Multiple-valued quantum circuits are promising choices for future quantum computing technology, since the multiple-valued quantum system is more compact than the corresponding binary quantum system. Grover’s quantum search algorithm requires a sub-circuit called oracle, which takes a set of inputs and gives an output stating whether a given search condition on the inputs is satisfied or not. Equality, less-than and greater-than comparisons are widely used as search conditions. In this paper, the authors show design of quantum ternary equality, less-than, and greater-than comparators on the top of ion-trap realizable 1-qutrit gates and 2-qutrit Muthukrishnan-Stroud gates.