Quaternary quantum algorithm for determining properties of quaternary logic function

A multiple-valued (d-dimensional with d >; 2) quantum system enables a much more compact and efficient information encoding than for binary (d = 2) quantum system. As multiple-valued quantum system is physically realizable, it is worth to explore multiple-valued quantum algorithm. In this paper, we propose quaternary (4-dimensional) quantum algorithm for testing whether a quaternary logic function is either constant or balanced. In classical computer, this test would require at least 4^n-1 +1 function evaluations, where n is the number of inputs of the function. But the proposed quantum algorithm requires only one function evaluation.