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

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

Localization of Narrowband Single Photon Emitters in Nanodiamonds

© 2016 American Chemical Society. Diamond nanocrystals that host room temperature narrowband single photon emitters are highly sought after for applications in nanophotonics and bioimaging. However, current understanding of the origin of these emitters is extremely limited. In this work, we demonstrate that the narrowband emitters are point defects localized at extended morphological defects in individual nanodiamonds. In particular, we show that nanocrystals with defects such as twin boundaries and secondary nucleation sites exhibit narrowband emission that is absent from pristine individual nanocrystals grown under the same conditions. Critically, we prove that the narrowband emission lines vanish when extended defects are removed deterministically using highly localized electron beam induced etching. Our results enhance the current understanding of single photon emitters in diamond and are directly relevant to fabrication of novel quantum optics devices and sensors

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 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

Soil Settlement and Uplift Damage to Architectural Heritage Structures in Belgium: Country-Scale Results from an InSAR-Based Analysis

Soil movement may be induced by a wide variety of natural and anthropogenic causes, which are detectable in the local scale, but may influence the movement of the soil over vast geographical expanses. Space borne interferometric synthetic aperture radar (InSAR) measurements of ground movement provide a method for the remote sensing of soil settlement and uplift over wide geographic areas. Based on this settlement and uplift evaluation, the assessment of the potential damage to architectural heritage structures is possible. In this paper an interdisciplinary monitoring and analysis method is presented that processes satellite, cadastral, patrimonial and building geometry data, used for the calculation of settlement and uplift damage to architectural heritage structures in Belgium. It uses processed InSAR data for the determination of the soil movement profile around each case study, of which the typology is determined from patrimonial information databases and the geometry is calculated from digital elevation models. The impact on the historic structures is calculated from the determined soil movement profile based on various soilstructure interaction models for buildings. The resulting damage is presented in terms of a numerical index illustrating its severity according to different criteria. In this way the potential soil movement damage is quantified in a large number of buildings in an easily interpretable and user-friendly fashion. The processing of InSAR data collected over the previous 3 decades allows the determination of the progress of settlement- and uplift-induced damage in this time period. With the integration of newly acquired and more accurate data, the methodology will continue to produce results in the coming years, both for the evaluation of soil settlement and uplift in Belgium as for introducing related damage risk data for existing architectural heritage buildings. Results of the analysis chain are presented in terms of potential current damage for selected areas and buildings

The Electrical-Thermal Switching in Carbon Black-Polymer Composites as a Local Effect

Following the lack of microscopic information about the intriguing well-known electrical-thermal switching mechanism in Carbon Black-Polymer composites, we applied atomic force microscopy in order to reveal the local nature of the process and correlated it with the characteristics of the widely used commercial switches. We conclude that the switching events take place in critical interparticle tunneling junctions that carry most of the current. The macroscopic switched state is then a result of a dynamic-stationary state of fast switching and slow reconnection of the corresponding junctions.Comment: 14 pages, 5 figures,Typographic correctio

Multi-Scale Stochastic Simulation of Diffusion-Coupled Agents and Its Application to Cell Culture Simulation

Many biological systems consist of multiple cells that interact by secretion and binding of diffusing molecules, thus coordinating responses across cells. Techniques for simulating systems coupling extracellular and intracellular processes are very limited. Here we present an efficient method to stochastically simulate diffusion processes, which at the same time allows synchronization between internal and external cellular conditions through a modification of Gillespie's chemical reaction algorithm. Individual cells are simulated as independent agents, and each cell accurately reacts to changes in its local environment affected by diffusing molecules. Such a simulation provides time-scale separation between the intra-cellular and extra-cellular processes. We use our methodology to study how human monocyte-derived dendritic cells alert neighboring cells about viral infection using diffusing interferon molecules. A subpopulation of the infected cells reacts early to the infection and secretes interferon into the extra-cellular medium, which helps activate other cells. Findings predicted by our simulation and confirmed by experimental results suggest that the early activation is largely independent of the fraction of infected cells and is thus both sensitive and robust. The concordance with the experimental results supports the value of our method for overcoming the challenges of accurately simulating multiscale biological signaling systems

Plato's Cave Algorithm: Inferring Functional Signaling Networks from Early Gene Expression Shadows

Improving the ability to reverse engineer biochemical networks is a major goal of systems biology. Lesions in signaling networks lead to alterations in gene expression, which in principle should allow network reconstruction. However, the information about the activity levels of signaling proteins conveyed in overall gene expression is limited by the complexity of gene expression dynamics and of regulatory network topology. Two observations provide the basis for overcoming this limitation: a. genes induced without de-novo protein synthesis (early genes) show a linear accumulation of product in the first hour after the change in the cell's state; b. The signaling components in the network largely function in the linear range of their stimulus-response curves. Therefore, unlike most genes or most time points, expression profiles of early genes at an early time point provide direct biochemical assays that represent the activity levels of upstream signaling components. Such expression data provide the basis for an efficient algorithm (Plato's Cave algorithm; PLACA) to reverse engineer functional signaling networks. Unlike conventional reverse engineering algorithms that use steady state values, PLACA uses stimulated early gene expression measurements associated with systematic perturbations of signaling components, without measuring the signaling components themselves. Besides the reverse engineered network, PLACA also identifies the genes detecting the functional interaction, thereby facilitating validation of the predicted functional network. Using simulated datasets, the algorithm is shown to be robust to experimental noise. Using experimental data obtained from gonadotropes, PLACA reverse engineered the interaction network of six perturbed signaling components. The network recapitulated many known interactions and identified novel functional interactions that were validated by further experiment. PLACA uses the results of experiments that are feasible for any signaling network to predict the functional topology of the network and to identify novel relationships