Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single-qubit-gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as a resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N-qubit state, interacting with this type of error channel, to present an oscillatory behavior, and we show that for the initial canonical cluster state, the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, the fast application of the set of projective measurements does not necessarily imply high gate fidelity, and likewise the slow application thereof does not necessarily imply low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.

Two-dimensional semimetal-insulator transition in HgTe-based quantum wells induced by a longitudinal magnetic field

A metal-insulator transition in a two-dimensional semimetal based on HgTe quantum wells is discovered. The transition is induced by a magnetic field applied parallel to the plane of the quantum well. The threshold behavior of the activation energy as a function of the magnetic-field strength and an abrupt reduction of the Hall resistance at the onset of the transition suggest that the observed effect originates from the formation of an excitonic insulator.

Utility Harmonic Impedance Measurement Based on Data Selection

Determination of the utility harmonic impedance based on measurements is a significant task for utility power-quality improvement and management. Compared to those well-established, accurate invasive methods, the noninvasive methods are more desirable since they work with natural variations of the loads connected to the point of common coupling (PCC), so that no intentional disturbance is needed. However, the accuracy of these methods has to be improved. In this context, this paper first points out that the critical problem of the noninvasive methods is how to select the measurements that can be used with confidence for utility harmonic impedance calculation. Then, this paper presents a new measurement technique which is based on the complex data-based least-square regression, combined with two techniques of data selection. Simulation and field test results show that the proposed noninvasive method is practical and robust so that it can be used with confidence to determine the utility harmonic impedances.

Electronic Structure Calculations in a 2D SixGe1-x Alloy Under an Applied Electric Field.

The recent advances and promises in nanoscience and nanotechnology have been focused on hexagonal materials, mainly on carbon-based nanostructures. Recently, new candidates have been raised, where the greatest efforts are devoted to a new hexagonal and buckled material made of silicon, named Silicene. This new material presents an energy gap due to spin-orbit interaction of approximately 1.5 meV, where the measurement of quantum spin Hall effect(QSHE) can be made experimentally. Some investigations also show that the QSHE in 2D low-buckled hexagonal structures of germanium is present. Since the similarities, and at the same time the differences, between Si and Ge, over the years, have motivated a lot of investigations in these materials. In this work we performed systematic investigations on the electronic structure and band topology in both ordered and disordered SixGe1-x alloys monolayer with 2D honeycomb geometry by first-principles calculations. We show that an applied electric field can tune the gap size for both alloys. However, as a function of electric field, the disordered alloy presents a W-shaped behavior, similarly to the pure Si or Ge, whereas for the ordered alloy a V-shaped behavior is observed.

Unconventional Hall effect near charge neutrality point in a two-dimensional electron-hole system

The transport properties of the two-dimensional system in HgTe-based quantum wells containing simultaneously electrons and holes of low densities are examined. The Hall resistance, as a function of perpendicular magnetic field, reveals an unconventional behavior, different from the classical N-shaped dependence typical for bipolar systems with electron-hole asymmetry. The quantum features of magnetotransport are explained by means of numerical calculation of the Landau level spectrum based on the Kane Hamiltonian. The origin of the quantum Hall plateau sigma(xy) = 0 near the charge neutrality point is attributed to special features of Landau quantization in our system.

A novel self consistent calculation approach for the capacitance-voltage characteristics of semiconductor quantum wire transistors based on a split-gate configuration

Purpose - The purpose of this paper is to develop an efficient numerical algorithm for the self-consistent solution of Schrodinger and Poisson equations in one-dimensional systems. The goal is to compute the charge-control and capacitance-voltage characteristics of quantum wire transistors. Design/methodology/approach - The paper presents a numerical formulation employing a non-uniform finite difference discretization scheme, in which the wavefunctions and electronic energy levels are obtained by solving the Schrodinger equation through the split-operator method while a relaxation method in the FTCS scheme ("Forward Time Centered Space") is used to solve the two-dimensional Poisson equation. Findings - The numerical model is validated by taking previously published results as a benchmark and then applying them to yield the charge-control characteristics and the capacitance-voltage relationship for a split-gate quantum wire device. Originality/value - The paper helps to fulfill the need for C-V models of quantum wire device. To do so, the authors implemented a straightforward calculation method for the two-dimensional electronic carrier density n(x,y). The formulation reduces the computational procedure to a much simpler problem, similar to the one-dimensional quantization case, significantly diminishing running time.

Evaluation of reference-based two-color methods for measurement of gene expression ratios using spotted cDNA microarrays

Abstract Background Spotted cDNA microarrays generally employ co-hybridization of fluorescently-labeled RNA targets to produce gene expression ratios for subsequent analysis. Direct comparison of two RNA samples in the same microarray provides the highest level of accuracy; however, due to the number of combinatorial pair-wise comparisons, the direct method is impractical for studies including large number of individual samples (e.g., tumor classification studies). For such studies, indirect comparisons using a common reference standard have been the preferred method. Here we evaluated the precision and accuracy of reconstructed ratios from three indirect methods relative to ratios obtained from direct hybridizations, herein considered as the gold-standard. Results We performed hybridizations using a fixed amount of Cy3-labeled reference oligonucleotide (RefOligo) against distinct Cy5-labeled targets from prostate, breast and kidney tumor samples. Reconstructed ratios between all tissue pairs were derived from ratios between each tissue sample and RefOligo. Reconstructed ratios were compared to (i) ratios obtained in parallel from direct pair-wise hybridizations of tissue samples, and to (ii) reconstructed ratios derived from hybridization of each tissue against a reference RNA pool (RefPool). To evaluate the effect of the external references, reconstructed ratios were also calculated directly from intensity values of single-channel (One-Color) measurements derived from tissue sample data collected in the RefOligo experiments. We show that the average coefficient of variation of ratios between intra- and inter-slide replicates derived from RefOligo, RefPool and One-Color were similar and 2 to 4-fold higher than ratios obtained in direct hybridizations. Correlation coefficients calculated for all three tissue comparisons were also similar. In addition, the performance of all indirect methods in terms of their robustness to identify genes deemed as differentially expressed based on direct hybridizations, as well as false-positive and false-negative rates, were found to be comparable. Conclusion RefOligo produces ratios as precise and accurate as ratios reconstructed from a RNA pool, thus representing a reliable alternative in reference-based hybridization experiments. In addition, One-Color measurements alone can reconstruct expression ratios without loss in precision or accuracy. We conclude that both methods are adequate options in large-scale projects where the amount of a common reference RNA pool is usually restrictive.