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We present a method of synthesizing ternary Galois field (GF(3)) based reversible/quantum logic circuits without any ancillary trits/qutrits and hence without any garbage outputs. We realize multi input ternary Toffoli gate and square functions of GF(3) variables using linear ion trap realizable Muthukrishnan-Stroud (M-S) gates and shift gates in the absence of ancillary qutrits. Then based on the...
A convex polyhedron P is k-equiprojective if for all of its orthogonal projections, except those parallel to the faces of P, the number of vertices in the shadow boundary is k. Finding an algorithm to construct all equiprojective polyhedra is an open problem first posed in 1968. In this paper we give lower bounds on the value of k and the size of an equiprojective polyhedron. We prove that there is...
The problem of cutting a convex polygon P out of a piece of paper Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or rays cuts. In this paper we consider yet another variation of the problem where Q is a circle and P is convex...
We present the design of quaternary quantum version of reversible circuits such as Toffoli gate, modified Fredkin gate, mux, demux, encoder-decoder using linear ion realizable quaternary Muthukrishnan-Stroud gates. Our realization of quaternary Toffoli gate is more efficient than the previous realization and other quaternary circuits are realized for the time in literature.
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