A Quantum Optics Argument for the #P-hardness of a Class of   Multidimensional Integrals
  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. 
Peter P. Rohde, Dominic W. Berry, Keith R. Motes, Jonathan P. Dowling
quant-ph