We discuss the embedding of R-Parity preserving Minimal Left Right Supersym-metric models into Pati-Salam and SO(10) GUTs.

This paper proposes a genetic algorithm for designing combinational logic circuits and studies four different case examples: 2-to-1 multiplexer, one-bit full adder, four-bit parity checker and a two-bit multiplier. The objective of this work is to generate a functional circuit with the minimum number of gates.

The precise result we will prove is that the PARITY language cannot be decided by AC circuits, even if they are allowed to be of size 2 o(1) , even if they are allowed to include gates that test whether the sum of their inputs is non-zero modulo 3, and even if they are allowed to be completely non-uniform. Since the NC parity circuits are very uniform, this is more than enough to separate AC fr...

We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as spin-1/2 particles) can be used to exactly implement an n-qubit parity gate, which is equivalent in constant depth to an n-qubit fanout gate. Either isotropic or nonisotropic versions of the interaction can be used. We generalize our basic results by showing that any Hamiltonian (acting on suitably encoded logical qubit...

In his seminal paper on probabilistic Turing machines, Gill 13] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. We also show that PP is closed under a variety of polynomial-time truth-table reductions. Consequences in complexity theory include the deenite collapse and (assuming P 6 = PP) separation of certain query hierarchies over ...

We demonstrate that the unbounded fan-out gate is very powerful. Constantdepth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf ) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[t], and Counting. Classically, we need logarithmic depth even if we can use unbound...

We show that the integrable Lindblad superoperators found recently can be used to build nonunitary quantum circuits with two-site gates by demonstrating $\check{R}$-matrices are completely positive and trace preserving. Using bond-site transformation, we obtain corresponding three-site gates. When restricted diagonals of density matrix, these models reduce classical cellular automata. This appr...

This paper presents theory and practical implementation of a method for multi-level logic synthesis of speedindependent circuits. An initial circuit implementation is assumed to satisfy the monotonous cover conditions but is technology independent. The proposed method performs both combinational (inserting new gates) and sequential (inserting new memory elements) decomposition of complex gates ...