We describe an algorithm to compute the extremal eigenvalues and
corresponding eigenvectors of a symmetric matrix by solving a sequence of
Quadratic Binary Optimization problems. This algorithm is robust across many
different classes of symmetric matrices, can compute the eigenvector/eigenvalue
pair to essentially arbitrary precision, and with minor modifications can also
solve the generalized eigenvalue problem. Performance is analyzed on small
random matrices and selected larger matrices from practical applications.
Description
A QUBO Algorithm to Compute Eigenvectors of Symmetric Matrices
%0 Generic
%1 krakoff2021algorithm
%A Krakoff, Benjamin
%A Mniszewski, Susan M.
%A Negre, Christian F. A.
%D 2021
%K quantumcomputing
%R 10.1371/journal.pone.0267954
%T A QUBO Algorithm to Compute Eigenvectors of Symmetric Matrices
%U http://arxiv.org/abs/2104.11311
%X We describe an algorithm to compute the extremal eigenvalues and
corresponding eigenvectors of a symmetric matrix by solving a sequence of
Quadratic Binary Optimization problems. This algorithm is robust across many
different classes of symmetric matrices, can compute the eigenvector/eigenvalue
pair to essentially arbitrary precision, and with minor modifications can also
solve the generalized eigenvalue problem. Performance is analyzed on small
random matrices and selected larger matrices from practical applications.
@misc{krakoff2021algorithm,
abstract = {We describe an algorithm to compute the extremal eigenvalues and
corresponding eigenvectors of a symmetric matrix by solving a sequence of
Quadratic Binary Optimization problems. This algorithm is robust across many
different classes of symmetric matrices, can compute the eigenvector/eigenvalue
pair to essentially arbitrary precision, and with minor modifications can also
solve the generalized eigenvalue problem. Performance is analyzed on small
random matrices and selected larger matrices from practical applications.},
added-at = {2023-01-26T14:31:50.000+0100},
author = {Krakoff, Benjamin and Mniszewski, Susan M. and Negre, Christian F. A.},
biburl = {https://www.bibsonomy.org/bibtex/2e7b453639d44667d1ec4de3645ee06be/cmcneile},
description = {A QUBO Algorithm to Compute Eigenvectors of Symmetric Matrices},
doi = {10.1371/journal.pone.0267954},
interhash = {37ec7daab6ca0cbd6d2dbb394afa0bb8},
intrahash = {e7b453639d44667d1ec4de3645ee06be},
keywords = {quantumcomputing},
note = {cite arxiv:2104.11311Comment: 14 pages, 9 figures},
timestamp = {2023-01-26T14:31:50.000+0100},
title = {A QUBO Algorithm to Compute Eigenvectors of Symmetric Matrices},
url = {http://arxiv.org/abs/2104.11311},
year = 2021
}