Entangled Quantum States Generated by Shor's Factoring Algorithm

The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated during the pre-processing stage of the algorithm and remains nearly constant during the quantum Fourier transform stage. The entanglement is found to be correlated with the speedup achieved by the quantum algorithm compared to classical algorithms.Comment: 7 pages, 4 figures submitted to Phys. Rev.

ZnJ2 Is a Member of a Large Chaperone Family in the Chloroplast of Photosynthetic Organisms that Features a DnaJ-Like Zn-Finger Domain.

Photosynthesis is performed by large complexes, composed of subunits encoded by the nuclear and chloroplast genomes. Assembly is assisted by general and target-specific chaperones, but their mode of action is yet unclear. We formerly showed that ZnJ2 is an algal chaperone resembling BSD2 from land plants. In algae, it co-migrates with the rbcL transcript on chloroplast polysomes, suggesting it contributes to the de-novo synthesis of RbcL (Doron et al., 2014). ZnJ2 contains four CXXCXGXG motifs, comprising a canonical domain typical also of DnaJ-type I (DNAJA). It contributes to the binding of protein substrates to DnaK and promotes an independent oxidoreductase activity (Mattoo et al., 2014). To examine whether ZnJ2 has oxidoreductase activity, we used the RNaseA assay, which measures the oxidation-dependent reactivation of reduced-denatured RNaseA. Although ZnJ2 assisted the native refolding of reduced-denatured RNaseA, its activity was restricted to an oxidizing environment. Thus, ZnJ2 did not carry the exclusive responsibility for the formation of disulfide bridges, but contributed to the stabilization of its target polypeptides, until they reached their native state. A ZnJ2 cysteine deficient mutant maintained a similar holding chaperone activity as the wild-type and did not induce the formation of disulfide bonds. ZnJ2 is devoid of a J-domain. It thus does not belong to the J-domain co-chaperones that target protein substrates to DnaK. As expected, in vitro, its aggregation-prevention activity was not synergic to the ATP-fueled action of DnaK/DnaJ/GrpE in assisting the native refolding of denatured malate dehydrogenase, nor did it show an independent refolding activity. A phylogenetic analysis showed that ZnJ2 and BSD2 from land plants, are two different proteins belonging to a larger group containing a cysteine-rich domain, that also includes the DNAJAs. Members of this family are apparently involved in specific assembly of photosynthetic complexes in the chloroplast

Erawatch (European research area support)

Issued as final reportErawatch Network ASB

Algebraic analysis of quantum search with pure and mixed states

An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process, which turns out to be confined to a four-dimensional subspace of the Hilbert space. This work unifies and generalizes earlier results on the time evolution of the amplitudes during the quantum search, the optimal number of iterations and the success probability. Furthermore, it enables a direct generalization to the case in which the initial state is a mixed state, providing an exact formula for the success probability.Comment: 13 page

Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure

The Groverian entanglement measure, G(psi), is applied to characterize a variety of pure quantum states |psi> of multiple qubits. The Groverian measure is calculated analytically for certain states of high symmetry, while for arbitrary states it is evaluated using a numerical procedure. In particular, it is calculated for the class of Greenberger-Horne-Zeilinger states, the W states as well as for random pure states of n qubits. The entanglement generated by Grover's algorithm is evaluated by calculating G(psi) for the intermediate states that are obtained after t Grover iterations, for various initial states and for different sets of the marked states.Comment: 28 pages, 5 figure

Reduction of Soil-Borne Plant Pathogens Using Lime and Ammonia Evolved from Broiler Litter

In laboratory and micro-plots simulations and in a commercial greenhouse, soil ammonia (NH3) and pH were manipulated as means to control soil-borne fungal pathogens and nematodes. Soil ammonification capacity was increased by applying low C/N ratio broiler litter at 1–8% (w/w). Soil pH was increased using lime at 0.5–1% (w/w). This reduced fungi (Fusarium oxysporum f. sp. dianthi and Sclerotium rolfsii) and root-knot nematode (Meloidogyne javanica) in lab tests below detection. In a commercial greenhouse, broiler litter (25 Mg ha−1) and lime (12.5 Mg ha−1) addition to soil in combination with solarization significantly reduced M. javanica induced root galling of tomato test plants from 47% in the control plots (solarization only) to 7% in treated plots. Root galling index of pepper plants, measured 178 days after planting in the treated and control plots, were 0.8 and 1.5, respectively, which was statistically significantly different. However, the numbers of nematode juveniles in the root zone soil counted 83 and 127 days after pepper planting were not significantly different between treatments. Pepper fruit yield was not different between treatments. Soil disinfection and curing was completed within one month, and by the time of bell-pepper planting the pH and ammonia values were normal

