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.

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

Versatile multicolor nanodiamond probes for intracellular imaging and targeted labeling

© 2018 The Royal Society of Chemistry. We report on the sizable production of fluorescent nanodiamonds (FNDs) containing a near infrared (NIR) color center-namely the silicon vacancy (SiV) defect, and their first demonstration inside cells for bio-imaging. We further demonstrate a concept of multi-color bio-imaging using FNDs to investigate intercellular processes using two types of FNDs. Due to their specific spectral properties, SiV FNDs can be distinguished from common nitrogen-vacancy (NV) FNDs and show a distinct initial spreading throughout the cell interior. The reported results are the first demonstration of multi-color labeling with FNDs that are especially interesting for in vivo bio-imaging due to their stable fluorescence

Formation of Multipartite Entanglement Using Random Quantum Gates

The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a non-local geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the non-local geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and non-local interactions between the qubits.Comment: 7 pages, 5 figure

Structural studies demonstrating a bacteriophage-like replication cycle of the eukaryote-infecting \u3ci\u3eParamecium bursaria\u3c/i\u3e chlorella virus-1

A fundamental stage in viral infection is the internalization of viral genomes in host cells. Although extensively studied, the mechanisms and factors responsible for the genome internalization process remain poorly understood. Here we report our observations, derived from diverse imaging methods on genome internalization of the large dsDNA Paramecium bursaria chlorella virus-1 (PBCV-1). Our studies reveal that early infection stages of this eukaryotic- infecting virus occurs by a bacteriophage-like pathway, whereby PBCV-1 generates a hole in the host cell wall and ejects its dsDNA genome in a linear, base-pair-by-base-pair process, through a membrane tunnel generated by the fusion of the virus internal membrane with the host membrane. Furthermore, our results imply that PBCV-1 DNA condensation that occurs shortly after infection probably plays a role in genome internalization, as hypothesized for the infection of some bacteriophages. The subsequent perforation of the host photosynthetic membranes presumably enables trafficking of viral genomes towards host nuclei. Previous studies established that at late infection stages PBCV-1 generates cytoplasmic organelles, termed viral factories, where viral assembly takes place, a feature characteristic of many large dsDNA viruses that infect eukaryotic organisms. PBCV-1 thus appears to combine a bacteriophage-like mechanism during early infection stages with a eukaryotic-like infection pathway in its late replication cycle. Author summary -- Although extensively studied, the mechanisms responsible for internalization of viral genomes into their host cells remain unclear. A particularly interesting case of genome release and internalization is provided by the large Paramecium bursaria chlorella virus-1 (PBCV-1), which infects unicellular eukaryotic photosynthetic chlorella cells. In order to release its long dsDNA genome and to enable its translocation to the host nucleus, PBCV-1 must overcome multiple hurdles, including a thick host cell wall and multilayered chloroplast membranes that surround the host cytoplasm. Our observations indicate that these obstacles are dealt with perforations of the host wall, the host cellular membrane, and the host photosynthetic membranes by viral-encoded proteins. Furthermore, our results highlight a bacteriophage-like nature of early PBCV-1 infection stages, thus implying that this virus uniquely combines bacteriophage-like and eukaryotic-like pathways to accomplish its replication cycle

Electromigration-Induced Flow of Islands and Voids on the Cu(001) Surface

Electromigration-induced flow of islands and voids on the Cu(001) surface is studied at the atomic scale. The basic drift mechanisms are identified using a complete set of energy barriers for adatom hopping on the Cu(001) surface, combined with kinetic Monte Carlo simulations. The energy barriers are calculated by the embedded atom method, and parameterized using a simple model. The dependence of the flow on the temperature, the size of the clusters, and the strength of the applied field is obtained. For both islands and voids it is found that edge diffusion is the dominant mass-transport mechanism. The rate limiting steps are identified. For both islands and voids they involve detachment of atoms from corners into the adjacent edge. The energy barriers for these moves are found to be in good agreement with the activation energy for island/void drift obtained from Arrhenius analysis of the simulation results. The relevance of the results to other FCC(001) metal surfaces and their experimental implications are discussed.Comment: 9 pages, 13 ps figure

Virus–host interactions: insights from the replication cycle of the large \u3ci\u3eParamecium bursaria\u3c/i\u3e chlorella virus

The increasing interest in cytoplasmic factories generated by eukaryotic-infecting viruses stems from the realization that these highly ordered assemblies may contribute fundamental novel insights to the functional significance of order in cellular biology. Here, we report the formation process and structural features of the cytoplasmic factories of the large dsDNA virus Paramecium bursaria chlorella virus 1 (PBCV-1). By combining diverse imaging techniques, including scanning transmission electron microscopy tomography and focused ion beam technologies, we show that the architecture and mode of formation of PBCV-1 factories are significantly different from those generated by their evolutionary relatives Vaccinia and Mimivirus. Specifically, PBCV-1 factories consist of a network of single membrane bilayers acting as capsid templates in the central region, and viral genomes spread throughout the host cytoplasm but excluded from the membranecontaining sites. In sharp contrast, factories generated by Mimivirus have viral genomes in their core, with membrane biogenesis region located at their periphery. Yet, all viral factories appear to share structural features that are essential for their function. In addition, our studies support the notion that PBCV-1 infection, which was recently reported to result in significant pathological outcomes in humans andmice, proceeds througha bacteriophage -like infection pathway

Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer performing Shor's factoring algorithm [A. Ukena and A. Shimizu, Phys. Rev. A69 (2004) 022301], it needs to be generalized for it to be applicable to a large class of algorithms and/or other models such as measurement-based quantum computers. To treat such general cases, we first generalize the indices for the superposition of macroscopically distinct states. We then generalize the conjecture, using the generalized indices, in such a way that it is unambiguously applicable to general models if a quantum algorithm achieves exponential speedup. On the basis of this generalized conjecture, we further extend the conjecture to Grover's quantum search algorithm, whose speedup is large but quadratic. It is shown that this extended conjecture is also correct. Since Grover's algorithm is a representative algorithm for unstructured problems, the present result further supports the conjecture.Comment: 18 pages, 5 figures. Fixed typos throughout the manuscript. This version has been publishe

Electromigration-Induced Propagation of Nonlinear Surface Waves

Due to the effects of surface electromigration, waves can propagate over the free surface of a current-carrying metallic or semiconducting film of thickness h_0. In this paper, waves of finite amplitude, and slow modulations of these waves, are studied. Periodic wave trains of finite amplitude are found, as well as their dispersion relation. If the film material is isotropic, a wave train with wavelength lambda is unstable if lambda/h_0 < 3.9027..., and is otherwise marginally stable. The equation of motion for slow modulations of a finite amplitude, periodic wave train is shown to be the nonlinear Schrodinger equation. As a result, envelope solitons can travel over the film's surface.Comment: 13 pages, 2 figures. To appear in Phys. Rev.