By Saleem Mohammed Ridha Taha (auth.)

This publication opens the door to a brand new attention-grabbing and bold global of reversible and quantum computing learn. It provides the state-of-the-art required to go back and forth round that international adequately. best global universities, businesses and govt associations are in a race of constructing new methodologies, algorithms and circuits on reversible common sense, quantum common sense, reversible and quantum computing and nano-technologies. during this publication, twelve reversible common sense synthesis methodologies are awarded for the 1st time in one literature with a few new proposals. additionally, the sequential reversible common sense circuitries are mentioned for the 1st time in a booklet. Reversible good judgment performs an enormous function in quantum computing. Any growth within the area of reversible good judgment should be without delay utilized to quantum common sense. one of many targets of this publication is to teach the applying of reversible common sense in quantum computing. a brand new implementation of wavelet and multiwavelet transforms utilizing quantum computing is played for this function. Researchers in academia or and graduate scholars, who paintings in good judgment synthesis, quantum computing, nano-technology, and coffee strength VLSI circuit layout, might be drawn to this book.

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**Additional resources for Reversible Logic Synthesis Methodologies with Application to Quantum Computing**

**Example text**

19. The circuit contains ﬁve nodes and eight leaves. One leaf is of value 0, three leaves are of value 1, and four leaves are of value 2. By following the same procedure in realizing F using Davio0, it is possible to make realizations of F using Davio1 and Davio2. The following is the realization of F using the hybrid (S/D0) expansion.

Step 1: Expanding nodes. Expand the non-symmetric function F in the root node (0, 0, 0) according to Eq. 5), as follows: F0 ¼ Fða ¼ 0Þ ¼ 0 b þ 2 1 b þ 2 2 b into node ð1; 0; 0Þ; F1 ¼ Fða ¼ 1Þ ¼ 2 b into node ð0; 1; 0Þ; F2 ¼ Fða ¼ 2Þ ¼ 0 b þ 2 1 b þ 2 2 b into node ð0; 0; 1Þ: For simplicity, the nodes in Fig. 17 are enumerated. So, the above nodes (1, 0, 0), (0, 1, 0) and (0, 0, 1) are the nodes 1, 2 and 3, respectively, in Fig. 17. The three nodes are not constant value. 50 3 Methods of Reversible Logic Synthesis z 12 18 2 1 2 y 2 b b 0 21 x 2 b 0 b 10 1 6, 10 b 11 b 0 2 0 1 3 a b 2 b 0 1 b 9 b 2 20 b 15 1 2 a b 2 a 0 1 8 b b 7 1 0 1 b 1 5, 7 5 0 b b 14 b 13 4 Fig.

37). 1 The matrix that is constructed from the permutations of many basis functions of the same type of the corresponding spectral transform is called Generalized Basis Functions Matrix (GBFM) [3, 5, 6]. 2 From the total space of the all possible GBFMs, the matrices that produce reversible expansions are called Reversible Generalized Basis Function Matrices (RGBFM) [3, 5, 6]. A necessary and sufﬁcient condition to generate the reversible ternary Shannon expansions is that the order of the permuted basis functions in the GBFM should satisfy the following constraint: in any given row or column the elements in that row or column are different than the elements in the adjacent positions of the other rows or columns.

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