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From what I can understand from the source code, the circuit is converted into a DAG before the decomposition transpiler is performed onto the DAG circuit.

How does converting to a DAG circuit help us recognise the gate operations needed to reach a certain state say for example the entangled state $\frac{1}{\sqrt{2}}(|00\rangle +|11\rangle)$. Or basically, how does that decomposition work?

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    $\begingroup$ This answer may help giving you an idea $\endgroup$
    – epelaez
    Jun 28, 2021 at 18:11

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