Experimental Realization of Br\"{u}schweiler's exponentially fast search algorithm in a homo-nuclear system

Compared with classical search algorithms, Grover quantum algorithm [ Phys. Rev. Lett., 79, 325(1997)] achieves quadratic speedup and Bruschweiler hybrid quantum algorithm [Phys. Rev. Lett., 85, 4815(2000)] achieves an exponential speedup. In this paper, we report the experimental realization of the Bruschweiler$ algorithm in a 3-qubit NMR ensemble system. The pulse sequences are used for the algorithms and the measurement method used here is improved on that used by Bruschweiler, namely, instead of quantitatively measuring the spin projection of the ancilla bit, we utilize the shape of the ancilla bit spectrum. By simply judging the downwardness or upwardness of the corresponding peaks in an ancilla bit spectrum, the bit value of the marked state can be read out, especially, the geometric nature of this read-out can make the results more robust against errors.Comment: 10 pages and 3 figure

Analysis and computation for a class of semilinear elliptic boundary value problems

AbstractIn this paper, with the help of super-solutions and sub-solutions, we set up a general framework and get a positive threshold Λ for solution existence and non-existence of a class of semilinear elliptic Dirichlet boundary value problems. Moreover, a result on multiplicity is obtained when λ is large enough. We also give a numerical method to solve and visualize the positive solutions of the problem. Theoretical results are illustrated by numerical simulation

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment

Effects of Understory Vegetation and Litter on Plant Nitrogen (N), Phosphorus (P), N∶P Ratio and Their Relationships with Growth Rate of Indigenous Seedlings in Subtropical Plantations

Establishing seedlings in subtropical plantations is very important for forest health, succession and management. Information on seedling nutrient concentrations is essential for both the selection of suitable indigenous tree species to accelerate succession of the established plantation and sustainable forest management. In this study, we investigated the concentrations of nitrogen ([N]), phosphorus ([P]), and N∶P ratio in leaves, stems and roots of seedlings of three indigenous tree species (Castanopsis chinensis, Michelia chapensis and Psychotria rubra) transplanted with removing or retaining understory vegetation and litter at two typical subtropical forest plantations (Eucalyptus plantation and native species plantation). We also measured the relative growth rate (RGR) of seedling height, and developed the relationships between RGR and leaf [N], [P] and N∶P ratio. Results showed that treatments of understory vegetation and associated litter (i.e. removal or retained) generally had no significant effects on leaf [N], [P], N∶P ratio and RGR of the transplanted tree seedlings for the experimental period. But among different species, there were significant differences in nutrient concentrations. M. chapensis and P. rubra had higher [N] and [P] compared to C. chinensis. [N] and [P] also varied among different plant tissues with much higher values in leaves than in roots for all indigenous species. RGR of indigenous tree seedlings was mostly positively correlated with leaf [N] and [P], but negatively correlated with leaf N∶P ratio. Considering the low [P] and high N∶P ratio observed in the introduced indigenous tree seedlings, we propose that the current experimental plantations might be P limited for plant growth