Application Of Computation Research Articles

Monolithically integrated femtosecond optical parametric oscillators

Synchronously pumped optical parametric oscillators (OPOs) are highly efficient sources of long-wavelength pulses and nonclassical light, making them invaluable for applications in spectroscopy, metrology, multi-photon microscopy, and quantum computation. Typical systems based on free-space cavities either operate non-degenerately, which limits their efficiency, or use active feedback control to achieve degenerate operation, which limits these systems to dedicated low-noise environments. In this work, we demonstrate a femtosecond monolithically integrated OPO. In contrast with bulk OPOs, our monolithic 10 GHz cavity, based on reverse-proton-exchanged lithium niobate, operates stably without active locking. By detuning the repetition rate of the free-running pump laser from the cavity free spectral range, we control the intracavity pulse dynamics and observe many of the operating regimes previously encountered in free-space degenerate OPOs, such as box-pulsing and quadratic bright-dark solitons (simultons), in addition to non-degenerate operation. When operated in the simulton regime and pumped with 125 fs pulses at 1 µm, this monolithic OPO chip outputs broadband sech2 pulses (63 nm, 3 dB) with tens of milliwatts of average power.

A Binary Characterization Method for Shape Convexity and Applications

Convexity prior is one of the main cues for human vision and shape completion with important applications in image processing and computer vision. This paper provides a computable characterization method for shape convexity, and illustrates its applications in image segmentation and convex hull computation. We prove that the convexity of a region is equivalent to a series of quadratic inequality constraints on its indicator function. By incorporating this result, models are proposed for image segmentation with convexity prior and convex hull computation of clean and noisy data sets, respectively. Then, these models are summarized into a unified optimization problem on binary function(s) with the quadratic inequality constraints. Numerical method is proposed by linearizing the quadratic constraints. The linearization problem is solved by a proximal alternating direction method of multipliers, the convergence of which is guaranteed under some proper conditions. Numerical experiments demonstrate the efficiency and effectiveness of the proposed methods for image segmentation and convex hull computation.

A Newton’s iteration converges quadratically to nonisolated solutions too

The textbook Newton’s iteration is practically inapplicable on nonisolated solutions of unregularized nonlinear systems. With a simple modification, a version of Newton’s iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined. Furthermore, the iteration serves as a de facto regularization mechanism for computing singular zeros from empirical data. Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a solution of the underlying system with an error bound in the same order of the data accuracy. Geometrically, the iteration approximately converges to the nearest point on the solution manifold. This extension simplifies nonlinear system modeling by eliminating the zero isolation process and enables a wide range of applications in algebraic computation.

High-Order Lohner-Type Algorithm for Rigorous Computation of Poincaré Maps in Systems of Delay Differential Equations with Several Delays

We present a Lohner-type algorithm for rigorous integration of systems of delay differential equations (DDEs) with multiple delays, and its application in computation of Poincaré maps, to study the dynamics of some bounded, eternal solutions. The algorithm is based on a piecewise Taylor representation of the solutions in the phase space, and it exploits the smoothing of solutions occurring in DDEs to produce enclosures of solutions of a high order. We apply the topological techniques to prove various kinds of dynamical behaviour, for example, existence of (apparently) unstable periodic orbits in Mackey–Glass equation (in the regime of parameters where chaos is numerically observed) and persistence of symbolic dynamics in a delay-perturbed chaotic ODE (the Rössler system).

Transport measurement of fractional charges in topological models

The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme in which both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su–Schrieffer–Heeger (SSH) model, both the e/2 charge of the TFC and its distribution can be verified. As for the disorder effect, it is shown that the Anderson disorder, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while having little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the 2e/3 TFC in the breathing kagome model could be confirmed even in the presence of disorder effect. These conclusions about spatial dimension and disorder effect are quite universal, which also applies to other topological systems such as topological classic wave system.

Editorial for the special issue on architecture, algorithms and applications of high performance sparse matrix computations

Editorial for the special issue on architecture, algorithms and applications of high performance sparse matrix computations

Breaking the Chains of Health Data

Breaking the Chains of Health Data

Geometric triangulation uncertainty for sustainable urban underwater localization in presence of malicious virtual node

Sustainability of urban underwater sensor networks (uUWSNs) depends critically on the efficient triangulation during the localization process. There is very limited literature on sustainable range-free localization in uUWSNs. To address this issue, we improve localization method based on triangulation approach through convex optimization with Geometric Dilution of Precision (GDOP). We define “geometric triangulation uncertainty”. A sustainable scheme is proposed for identification of underwater nodesto modify a two-mode Gaussian Mixture Model. The proposed method is then compared to a weighted least square model for different threshold levels of maximum node range and associated triangulation uncertainties. The convex formulation is then solved using semidefinite programming to obtain optimal position of target in presence of a malicious virtual node. Theproposed method is verified using Cramer’s Rao lower bound in terms of RMS errors and cumulative errors. It exhibits close to ideal performance whenever perturbations associated with geometric triangulation uncertainty is bounded. The performance of the proposed method exceeds that of the weighted least squares method, which means that the proposed technique shall find immense application in intelligent computation of urban underwater scenarios, where the amount of sensor information exchange critically depends upon terrain environment and surrounding disturbances.

