Hishamuddin Zainuddin

Interacting two-fluid viscous dark energy models in a non-flat universe

We study the evolution of the dark energy parameter within the scope of a spatially non-flat and isotropic Friedmann-Robertson- Walker model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions that do not have a Big Rip singularity, and concluded that in both non-interacting and interacting cases the non-flat open Universe crosses the pha ntom region. We find that during the evolution of the Universe, the equation of state f or dark energy!D changes from ! eff D > −1 to ! eff D < −1, which is consistent with recent observations.

An efficient modeling and simulation of quantum key distribution protocols using OptiSystem

In this paper, we propose a modeling and simulation framework for quantum key distribution protocols using commercial photonic simulator OptiSystem™. This simulation framework emphasize on experimental components of quantum key distribution. We simulate BB84 operation with several security attacks scenario and noise immune key distribution in this work. We also investigate the efficiency of simulators inbuilt photonic components in terms of experimental configuration. This simulation provides a study to analyze the impact of experimental photonic components in quantum key distribution process.

Jensen–Shannon divergence and non-linear quantum dynamics

Abstract Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen–Shannon distance information. Among all possible implications, it is shown that the non-linear Schrodinger equation preserves the symplectic structure of the complex Hilbert space, hence a Hamiltonian dynamics. The canonically projected dynamics is obtained on the corresponding projective Hilbert space of pure state density operators.

A quantum algorithm for minimal spanning tree

Quantum computing algorithms are considered for several problems in graph theory. Classical algorithms involve searching over some space for finding the minimal spanning tree problem in a graph. We modify classical Primpsilas algorithm and replace quantum search instead of classical search, of which it will lead to more efficient algorithm. Also we proposed the structure for non-classical algorithms and design the various phases of the probabilistic quantum-classical algorithm for classical and quantum parts. Finally, we represent the result of implementing and simulating Primpsilas algorithm in the probabilistic quantum-classical algorithm.

A Hybrid Algorithm for the Shortest-Path Problem in the Graph

Quantum algorithms run on quantum computers are qualitatively different from those that run on classical computers. Quantum computing algorithms can be used for several problems in graph theory. Most of the classical algorithms involve searching over some space for finding the shortest-paths problem between two points in a graph and a minimal weight spanning tree. We modified classical Dijkstras algorithm and implement quantum search instead of classical search, of which it will lead to more efficient algorithm. Also we proposed the structure for non-classical algorithms and design the various phases of the probabilistic quantum-classical algorithm for classical and quantum parts. Finally, we represent the result of implementing and simulating Dijkstras algorithm as the probabilistic quantum-classical algorithm.

Computation of Quantum Bound States on a Singly Punctured Two-Torus

We study a quantum mechanical system on a singly punctured two-torus with bound states described by the Maass waveforms which are eigenfunctions of the hyperbolic Laplace—Beltrami operator. Since the discrete eigenvalues of the Maass cusp form are not known analytically, they are solved numerically using an adapted algorithm of Hejhal and Then to compute Maass cusp forms on the punctured two-torus. We report on the computational results of the lower lying eigenvalues for the punctured two-torus and find that they are doubly-degenerate. We also visualize the eigenstates of selected eigenvalues using GridMathematica.

Bianchi Type III String Cosmological Models for Perfect Fluid Distribution in General Relativity

Some geometrical aspects of Bianchi type III space‐time are investigated. This is followed by the study of Bianchi type III string cosmological models with perfect fluid distribution of matter.

Implementation of BB84 Protocol on 802.11i

Quantum key distribution is a new method in key distribution system in cryptography used to transmit secret key between two legitimate parties. This method is an invention in quantum cryptography as part of quantum mechanics which solves the key distribution’s problem in cryptosystem by providing a secure communication channel between two parties with absolute security guaranteed by the laws of physics. Communication not only occurred in wired medium but also in wireless medium. WLAN as a wireless medium are much noisier and less reliable in general than wired mediums. This type of noise will generate different numbers of key length and also different level of error rate estimation. Thus, how much secure of the data could be protected on wireless communication? In this study, we implement BB84 protocol on 802.11i wireless local area network (WLAN) to show the affect of noise and eavesdropper could make the data transmission is much secure in wireless medium. In our study shows that implementation of BB84 in 802.11i is able to secure the key distribution from being stealing by the third party.

Wigner functions for gauge equivalence classes of unitary irreducible representations of noncommutative quantum mechanics

Abstract While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge dependencies. This paper deals with the construction of Wigner functions of NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge equivalence classes of unitary irreducible representations (UIRs) of the Lie group GNC which has been identified as the kinematical symmetry group of NCQM in an earlier paper. This general construction of Wigner functions for NCQM, in turn, yields the special cases of Landau and symmetric gauges of NCQM.

Computing quantum bound states on triply punctured two-sphere surface

We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.