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A canonical reference for gate decompositions is Barenco et al., Elementary gates for quantum computation. In particular, it also contains recipes to decompose an arbitrary $n$-qubit unitary into elementary gates (which, by parameter counting, requires about $4^n$ gates, assuming each gate has one real parameter.)


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I believe this Q&A answers your question about decomposition in detail: Minimum number of 2 qubit gates to build any unitary In short, you are correct that the lower bound for a number of 2-qubit gates necessary to implement an arbitrary unitary $U$ is $\Omega(4^n)$ where $n$ is the number of qubits. I am not entirely sure what authors meant, but perhaps ...


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