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I was reading the Qiskit tutorial on circuit properties and there is a section (Unitary Factors) which states that even though an example circuit is made of 12 qubits, it may not need 12 qubits to run.

The original circuit: here

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The layers of the circuit: here

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It is stated that: We can see that at the end of the computation there are three independent sets of qubits. Thus, our 12 qubit computation is actual two two qubit calculations and a single eight qubit computation.

I am struggling to understand where in this diagram it is illustrating that we only need two 2 qubit calculations and one 8 qubit calculation.

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Look at the picture of layer #9. It tells you explicitly how to group the qubits. There's a pair (q0,q5), another pair (q3,q8) and the rest of the qubits (q1,q2,q4,q6,q7,q9,q10,11). To see the relevance, look back to the circuit. Start with qubits 0 and 5. You can see that there's a two-qubit gate between them, but there are no two-qubit gates going from one of those to any other qubit. So qubits 0 and 5 will be in a product state from everything else (assuming they start in a product state), and you can perform that part of the computation independently from everything else. The same is true for the qubit pair 3 and 8.

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