Quantum SDP-Solvers: Better upper and lower bounds

Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the number $m$ of constraints, but worse in terms of various other parameters. In this paper we improve their algorithms in several ways, getting better dependence on those other parameters. To this end we develop new techniques for quantum algorithms, for instance a general way to efficiently implement smooth functions of sparse Hamiltonians, and a generalized minimum-finding procedure. We also show limits on this approach to quantum SDP-solvers, for instance for combinatorial optimizations problems that have a lot of symmetry. Finally, we prove some general lower bounds showing that in the worst case, the complexity of every quantum LP-solver (and hence also SDP-solver) has to scale linearly with $mn$ when $m\approx n$, which is the same as classical.Comment: v4: 69 pages, small corrections and clarifications. This version will appear in Quantu

Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE

In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to assess the feasibility of employing the automatic differentiation tool TAPENADE for this purpose on a large Fortran codebase that is the result of many years of continuous development. As a starting point we will describe the special structure of finite element codes and the implications that this code design carries for an efficient calculation of the Jacobian matrix. We will also propose a first approach towards improving the efficiency of such a method. Finally, we will present a functioning method for the automatic implementation of the Jacobian calculation in a finite element software, but will also point out important shortcomings that will have to be addressed in the future.Comment: 17 pages, 9 figure

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Applying an abstract data structure description approach to parallelizing scientific pointer programs

Even though impressive progress has been made in the area of parallelizing scientific programs with arrays, the application of similar techniques to programs with pointer data structures has remained difficult. Unlike arrays which have a small number of well-defined properties that can be utilized by a parallelizing compiler, pointer data structures are used to implement a wide variety of structures that exhibit a much more diverse set of properties. The complexity and diversity of such properties means that, in general, scientific programs with pointer data structures cannot be effectively analyzed by an optimizing and parallelizing compiler.In order to provide a system in which the compiler can fully utilize the properties of different types of pointer data structures, we have developed a mechanism for the Abstract Description of Data Structures (ADDS). With our approach, the programmer can explicitly describe important properties such as dimensionality of the pointer data structure, independence of dimensions, and direction of traversal. These abstract descriptions of pointer data structures are then used by the compiler to guide analysis, optimization, and parallelization.In this paper we summarize the ADDS approach through the use of numerous examples of data structures used in scientific computations, we illustrate how such declarations are natural and non-tedious to specify, and we show how the ADDS declarations can be used to improve compile-time analysis. In order to demonstrate the viability of our approach, we show how such techniques can be used to parallelize an important class of scientific codes which naturally use recursive pointer data structures. In particular, we use our approach to develop the parallelization of an N-body simulation that is based on a relatively complicated pointer data structure, and we report the speedup results for a Sequent multiprocessor

QTM: computational package using MPI protocol for quantum trajectories method

The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,} so-called quantum jumps are applied at {a} randomly selected point in time. {The} obtained system state is called as a trajectory. After averaging many single trajectories{,} we obtain the approximation of the behavior of {a} quantum system.} {This fact also allows} us to use parallel computation methods. In the article{,} we discuss the QTM package which is supported by the MPI technology. Using MPI allowed {utilizing} the parallel computing for calculating the trajectories and averaging them -- as the effect of these actions{,} the time {taken by} calculations is shorter. In spite of using the C++ programming language, the presented solution is easy to utilize and does not need any advanced programming techniques. At the same time{,} it offers a higher performance than other packages realizing the QTM. It is especially important in the case of harder computational tasks{,} and the use of MPI allows {improving the} performance of particular problems which can be solved in the field of open quantum systems.Comment: 28 pages, 9 figure

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Sparse cross-products of metadata in scientific simulation management

Managing scientific data is by no means a trivial task even in a single site environment with a small number of researchers involved. We discuss some issues concerned with posing well-specified experiments in terms of parameters or instrument settings and the metadata framework that arises from doing so. We are particularly interested in parallel computer simulation experiments, where very large quantities of warehouse-able data are involved. We consider SQL databases and other framework technologies for manipulating experimental data. Our framework manages the the outputs from parallel runs that arise from large cross-products of parameter combinations. Considerable useful experiment planning and analysis can be done with the sparse metadata without fully expanding the parameter cross-products. Extra value can be obtained from simulation output that can subsequently be data-mined. We have particular interests in running large scale Monte-Carlo physics model simulations. Finding ourselves overwhelmed by the problems of managing data and compute ¿resources, we have built a prototype tool using Java and MySQL that addresses these issues. We use this example to discuss type-space management and other fundamental ideas for implementing a laboratory information management system