In this paper there is this sentence:
[...] the description of a $2^n\times2^n$ unitary matrix $U$ (which is a poly($n$)-size quantum circuit)
According to the meaning of "which" in English, in contrast to "that", the sentence means that the effect of any unitary matrix $U$ can be done by a quantum circuit composed by $m$ quantum gates, with $m$ polynomial in the number of qubits $n$. I assume that the quantum gates act on 1 or 2 qubits (or a fixed number of qubit), else the sentence is trivial ($U$ is a quantum gate itself).
However, I think that this is not true. In particular, I think that an $m$ exponential in $n$ is needed for preparing an arbitrary state, which is a simpler task than simulating the effect of an arbitrary $U$. Can you confirm and suggest a reference?