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={L. Chakhmakhchyan and N. Cerf and R. 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… Expand

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References

SHOWING 1-10 OF 27 REFERENCES
Mathematical Foundations of Computer Science
  • A. Blikle
  • Computer Science
  • Lecture Notes in Computer Science
  • 1974
Ann
Phys
  • Rev. Lett. 114, 060501
  • 2015
Quantum Inf
  • Comput. 14, 541
  • 2014
Phys
  • Rev. Lett. 116, 020401
  • 2016
Phys
  • Rev. Lett. 116, 123601
  • 2016
S
  • Höfling, C.-Yang Lu, J.-W. Pan, Phys. Rev. Lett. 116, 020401
  • 2016
C
  • Sparrow et al., Science 349, 711
  • 2015
Quantum Information and Computation 14
  • 541
  • 2014
P
  • C. Humphreys et al., Science 339, 798 (2013); M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari et al., ibid. 339, 794 (2013); M. Tilmann, B. Dakić, R. Heilmann et al., Nat. Photon. 7, 540 (2013); A. Crespi, R. Osellame, R. Ramponi et al., ibid. 7, 545
  • 2013
...
1
2
3
...