PANSATZ: Pulse-based Ansatz for Variational Quantum Algorithms

We develop and implement a novel pulse-based ansatz, which we call PANSATZ, for more efficient and accurate implementations of variational quantum algorithms (VQAs) on today's noisy intermediate-scale quantum (NISQ) computers. Our approach is applied to quantum chemistry. Specifically, finding the ground-state energy associated with the electron configuration problem, using the variational quantum eigensolver (VQE) algorithm for several molecules. We manage to achieve chemical accuracy both in simulation for several molecules and on one of IBM's NISQ devices for the $H_2$ molecule in the STO-3G basis. Our results are compared to a gate-based ansatz and show significant latency reduction - up to $7\times$ shorter ansatz schedules. We also show that this ansatz has structured adaptivity to the entanglement level required by the problem

Multiblock High Order Large Eddy Simulation of Powered Fontan Hemodynamics: Towards Computational Surgery

Children born with only one functional ventricle must typically undergo a series of three surgeries to obtain the so-called Fontan circulation in which the blood coming from the body passively flows from the Vena Cavae (VCs) to the Pulmonary Arteries (PAs) through the Total Cavopulmonary Connection (TCPC). The circulation is inherently inefficient due to the lack of a subpulmonary ventricle. Survivors face the risk of circulatory sequelae and eventual failure for the duration of their lives. Current efforts are focused on improving the outcomes of Fontan palliation, either passively by optimizing the TCPC, or actively by using mechanical support. We are working on a chronic implant that would be placed at the junction of the TCPC, and would provide the necessary pressure augmentation to re-establish a circulation that recapitulates a normal two-ventricle circulation. This implant is based on the Von Karman viscous pump and consists of a vaned impeller that rotates inside the TCPC. To evaluate the performance of such a device, and to study the flow features induced by the presence of the pump, Computational Fluid Dynamics (CFD) is used. CFD has become an important tool to understand hemodynamics owing to the possibility of simulating quickly a large number of designs and flow conditions without any harm for patients. The transitional and unsteady nature of the flow can make accurate simulations challenging. We developed and in-house high order Large Eddy Simulation (LES) solver coupled to a recent Immersed Boundary Method (IBM) to handle complex geometries. Multiblock capability is added to the solver to allow for efficient simulations of complex patient specific geometries. Blood simulations are performed in a complex patient specific TCPC geometry. In this study, simulations without mechanical assist are performed, as well as after virtual implantation of the temporary and chronic implants being developed. Instantaneous flow structures, hepatic factor distribution, and statistical data are presented for all three cases

Boundary Closures for Fourth-order Energy Stable Weighted Essentially Non-Oscillatory Finite Difference Schemes

A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations

On the role of spectral properties of viscous flux discretization for flow simulations on marginally resolved grids

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with better properties at high wavenumbers, denoted as $\alpha$-damping type discretization, produced superior solutions compared to the other class of methods. The proposed compact $\alpha$-damping method converged towards the direct numerical simulation (DNS) solution at lower grid resolution compared with the other class of methods and is, therefore, a better candidate for high fidelity large-eddy simulations (LES) and DNS studies.Comment: 1

Childhood socioeconomic position and objectively measured physical capability levels in adulthood: a systematic review and meta-analysis

<p><b>Background:</b> Grip strength, walking speed, chair rising and standing balance time are objective measures of physical capability that characterise current health and predict survival in older populations. Socioeconomic position (SEP) in childhood may influence the peak level of physical capability achieved in early adulthood, thereby affecting levels in later adulthood. We have undertaken a systematic review with meta-analyses to test the hypothesis that adverse childhood SEP is associated with lower levels of objectively measured physical capability in adulthood.</p> <p><b>Methods and Findings:</b> Relevant studies published by May 2010 were identified through literature searches using EMBASE and MEDLINE. Unpublished results were obtained from study investigators. Results were provided by all study investigators in a standard format and pooled using random-effects meta-analyses. 19 studies were included in the review. Total sample sizes in meta-analyses ranged from N = 17,215 for chair rise time to N = 1,061,855 for grip strength. Although heterogeneity was detected, there was consistent evidence in age adjusted models that lower childhood SEP was associated with modest reductions in physical capability levels in adulthood: comparing the lowest with the highest childhood SEP there was a reduction in grip strength of 0.13 standard deviations (95% CI: 0.06, 0.21), a reduction in mean walking speed of 0.07 m/s (0.05, 0.10), an increase in mean chair rise time of 6% (4%, 8%) and an odds ratio of an inability to balance for 5s of 1.26 (1.02, 1.55). Adjustment for the potential mediating factors, adult SEP and body size attenuated associations greatly. However, despite this attenuation, for walking speed and chair rise time, there was still evidence of moderate associations.</p> <p><b>Conclusions:</b> Policies targeting socioeconomic inequalities in childhood may have additional benefits in promoting the maintenance of independence in later life.</p&gt