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

Understand

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.