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For measuring 2 qubits, there are 4 possible outcomes, corresponding to projectors $$ P_{00}=|00\rangle\langle 00|,\qquad P_{01}=|01\rangle\langle 01|,\qquad P_{10}=|10\rangle\langle 10|,\qquad P_{11}=|11\rangle\langle 11|. $$ So, if you have a state $|\psi\rangle$, you get the outcome $x$ with probability $p_x=\langle\psi|P_x|\psi\rangle$. This immediately ...


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My understanding of the OP's question is that there is some restriction imposed that a gates can only act on Adjacent Qubits. While this isn't necessary, we can still work with this restriction using SWAP gates to make non-adjacent qubit adjacent. If the Control qubits are $i$ and $j$; and target qubit is $k$. Such that $i+1<j$ and $j+1<k$. Then we can ...


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