  The reversible logic can be used in various research areas, e.g. quantum
computation, cryptography and signal processing. In the paper we study
reversible logic circuits with additional inputs, which consist of NOT, CNOT
and C\textsuperscript{2}NOT gates. We consider a set $F(n,q)$ of all
transformations $\mathbb B^n \to \mathbb B^n$ that can be realized by
reversible circuits with $(n+q)$ inputs. An analogue of Lupanov's method for
the synthesis of reversible logic circuits with additional inputs is described.
We prove upper asymptotic bounds for the Shannon gate complexity function
$L(n,q)$ and the depth function $D(n,q)$ in case of $q > 0$: $L(n,q_0) \lesssim
2^n$ if $q_0 \sim n 2^{n-o(n)}$ and $D(n,q_1) \lesssim 3n$ if $q_1 \sim 2^n$.