High-throughput calculations of charged point defect properties with semi-local density functional theory—performance benchmarks for materials screening applications

Calculations of point defect energetics with Density Functional Theory (DFT) can provide valuable insight into several optoelectronic, thermodynamic, and kinetic properties. These calculations commonly use methods ranging from semi-local functionals with a-posteriori corrections to more computationally intensive hybrid functional approaches. For applications of DFT-based high-throughput computation for data-driven materials discovery, point defect properties are of interest, yet are currently excluded from available materials databases. This work presents a benchmark analysis of automated, semi-local point defect calculations with a-posteriori corrections, compared to 245 “gold standard” hybrid calculations previously published. We consider three different a-posteriori correction sets implemented in an automated workflow, and evaluate the qualitative and quantitative differences among four different categories of defect information: thermodynamic transition levels, formation energies, Fermi levels, and dopability limits. We highlight qualitative information that can be extracted from high-throughput calculations based on semi-local DFT methods, while also demonstrating the limits of quantitative accuracy.

Digital and analog resistive switching in Lu-doped piezoelectric [formula omitted] film

Recently, in the field of artificial intelligence, neuromorphic devices have received significant attention for building artificial neural networks. Nano-scale resistive random access memory (RRAM) is one of the emerging electrical components for neuromorphic computing. In the present study, the synaptic characteristics are investigated in the piezoelectric BiFe1−xLuxO3 (BFLO) and Bi1−xLuxFeO3 (BLFO) (x = 0.05) based RRAM devices in a vertical configuration. Both devices show bipolar resistive switching behavior with good endurance characteristics. However, analog switching with potentiation and depression response is observed in Ag/BFLO/FTO device. The change in resistance and leakage current flow across the device is explained by the space charge limiting current conduction mechanism with regard to thermally generated and injected charge carriers. Both films possess strong electro-mechanical response with the ferroelectric and ferro-elastic domain walls oriented along 710, 1090, and 1800 directions. The electro-mechanical response and resistive switching properties make the materials viable for sensing, energy harvesting, and non-volatile memory technology. Moreover, the BFLO-based synaptic device has potential application in neuromorphic computation.

Quantum Phase Recognition via Quantum Kernel Methods

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an important class of Quantum Phase Recognition (QPR) problems, which are crucially important in understanding many-particle quantum systems. We prove that, under widely believed complexity theory assumptions, there exists a wide range of QPR problems that cannot be efficiently solved by classical learning algorithms with classical resources. Whereas using a quantum computer, we prove the efficiency and robustness of quantum kernel methods in solving QPR problems through Linear order parameter Observables. We numerically benchmark our algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in predicting such quantum phase transitions in many-particle systems.

Perfect state transfer on weighted bi-Cayley graphs over abelian groups

The study of perfect state transfer on graphs has attracted extensive attention because of its application in quantum information and computation. This paper establishes necessary and sufficient conditions for a weighted bi-Cayley graph having perfect state transfer over any given finite abelian group. As special cases of weighted bi-Cayley graphs, the results in this paper can apply to examine weighted Cayley graphs having perfect state transfer over dihedral groups, generalized dihedral groups, semi-dihedral groups and dicyclic groups.

Optical analog computing enabled broadband structured light.

Mathematically, any function can be expressed as the operation form of another function. Here, the idea is introduced into an optical system to generate structured light. In the optical system, a mathematical function is represented by an optical field distribution, and any structured light field can be generated by performing different optical analog computations for any input optical field. In particular, optical analog computing has a good broadband performance, as it can be achieved based on the Pancharatnam-Berry phase. Therefore, our scheme can provide a flexible way to generate broadband structured light, and this is theoretically and experimentally demonstrated. It is envisioned that our work may inspire potential applications in high-resolution microscopy and quantum computation.

Recent progress on Majorana in semiconductor-superconductor heterostructures—engineering and detection

Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) that have potential applications in topological quantum computation. Though MZMs have been predicted on many platforms, their existence of them is still under debate. In this paper, we review the recent progress of engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review the protocols of implementing topological quantum computation by hybrid semiconductor-superconductor nanowires.

