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Reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs are considered. For such circuits implementing maps  f  :Z   2  n$\begin{array}{} \displaystyle \mathbb Z_2^n \end{array}$    →Z   2  n$\begin{array}{} \displaystyle \mathbb Z_2^n \end{array}$   , we study the Shannon complexity function  L ( n ,  q ) under the condition that the number of additional inputs is  q  =  O ( n  2 ). For this range of  q , it is shown that  L ( n ,  q ) ≍  n 2  n   / log 2   n . The growth order  L ( n ,  q ) ≍  n 2  n   / log 2  ( n  +  q ) for all  q  ≲  n 2  n −⌈ n / ϕ ( n )⌉ , where  ϕ ( n ) → ∞ and  n  /  ϕ ( n ) − log 2   n  → ∞ as  n  → ∞, is evaluated.

Synthesis of reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs