Related papers: An algorithm for the optimization of finite elemen…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…
Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…
Numerous code optimization techniques, including loop nest optimizations, have been developed over the last four decades. Loop optimization techniques transform loop nests to improve the performance of the code on a target architecture,…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…
Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain…
This work presents an optimization method for the synthesis of finite state machines. The focus is on the reduction in the on-chip area and the cost of the circuit. A list of finite state machines from MCNC91 benchmark circuits have been…
We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance. We investigate if…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
We study a class of entangling gates for trapped atomic ions and demonstrate the use of numeric optimization techniques to create a wide range of fast, error-robust gate constructions. Our approach introduces a framework for numeric…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. It has been suggested that finding an MIS is equivalent to computing a maximum matching of the network, where…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
A linear time algorithm to find a set of nearest elements in a mesh.
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection…
Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline.…