The action of the S-duality Sl(2, Z) group on the moduli of the Calabi-Yau manifold W IP 11226 appearing in the rank two dual pair (K 3 × T 2/W IP 11226) is defined by interpreting the N =4 to N =2 flow, for SU(2) supersymmetric YangMills, in terms of the Calabi-Yau moduli. The different singularity loci are mapped in a one to one way, and the (N =2 limit/point particle limit) is obtained in bo...

There are two major approaches to the synthesis of logic circuits. One is based on a predominantly algebraic factorization leading to AND/OR logic optimization. The other is based on classical Reed-Muller decompositionmethod and its related decision diagrams, which have been shown to be efficient for XOR-intensive arithmetic functions. Both approaches share the same characteristics: while one i...

The salient features of the information-processing in Simon’s period-finding algorithm and Shor’s factorization algorithm can be given a similar geometric formulation, in terms of the subspace structure of Hilbert space, to Deutsch’s original XOR algorithm. From this perspective, the XOR algorithm is really a special case of Simon’s algorithm, and all three algorithms can be seen as exploiting ...

Most of Exclusive-OR(XOR) logic gates on quantum-dot cellular automata(QCA) is based on configuration of 2-input, and they are hardly to be scalable and exists unbearable noise because they are only focused on decrease of latency and space. In this paper, we propose how to make a scalable logic using a wire crossing technique, and give examples of two expanded XOR gate using typical logic gates...