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With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle point problems with interlayer Tresca friction conditions and the mixed finite element method are proposed and analyzed. Then, the convergence of the numerical solution of the mixed finite element method is theoretically proven, and the corresponding algebraic dual algorithm is given. Finally, through numerical experiments, the mixed finite element method is not only compared with the layer decomposition method, but also its convergence relationship with respect to the spatial discretization parameter $H$ is verified.

Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using repeated addition, while division can be performed using repeated subtraction. In this paper we present two designs using the reversible $R^3$ gate to perform the quantum half adder/ subtractor and the quantum full adder/subtractor. The proposed half adder/subtractor design can be used to perform different logical operations, such as $AND$, $XOR$, $NAND$, $XNOR$, $NOT$ and copy of basis. The proposed design is compared with the other previous designs in terms of the number of gates used, the number of constant bits, the garbage bits, the quantum cost and the delay. The proposed designs are implemented and tested using GAP software.

We present new algorithms to synthesize exact universal reversible gate library for various types of gates and costs. We use the powerful algebraic software GAP for implementation and examination of our algorithms and the reversible logic synthesis problems have been reduced to group theory problems. It is shown that minimization of arbitrary cost functions of gates and orders of magnitude are faster than its previously counterparts for reversible logic synthesis. Experimental results show that a significant improvement over the previously proposed synthesis algorithm is obtained compared with the existing approaches to reversible logic synthesis.

We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in implementing the current algorithm., Comment: 19 pages, 7 figures

In this paper, an analytical solution of the two-qubit Rabi model for the general case is presented. Furthermore, a comparison between the information entropies and the Von Neumann entropy $(\rho_{A})$ is given for some special values of the qubit-photon coupling constants in case of the detuning parameters. It is demonstrated that oscillations of the occupation probabilities $\rho_{11}, \rho_{22}, \rho_{33}$ and $\rho_{44}$ are equivalent to the case of the spontaneous emission. The occupation probability $\rho_{11}$ reaches the case of sudden death, when the detuning parameters $\Delta_{2}$ equals zero., Comment: due to crucial error in the transformation

The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of {\it classicality} as the non-violation of these classical inequalities by quantum states of several multiqubit systems and compare it with the non-violation of Bell inequalities, that is, {\it locality}. We explore --numerically and analytically-- the relationship between several other quantum measures and discover the deep connection existing between them. The results are surprising due to the fact that these measures are very different in their nature and application. The cases for $n=2,3,4$ qubits and a generalization to systems with arbitrary number of qubits are studied here when discriminated according to their degree of mixture., Comment: To appear in Quantum Information Processing

Classifying researchers according to the quality of their published work rather than the quantity is a curtail issue. We attempt to introduce a new formula of the percentage range to be used for evaluating qualitatively the researchers' production. The suggested equation depends on the number of the single-author published papers and their citations to be added as a new factor to the known h-index. These factors give an advantage and make a clear evidence of innovative authors and reduce the known h-index for authors who are gaining citations by adding their names to multi-author papers. It is shown that various dimensions of ethical integrity and originality will be effective in this new index. An important scenario arising from the analysis is shown in terms of examples. It refers to larger differences between the h- and the new index which comes from the whole work and the one comes from the single-author papers only, is shown., Comment: 8 pages, 3 figures

I propose two simple indices to classify journals, published in Arabic language, and different researchers. These indices depend upon the known impact factor and h-index. The new indices give an easy way to judge the rank of any journal (output of any researcher) without looking for other journals (output of other researchers)., Comment: 4 pages, 3 figures

The dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi partite entanglement and the effects arising from the coupling to the reservoir. It is shown that despite losses, entanglement formation may still persist for relatively long times and it is especially robust against temperature dependence of the reservoir. Together with control of system parameters, the system may therefore be especially suited for quantum information processing. Furthermore, our results shed light on the evolution of open quantum many-body systems. For instance, due to intrinsic qubit-qubit couplings our model is related to a driven XY spin model., Comment: 15 pages, 7 figures

Considering ultracold atoms traversing a high-Q Fabry-Perot cavity, we theoretically demonstrate a quantum nondemolition measurement of the photon number. This fully quantum mechanical approach may be understood utilizing concepts as effective mass and group velocity of the atom. The various photon numbers induce a splitting of the atomic wave packet, and a time-of-flight measurement of the atom thereby reveals the photon number. While repeated atomic measurements increase the efficiency of the protocol, it is shown that by considering long interaction times only a few atoms are needed to resolve the photon number with almost perfect accuracy., Comment: 7 pages, 7 figures. Final version to appear in Phys. Rev. A

We propose a method for analyzing Berry phase for a multi-qubit system of superconducting charge qubits interacting with a microwave field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection found between the Berry phase and entanglement creations., Comment: 7 pages, 4 figures