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We propose a simpler and more efficient scheme for the implementation of themulti-valued Grover's quantum search. The multi-valued search generalizes theoriginal Grover's search by replacing qubits with qudits --- quantum systems of$d$ discrete states. The qudit database is exponentially larger than the qubitdatabase and thus it requires fewer particles to control. The Hadamard gate,which is the key elementary gate in the qubit implementation of Grover'ssearch, is replaced by a $d$-dimensional (complex-valued) unitary matrix $F$,the only condition for which is to have a column of equal moduli elementsirrespective of their phases; it can be realized through any physicalinteraction, which achieves an equal-weight superposition state. An example ofsuch a transformation is the $d$-dimensional discrete Fourier transform, usedin earlier proposals; however, its construction is much more costly than thatof 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} interactionstep.

Time-efficient implementation of quantum search with qudits