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arXiv · 1607.04960

A Quantum Optics Argument for the #P-hardness of a Class of Multidimensional Integrals

Peter P. Rohde·Dominic W. Berry·Keith R. Motes·Jonathan P. Dowling
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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.

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Peter P. Rohde, Dominic W. Berry, Keith R. Motes, Jonathan P. Dowling. 2016-07-18. A Quantum Optics Argument for the #P-hardness of a Class of Multidimensional Integrals. https://arxiv.org/abs/1607.04960

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