibts instead of $3$. What would be tensorial notation for this generalized circuit, what I think is $$U=\prod_{i=0}^{2}\prod_{k=0}^{q-1}I^{\otimes k}\otimes X\otimes I^{\otimes i}\otimes P_1\otimes I^{\otimes l-2-i-k}$$ is this the correct notation. The first $I$ tells how many qubits will be unaltered, the second $I$ adjusts the correct control, $P_1$ is the projection operator, and last $I$ does nothing on the remaining qubits. Ignore the part of this operator when the state is $0$ i.e. projection operator $P_0$ is omitted.

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  • $\begingroup$ You cannot just ignore $P_0$, if you do your operation is neither unitary nor entangling! $\endgroup$ – bRost03 Jun 10 at 4:27

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