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Consider the circuit below.

This is almost the same as the standard protocol to perform a non-local $CNOT_{0,3}$. The only difference is that I decomposed the upper local $CNOT_{0,1}$ into one Ising gate and some local rotational gates.

When I attempt a simulated process tomography over qubits $q_0,q_3$ and evaluate the fidelity w.r.t. the ideal $CNOT$ I get a fidelity $\approx$85%, with 100k shots.

Why does this happen? Does such a transpiling mess with the logic behind the non-local $CNOT$?

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