We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC◦MODm circuits. We show that the following holds for several types of gates G: by adding a gate of type G at the output, it is possible to obtain an equivalent probabilistic depth 2 circuit of quasipolynomial size consisting of a gate of type G at the output and a ...

Reversible Peres gates with more than two all over binary-valued control signals are discussed. Methods are disclosed for the low cost realization of this kind of Peres gates without requiring ancillary lines. It is shown that Peres gates with n control signals may be obtained with a quantum cost of 2n+1 – n – 2, using Feynman gates and controlled gates realizing the κ-th root of NOT, where κ =...

A method of designing compact multiple-input combinational logic circuits is proposed. We show that i) fundamental logic gates can be constructed by a small number of collision-based fusion gates, ii) multiple-input logic gates are constructed in a systematic manner, iii) the number of transistors in specific logic gates constructed by the proposed method is significantly smaller than that of c...

Abstract By an explicit construction, we show that an arbitrary two-qubit gate can be implemented by using at most 16 elementary one-qubit gates and 3 CNOT gates. We show that this construction is optimal; in the sense that these numbers of gates is the minimal possible ones. Moreover, we show that if the two-qubit gate belongs to SO(4), then we need only 12 elementary one-qubit gates and 2 CNO...