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At least 1,117 records · Page 62

Digital-analog quantum computation

Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. Here, we construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

97 MATHEMATICS AND COMPUTING↗

Radial Two-Dimensional Ion Crystals in a Linear Paul Trap

We experimentally study two-dimensional (2D) Coulomb crystals in the “radial-2D” phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 171 Yb + ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.

74 ATOMIC AND MOLECULAR PHYSICS↗

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗

A study of the Nordsieck-type predictor-corrector methods

Predictor-corrector schemes are discussed for the numerical integration of initial value problems by computer. Descloux formulas, which are considered modified Nordsieck formulas are studied because of their desirable stability and truncation properties along with the standard Nordsieck formulas. The stability of Nordsieck and modified Nordsieck algorithms are computed, and the results are graphed. Test problems are included as examples for comparing the efficiency of the algorithms.

Eiserike, H. M.↗

Impact of space shuttle orbiter reentry on mesospheric NOx.

Shuttle orbiter reentry will produce large amounts of nitric oxide (NO) through shock heating at mesospheric altitudes. The effects of this reentry are modeled by considering an impulsive source of NO in time-dependent equations including photochemistry and transport. The model uses an odd-nitrogen approach similar to Strobel's. Parameterized flux boundary conditions are imposed at the mesopause and stratopause and concentrations of the odd nitrogen species (NO, NO2, NO+, N(4S) and N(2D) are found numerically by a finite difference scheme. A localized disturbance can last many hours, depending on the effectiveness of eddy transport. Although the model is one-dimensional, effects of horizontal transport are also included approximately.

Stolarski, R. S.↗

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗

Vortex methods for two- and three-dimensional flow simulations

The point vortex and vortex blob methods for two dimensional flows are presented. Several results are discussed concerning the numerical analysis of the latter scheme, e.g., the preservation of globally conserved quantities and the analysis of the spatial discretization error resulting from the convection of fixed blobs of vorticity. An application to the two dimensional mixing layer is briefly described. The contour dynamics method is also discussed. The simulation of three dimensional flows with vortex methods is discussed. A natural way to represent the vorticity is in the form of closed tubes of filaments of vorticity, although other schemes are examined. Applications to aircraft trailing vortices and to a turbulent spot in a laminar boundary layer are presented. Hybrid schemes that use an Eulerian mesh to solve the Poisson equation for the velocity field are discussed. The goal of these schemes is to avoid the high cost of the Biot-Savart integration if many vortex elements are used while enjoying most of the advantages of pure Lagrangian schemes.

Leonard, A.↗

Improvements in Vibration-Analysis Technique

Two reports present details of vibration-analysis technique. Technique scheme for accurate and efficient numerical integration of coupled equations of motion of vehicle and its payload(s). Applicable to large stationary structures, land vehicles, airplanes, ships, or wherever vibration analysis done repeatedly after each of many design changes.

Engels, R. C.↗

Calculation of unsteady small disturbance transonic flow at arbitrary reduced frequency using an extended integral equation method.

A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.

Lamah, C. A.↗

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

On spectral multigrid methods for the time-dependent Navier-Stokes equations

A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.

Zang, T. A.↗

A finite element solution of three-dimensional inviscid rotational flows through curved ducts

A previously developed two-dimensional finite element algorithm for the solution of steady Euler equations is extended to three-dimensional problems. Starting with the general three-dimensional problem, the formulation of steady, rotational flows is presented. The boundary conditions for steady flows where the rotationality is introduced through entropy or total enthalpy gradients are introduced. A three-dimensional flow through a curved duct is analyzed as a sample problem, demonstrating the efficiency of the relaxation scheme. The accuracy of the numerical results is investigated by calculating the velocity and vorticity distributions at different sections of the channel, including the exit.

Ecer, A.↗

Numerical simulation of frontogenesis in a moist atmosphere

This paper describes the effects of condensation and evaporation on mesoscale frontal circulations in a two-dimensional numerical model. Utilizing an explicit scheme for the prediction of water vapor, cloud water and rainwater, the model is used to investigate the interactions between convection and the larger-scale environment. The model results are qualitatively compared with results of theoretical and observational studies, including those from the recent Severe Environmental Storms and Mesoscale Experiment-Atmospheric Variability Experiment (SESAME-AVE). Three major differences are observed in a comparison of the moist and dry simulations: (1) The speed of the upper- and lower-level jets was significantly higher in the moist case, (2) The intensity of the ageostrophic circulations in the moist simulation was much stronger, (3) The vertical velocity field in the moist case was characterized by a banded structure not present in the dry case.

Hsie, E.-Y.↗

On the development of hierarchical solution strategies for nonlinear finite element formulations

This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.

Padovan, J.↗

Multiple-scale turbulence closure modeling of confined recirculating flows

A multiple-scale turbulence closure scheme is developed for the numerical predictions of confined recirculating flows. This model is based on the multiple-time-scale concepts of Hanjalic et al. (1980) and takes into account the non-equilibrium spectra energy transfer mechanism. Problems concerning new formulation of energy transfer rate equations and subsequent model coefficient redefinition and energy spectrum partition are discussed. Comparisons are made with several experiments of internal recirculating flows for the purpose of model validation. Numerical results using the present model show significant improvement of predictive capability over that obtained with the single-scale k-epsilon model and show promising potential for complex turbulent flow predictions.

Chen, C. P.↗

A three dimensional calculation of elastic equilibrium for composite materials

A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.

Lustman, Liviu R.↗

On spectral multigrid methods for the time-dependent Navier-Stokes equations

A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.

Zang, T. A.↗

Quasi-steady flight to quasi-steady flight transition in a windshear - Trajectory guidance

The control (via the angle of attack) of the vertical flight of an aircraft taking off at maximum power in a horizontal wind shear with downdraft is investigated analytically. Optimal trajectories to recover the initial path inclination or to recover quasi-steady flight (the relative values of the velocity, path inclination, and angle of attack) are derived using a Chebyshev approach and shown to be nearly identical in the shear but divergent after the shear. These results are then applied to construct a trajectory-guidance control comprising a variable-gamma guidance scheme for the shear trajectory, a constant-gamma guidance scheme for the immediate postshear trajectory, and a constant-rate-of-climb guidance scheme for the aftershear trajectory. Numerical results demonstrating the near-optimal performance of the control are presented in tables and graphs.

Miele, A.↗