  Although many of works have been done in multivalued quantum logic synthesis,
the question whether multivalued quantum circuits are more efficient than the
conventional binary quantum circuits is still open. In this article we devote
to the optimization of generic multivalued quantum circuits. The multivalued
quantum Shannon decompositions (QSD) are improved so that the circuits obtained
are asymptotically optimal for all dimensionality d. The syntheses of uniformly
multifold controlled $R_y$ rotations are also optimized to make the circuits
further simplified. Moreover, the theoretical lower bound of complexity for
multivalued quantum circuits is investigated, and a quantity known as
efficiency index is proposed to evaluate the efficiency of synthesis of various
quantum circuits. The algorithm for qudit circuits given here is an efficient
synthesis routine which produces best known results for all dimensionality d,
and for both cases the number of qudit n is small and that is asymptotic. The
multivalued quantum circuits are indeed more efficient than the binary quantum
circuits. The facts, the leading factor of the lower bound of complexity for
qudit circuits is small by a factor of d-1 in comparison to that for qubit
circuits and the asymptotic efficiency index is increased with the increase of
dimensionality d, reveal the potential advantage of qudit circuits over generic
qubit circuits. The generic n-qudit circuits with $d\geq5$ and generic
two-ququart circuits synthesized by the algorithm given here are practical
circuits which are more efficient than the most efficient qubit circuits.
