Optimizing the discrete time quantum walk using a SU(2) coin

We present a generalized version of the discrete time quantum walk, using the SU(2) operation as the quantum coin. By varying the coin parameters, the quantum walk can be optimized for maximum variance subject to the functional form $\sigma^2 \approx N^2$ and the probability distribution in the position space can be biased. We also discuss the variation in measurement entropy with the variation of the parameters in the SU(2) coin. Exploiting this we show how quantum walk can be optimized for improving mixing time in an $n$-cycle and for quantum walk search.Comment: 6 pages, 6 figure

Decoherence on a two-dimensional quantum walk using four- and two-state particle

We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four-state and two-state particles. By quantifying the quantum correlations between the particle and position degree of freedom and between the two spatial ($x-y$) degrees of freedom using measurement induced disturbance (MID), we show that the two schemes using a two-state particle are more robust against decoherence than the Grover walk, which uses a four-state particle. We also show that the symmetries which hold for two-state quantum walks breakdown for the Grover walk, adding to the various other advantages of using two-state particles over four-state particles.Comment: 12 pages, 16 figures, In Press, J. Phys. A: Math. Theor. (2013

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2

Pseudo-Hermitian continuous-time quantum walks

In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.Comment: 13 page, 7 figure

Recurrence of biased quantum walks on a line

The Polya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely sensitive to the directional symmetry, any deviation from the equal probability to travel in each direction results in a change of the character of the walk from recurrent to transient. Applying our definition of the Polya number to quantum walks on a line we show that the recurrence character of quantum walks is more stable against bias. We determine the range of parameters for which biased quantum walks remain recurrent. We find that there exist genuine biased quantum walks which are recurrent.Comment: Journal reference added, minor corrections in the tex

Evaluation of Wuchereria bancrofti GST as a Vaccine Candidate for Lymphatic Filariasis

Lymphatic parasites survive for years in a complex immune environment by adopting various strategies of immune modulation, which includes counteracting the oxidative free radical damage caused by the host. We now know that the filarial parasites secrete antioxidant enzymes. Among these, the glutathione-S-transferases (GSTs) have the potent ability to effectively neutralize cytotoxic products arising from reactive oxygen species (ROS) that attack cell membranes. Thus, GSTs have the potential to protect the parasite against host oxidative stress. GSTs of several helminthes, including schistosomes, fasciola and the filarial parasite Seteria cervi, are also involved in inducing protective immunity in the host. The schistosome 28 kDa GST has been successfully developed into a vaccine and is currently in Phase II clinical trials. Thus, GST appears to be a potential target for vaccine development. Therefore, in the present study, we cloned W. bancrofti GST, and expressed and purified the recombinant protein. Immunization and challenge experiments showed that 61% of protection could be achieved against B. malayi infections in a jird model. In vitro studies confirm that the anti-WbGST antibodies participate in the killing of B. malayi L3 through an ADCC mechanism and enzymatic activity of WbGST appears to be critical for this larvicidal function

The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles

In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter (\emph{m}) squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for \emph{m}=0 is in agreement with Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.Comment: 16 Pages, 2 Figure

An ITPR1 Gene Deletion Causes Spinocerebellar Ataxia 15/16: A Genetic, Clinical and Radiological Description

The purpose of this study was to characterise a novel family with very slowly progressive pure spinocerebellar ataxia (SCA) caused by a deletion in the inositol 1,4,5-triphosphate receptor 1 (ITPR1) gene on chromosome 3. This is a detailed clinical, genetic, and radiological description of the genotype. Deletions in ITPR1 have been shown to cause SCA15/SCA16 in six families to date. A further Japanese family has been identified with an ITPR1 point mutation. The exact prevalence is as yet unknown, but is probably higher than previously thought. The clinical phenotype of the family is described, and videotaped clinical examinations are presented. Serial brain magnetic resonance imaging studies were carried out on one affected individual, and genetic analysis was performed on several family members. Protein analysis confirmed the ITPR1 deletion. Affected subjects display a remarkably slow, almost pure cerebellar syndrome. Serial magnetic resonance imaging shows moderate cerebellar atrophy with mild inferior parietal and temporal cortical volume loss. Genetic analysis shows a deletion of 346,487 bp in ITPR1 (the second largest ITPR1 deletion reported to date), suggesting SCA15 is due to a loss of ITPR1 function. Western blotting of lymphoblastoid cell line protein confirms reduced ITPR1 protein levels. SCA15 is a slowly or nonprogressive pure cerebellar ataxia, which appears to be caused by a loss of ITPR1 function and a reduction in the translated protein. Patients with nonprogressive or slowly progressive ataxia should be screened for ITPR1 defects

Discrete-time quantum walks on one-dimensional lattices

In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the return probability, which shows scaling behavior $P(0,t)\sim t^{-1}$ and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The average mixing time $M_{\epsilon}$ closes to the limiting probability in linear $N$ (size of the lattice) for large values of thresholds $\epsilon$. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.Comment: 17 pages research not