Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

@article{Chakhmakhchyan2017QuantuminspiredAF,
  title={Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices},
  author={Levon Chakhmakhchyan and Nicolas J. Cerf and Ra{\'u}l Garc{\'i}a-Patr{\'o}n},
  journal={Physical Review A},
  year={2017},
  volume={96},
  pages={022329}
}
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our… 

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