Version 1
: Received: 16 May 2017 / Approved: 17 May 2017 / Online: 17 May 2017 (06:22:36 CEST)
How to cite:
Erol, V.; Side, M. Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios. Preprints2017, 2017050128. https://doi.org/10.20944/preprints201705.0128.v1
Erol, V.; Side, M. Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios. Preprints 2017, 2017050128. https://doi.org/10.20944/preprints201705.0128.v1
Erol, V.; Side, M. Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios. Preprints2017, 2017050128. https://doi.org/10.20944/preprints201705.0128.v1
APA Style
Erol, V., & Side, M. (2017). Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios. Preprints. https://doi.org/10.20944/preprints201705.0128.v1
Chicago/Turabian Style
Erol, V. and Mert Side. 2017 "Detecting Quantum Speedup of HHL Algorithm for Linear Programming Scenarios" Preprints. https://doi.org/10.20944/preprints201705.0128.v1
Abstract
Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems, we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we look at quantum speedup ratios of HHL Algorithm for different scenarios of linear programming. In a first scenario we look quantum speedup ratio (S(N)) as a function of phase transition and the ratio (κ) between the greatest and smallest eigenvalues of the matrix in linear equation system. As a second scenario, we investigate the changes in S(N) as a function of κ and s, which is the coefficient for defining the matrix as s-sparse.
Keywords
linear programming; optimization; quantum algorithms; complexity
Subject
Computer Science and Mathematics, Computer Science
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
