  We propose a simpler and more efficient scheme for the implementation of the
multi-valued Grover's quantum search. The multi-valued search generalizes the
original Grover's search by replacing qubits with qudits --- quantum systems of
$d$ discrete states. The qudit database is exponentially larger than the qubit
database and thus it requires fewer particles to control. The Hadamard gate,
which is the key elementary gate in the qubit implementation of Grover's
search, is replaced by a $d$-dimensional (complex-valued) unitary matrix $F$,
the only condition for which is to have a column of equal moduli elements
irrespective of their phases; it can be realized through any physical
interaction, which achieves an equal-weight superposition state. An example of
such a transformation is the $d$-dimensional discrete Fourier transform, used
in earlier proposals; however, its construction is much more costly than that
of the far simpler matrix $F$. We present examples of how such a transform $F$
can be constructed in realistic qudit systems in a \emph{single} interaction
step.
