Mixed polarity reversible Peres gates

Reversible Peres gates with more than two all over binary-valued control signals are discussed. Methods are disclosed for the low-cost realisation 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 realising the κth root of NOT, where κ = 2^n-1. Proper distribution of the controlled gates and their inverses allows driving the reversible Peres gate with control signals of different polarities.