Magnetization Process of Nanoscale Iron Cluster

Low-temperature magnetization process of the nanoscale iron cluster in linearly sweeped fields is investigated by a numerical analysis of time-dependent Schr$\ddot{\rm o}$dinger equation and the quantum master equation. We introduce an effective basis method extracting important states, by which we can obtain the magnetization process effectively. We investigate the structure of the field derivative of the magnetization. We find out that the antisymmetric interaction determined from the lattice structure reproduces well the experimental results of the iron magnets and that this interaction plays an important role in the iron cluster. Deviations from the adiabatic process are also studied. In the fast sweeping case, our calculations indicate that the nonadiabatic transition dominantly occurs at the level crossing for the lowest field. In slow sweeping case, due to the influence of the thermal environment to the spin system, the field derivative of the magnetization shows an asymmetric behavior, the magnetic F$\ddot{\rm o}$hn effect, which explains the substructure of the experimental results in the pulsed field.Comment: 5 pages of text and 2 pages of 6 figures. To appear in J. Phys. Soc. Jp

Quantum and approximation algorithms for maximum witnesses of Boolean matrix products

The problem of finding maximum (or minimum) witnesses of the Boolean product of two Boolean matrices (MW for short) has a number of important applications, in particular the all-pairs lowest common ancestor (LCA) problem in directed acyclic graphs (dags). The best known upper time-bound on the MW problem for n\times n Boolean matrices of the form O(n^{2.575}) has not been substantially improved since 2006. In order to obtain faster algorithms for this problem, we study quantum algorithms for MW and approximation algorithms for MW (in the standard computational model). Some of our quantum algorithms are input or output sensitive. Our fastest quantum algorithm for the MW problem, and consequently for the related problems, runs in time \tilde{O}(n^{2+\lambda/2})=\tilde{O}(n^{2.434}), where \lambda satisfies the equation \omega(1, \lambda, 1) = 1 + 1.5 \, \lambda and \omega(1, \lambda, 1) is the exponent of the multiplication of an n \times n^{\lambda}$ matrix by an n^{\lambda} \times n matrix. Next, we consider a relaxed version of the MW problem (in the standard model) asking for reporting a witness of bounded rank (the maximum witness has rank 1) for each non-zero entry of the matrix product. First, by adapting the fastest known algorithm for maximum witnesses, we obtain an algorithm for the relaxed problem that reports for each non-zero entry of the product matrix a witness of rank at most \ell in time \tilde{O}((n/\ell)n^{\omega(1,\log_n \ell,1)}). Then, by reducing the relaxed problem to the so called k-witness problem, we provide an algorithm that reports for each non-zero entry C[i,j] of the product matrix C a witness of rank O(\lceil W_C(i,j)/k\rceil ), where W_C(i,j) is the number of witnesses for C[i,j], with high probability. The algorithm runs in \tilde{O}(n^{\omega}k^{0.4653} +n^2k) time, where \omega=\omega(1,1,1).Comment: 14 pages, 3 figure

Is there a shift to "active nanostructures"?

It has been suggested that an important transition in the long-run trajectory of nanotechnology development is a shift from passive to active nanostructures. Such a shift could present different or increased societal impacts and require new approaches for risk assessment. An active nanostructure “changes or evolves its state during its operation,” according to the National Science Foundation’s (2006) Active Nanostructures and Nanosystems grant solicitation. Active nanostructure examples include nanoelectromechanical systems (NEMS), nanomachines, self-healing materials, targeted drugs and chemicals, energy storage devices, and sensors. This article considers two questions: (a) Is there a “shift” to active nanostructures? (b) How can we characterize the prototypical areas into which active nanostructures may emerge? We build upon the NSF definition of active nanostructures to develop a research publication search strategy, with a particular intent to distinguish between passive and active nanotechnologies. We perform bibliometric analyses and describe the main publication trends from 1995 to 2008. We then describe the prototypes of research that emerge based on reading the abstracts and review papers encountered in our search. Preliminary results suggest that there is a sharp rise in active nanostructures publications in 2006, and this rise is maintained in 2007 and through to early 2008. We present a typology that can be used to describe the kind of active nanostructures that may be commercialized and regulated in the future