An Efficient Data-Independent Priority Queue and its Application to Dark Pools

We introduce a secure data-independent priority queue which supports polylogarithmic-time insertion operations and constant-time deletions and read-front (aka peek) operations as opposed to the originally introduced queue by Toft (PODC '11). Moreover, we minimize the number of comparisons required to perform different operations on Toft's priority queue. Data-independent data structures—first identified explicitly by Toft, and further elaborated by Mitchell and Zimmerman (STACS '14)—serve the purpose of computing on encrypted data without executing branching code which can be used to avoid prohibitively expensive operations in secure computation applications. Focusing on the costly sorting operations, we show significant asymptotic improvements over prior privacy preserving dark pool applications. Dark pools are securities-trading venues which attain ad-hoc order privacy, by matching orders outside of publicly visible exchanges via the so-called dark pool operators. In this paper, we describe an efficient and secure dark pool (implementing a full continuous double auction) based on our new priority queue. Our construction's security guarantees are cryptographic based on secure multiparty computation (MPC), and do not require that the dark pool operators are trusted. Our construction improves upon the asymptotic efficiency attained by previous efforts. Existing cryptographic dark pools process new orders in time which grows linearly in the size of the standing order book; ours does so in polylogarithmic time. We describe a concrete implementation of our MPC protocol with malicious security in the honest majority setting. We also report benchmarks of our implementation and compare them to prior works. Our protocol reduces the total running time by several orders of magnitude over prior secure dark pool solutions.

The relative Fresnel goos-Hänchen phase crossover and its applications in quantum computation

In this work, we present the relative Fresnel (Goos-Hänchen) phase crossover between the total internal reflection and diffusion regimes by employing polarization tomography. This powerful technique not only enables us to access information about the amplitude and relative phase of the state for total reflection but also facilitates the identification of the transition between these regimes. In all cases, the experimental data are in very good agreement with the theoretical predictions. As an application, we propose the use of the GH phase to implement a phase gate, which is an essential requirement for universal computation. In this context, our system offers a more cost-effective and alternative set up to implement the phase gate and simulate compensator devices.

Simultaneous Preparation of Two Optical Cat States Based on a Nondegenerate Optical Parametric Amplifier

AbstractThe cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, two optical cat states are prepared simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in this experiment, which saves half of the quantum resources of nonlinear cavities. The presented results make a step toward preparing the four‐component cat state, which has potential applications in fault‐tolerant quantum computation.

Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors

It is well known that Majorana zero modes can be harnessed for applications in topological quantum computation. Transitions away from the ground-state subspace, where computations are performed, are detrimental. The authors study the diabatic error which quantifies these transitions as Majorana zero modes are transported across a superconducting wire. Using the `piano key' approach for transport, the authors find that there exists an optimal number of keys which reduces the diabatic error.

Noncommutative Vieta theorem in Clifford geometric algebras

In this paper, we discuss a generalization of Vieta theorem (Vieta's formulas) to the case of Clifford geometric algebras. We compare the generalized Vieta formulas with the ordinary Vieta formulas for characteristic polynomial containing eigenvalues. We discuss Gelfand–Retakh noncommutative Vieta theorem and use it for the case of geometric algebras of small dimensions. We introduce the notion of a simple basis‐free formula for a determinant in geometric algebra and prove that a formula of this type exists in the case of arbitrary dimension. Using this notion, we present and prove generalized Vieta theorem in geometric algebra of arbitrary dimension. The results can be used in symbolic computation and various applications of geometric algebras in computer science, computer graphics, computer vision, physics, and engineering.

Low-energy Pipelined Hardware Design for Approximate Medium Filter

Image and video processing algorithms are currently crucial for many applications. Hardware implementation of these algorithms provides higher speed for large computation applications. Removing noise is often a typical pre-processing step to enhance the results of later analysis and processing. Median filter is a typical nonlinear filter that is very commonly used for impulse noise elimination in digital image processing. This article suggests a low-energy median filter hardware design for battery-based hardware applications. An approximate solution with high accuracy is investigated to speed up the filtering operation, reduce the area, and consume less power/energy. Pipelining and parallelism are used to optimize the speed and power of this technique. Non-pipelined, two different pipelined structures, and two parallel architectures versions are designed. The design versions are implemented first with a Virtex-5 LX110T FPGA and then using the UMC 130nm standard cell ASIC technology. The selection and the even-odd sorting-based median filters are also implemented for an equitable comparison with the standard median filtering techniques. The suggested non-pipelined median filter design enhances the throughput 35% more than the highest investigated state of the art. The pipelining enhances the throughput to more than twice its value. Additionally, the parallel architecture decreases the area and the consumed power by around 40%. The simulation results reveal that one of the suggested designs significantly decreases the area, with the same speed as the fastest design in the literature, without noticeably degrading the accuracy, and a significant decrease in energy consumption by about 60%.