A Quantum Optics Argument for the #P-hardness of a Class of Multidimensional Integrals
Quantum Physics
2016-07-19 v1
Abstract
Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large matrices using a simple quantum optics argument. In this way we prove that evaluating integrals in this class is \textbf{\#P}-hard. Our work provides a new approach for using methods from quantum physics to prove statements in computer science.
Keywords
Cite
@article{arxiv.1607.04960,
title = {A Quantum Optics Argument for the #P-hardness of a Class of Multidimensional Integrals},
author = {Peter P. Rohde and Dominic W. Berry and Keith R. Motes and Jonathan P. Dowling},
journal= {arXiv preprint arXiv:1607.04960},
year = {2016}
}
Comments
6 pages