Binary gates in three valued quantum computational logics

The standard theory of quantum computation relies on the idea that the qubit – the basic information quantity – is represented by a superposition of elements of the standard quantum computational basis B(2) = {|0i, |1i}. In the present paper we focus on the case of qutrits where the standard quantum computational bases is replaced by a three-valued computational basis B(3) = {|0i, | 1 2 i, |1i}. Recently in, unary gates on the Hilbert space C3 were considered. In this work we propose an extensive method that allows to extend binary gates to the framework of qutrits.