A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Multi-Output Galois Field Sum of Products Synthesis with New Quantum Cascades
ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
A Synthesis Method for MVL Reversible Logic
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
Quantum ternary parallel adder/subtractor with partially-look-ahead carry
Journal of Systems Architecture: the EUROMICRO Journal
GF(4) Based Synthesis of Quaternary Reversible/Quantum Logic Circuits
ISMVL '07 Proceedings of the 37th International Symposium on Multiple-Valued Logic
Irreversibility and heat generation in the computing process
IBM Journal of Research and Development
Logical reversibility of computation
IBM Journal of Research and Development
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Multiple-valued quantum circuits are promising choices for future quantum computing technology, since they have several advantages over binary quantum circuits. Quaternary logic has the advantage that classical binary functions can be very easily represented as quaternary functions by grouping two bits together into quaternary values. 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 is satisfied or not. Equality, less-than, and greater-than comparisons are widely used as search conditions. In this paper, we show synthesis of quaternary equality, less-than, and greater-than comparators on the top of ion-trap realizable 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates.