357 research outputs found
The Knowlton-Graham partition problem
A set partition technique that is useful for identifying wires in cables can
be recast in the language of 0--1 matrices, thereby resolving an open problem
stated by R.~L. Graham in Volume 1 of this journal. The proof involves a
construction of 0--1 matrices having row and column sums without gaps
Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition
We present the detailed process of converting the classical Fourier Transform
algorithm into the quantum one by using QR decomposition. This provides an
example of a technique for building quantum algorithms using classical ones.
The Quantum Fourier Transform is one of the most important quantum subroutines
known at present, used in most algorithms that have exponential speed up
compared to the classical ones. We briefly review Fast Fourier Transform and
then make explicit all the steps that led to the quantum formulation of the
algorithm, generalizing Coppersmith's work.Comment: 12 pages, 1 figure (generated within LaTeX). To appear in Journal of
Computational and Applied Mathematic
Simulating spin models on GPU
Over the last couple of years it has been realized that the vast
computational power of graphics processing units (GPUs) could be harvested for
purposes other than the video game industry. This power, which at least
nominally exceeds that of current CPUs by large factors, results from the
relative simplicity of the GPU architectures as compared to CPUs, combined with
a large number of parallel processing units on a single chip. To benefit from
this setup for general computing purposes, the problems at hand need to be
prepared in a way to profit from the inherent parallelism and hierarchical
structure of memory accesses. In this contribution I discuss the performance
potential for simulating spin models, such as the Ising model, on GPU as
compared to conventional simulations on CPU.Comment: 5 pages, 4 figures, elsarticl
Development of highly efficient and accurate real-space integration methods for Hartree-Fock and hybrid density functional calculations
The central focus of molecular electronic structure theory is to find approximate solutions to the electronic Schrödinger equation for molecules, and as such represents an essential part of any theoretical (in silico) study of chemical processes. However, a steep increase of the computational cost with increasing system size often prevents the application of accurate approximations to the molecules of interest.
The main focus of the present work is the efficient evaluation of Fock-exchange contributions, which typically represents the computational bottleneck in Hartree-Fock (HF) and hybrid density functional theory (DFT) calculations. This bottleneck is addressed by means of seminumerical integration, i.e., one electronic coordinate within the 4-center-2-electron integral tensor is represented analytically and one numerically.
In this way, an asymptotically linear scaling method for computing the exchange matrix (denoted as sn-LinK) is developed, enabling fast and accurate ab-initio calculations on large molecules, comprising hundreds or even thousands of atoms, even in combination with large atomic orbital basis sets.
The novel sn-LinK method comprises improvements to the numerical integration grids, a rigorous, batch-wise integral screening scheme, the optimal utilization of modern, highly parallel compute architectures (e.g., graphics processing units; GPUs), and an efficient combination of single- and double-precision arithmetic. In total, these optimizations enable over two orders of magnitude faster evaluation of Fock-exchange contributions.
Consequently, this greatly improved performance allows to perform previously unfeasible computations, which is also demonstrated at the example of an ab initio molecular dynamics simulation (AIMD) study on the hydrogen bond strengths within double-stranded DNA. In addition to Fock-exchange, the other two computational bottlenecks in hybrid-DFT applications – the evaluation of the Coulomb potential and the numerical integration of the semilocal exchange-correlation functional – are also addressed. Finally, more efficient methods to evaluate more accurate post-HF/DFT methods, namely the random-phase approximation (RPA) and the second-order approximate coupled cluster (CC2) method, are also put forward. In this way, the highly efficient methods introduced in this thesis cover some of the most substantial computational bottlenecks in electronic-structure theory – the evaluation of the Coulomb- and the exchange-interactions, the integration of the semilocal exchange-correlation functional, and the computation of post-Hartree-Fock correlation energies.
Consequently, computational chemistry studies on large molecules (>100 atoms) are accelerated by multiple orders of magnitude, allowing for much more accurate and thorough in-silico studies than ever before
Mean field mutation dynamics and the continuous Luria-Delbr\"uck distribution
The Luria-Delbr\"uck mutation model has a long history and has been
mathematically formulated in several different ways. Here we tackle the problem
in the case of a continuous distribution using some mathematical tools from
nonlinear statistical physics. Starting from the classical formulations we
derive the corresponding differential models and show that under a suitable
mean field scaling they correspond to generalized Fokker-Planck equations for
the mutants distribution whose solutions are given by the corresponding
Luria-Delbr\"uck distribution. Numerical results confirming the theoretical
analysis are also presented
Implementing Shor's algorithm on Josephson Charge Qubits
We investigate the physical implementation of Shor's factorization algorithm
on a Josephson charge qubit register. While we pursue a universal method to
factor a composite integer of any size, the scheme is demonstrated for the
number 21. We consider both the physical and algorithmic requirements for an
optimal implementation when only a small number of qubits is available. These
aspects of quantum computation are usually the topics of separate research
communities; we present a unifying discussion of both of these fundamental
features bridging Shor's algorithm to its physical realization using Josephson
junction qubits. In order to meet the stringent requirements set by a short
decoherence time, we accelerate the algorithm by decomposing the quantum
circuit into tailored two- and three-qubit gates and we find their physical
realizations through numerical optimization.Comment: 12 pages, submitted to Phys. Rev.
GUINEA-PIG++ : an upgraded version of the linear collider beam-beam interaction simulation code GUINEA-PIG
http://cern.ch/AccelConf/p07/PAPERS/THPMN010.PDFInternational audienceGUINEA-PIG++ is a newly developed object-oriented version of the Linear Collider beam-beam simulation program GUINEA-PIG. The main goals of this project are to provide an reliable, modular, documented and versatile framework enabling convenient implementation of new features and functionalities
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