New answers tagged state-preparation
3
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.)
2
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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