% Literature references for the ML Toolbox
% bibtex file for sphinxcontrib-bibtex

@misc{hafnian,
 author = {Quesada, N. and Gupt, B.},
    title = {hafnian},
      year = {2018},
        publisher = {GitHub},
	  journal = {GitHub repository},
	    howpublished = {\url{https://github.com/XanaduAI/hafnian}}
	   }

@book{termini2006imagination,
  title={Imagination and Rigor: Essays on Eduardo R. Caianiello's Scientific Heritage
},
  author={Termini, Settimo},
  year={2006},
  publisher={Springer}
}
@article{bjorklund2018faster,
  title={A faster hafnian formula for complex matrices and its benchmarking on the titan supercomputer},
  author={Bj{\"o}rklund, Andreas and Gupt, Brajesh and Quesada, Nicol{\'a}s},
  journal={arXiv preprint arXiv:1805.12498},
  year={2018}
}

@article{caianiello1953quantum,
  title={On quantum field theory—I: explicit solution of Dyson’s equation in electrodynamics without use of feynman graphs},
  author={Caianiello, Eduardo R},
  journal={Il Nuovo Cimento (1943-1954)},
  volume={10},
  number={12},
  pages={1634--1652},
  year={1953},
  publisher={Springer}
}
@article{banchi2019molecular,
  title={Molecular Docking with Gaussian Boson Sampling},
  author={Banchi, Leonardo and Fingerhuth, Mark and Babej, Tomas and Arrazola, Juan Miguel and others},
  journal={arXiv preprint arXiv:1902.00462},
  year={2019}
}


@article{killoran2018strawberry,
  title={Strawberry Fields: A Software Platform for Photonic Quantum Computing},
    author={Killoran, Nathan and Izaac, Josh and Quesada, Nicol{\'a}s and Bergholm, Ville and Amy, Matthew and Weedbrook, Christian},
      journal={arXiv preprint arXiv:1804.03159},
        year={2018}
	}


@book{rempala2007symmetric,
	title={Symmetric functionals on random matrices and random matchings problems},
	author={Rempala, Grzegorz and Wesolowski, Jacek},
	volume={147},
	year={2007},
	publisher={Springer Science \& Business Media}
}

@article{valiant1979complexity,
	title={The complexity of computing the permanent},
	author={Valiant, Leslie G},
	journal={Theoretical computer science},
	volume={8},
	number={2},
	pages={189--201},
	year={1979},
	publisher={Elsevier}
}

@article{bjorklund2008exact,
	title={Exact algorithms for exact satisfiability and number of perfect matchings},
	author={Bj{\"o}rklund, Andreas and Husfeldt, Thore},
	journal={Algorithmica},
	volume={52},
	number={2},
	pages={226--249},
	year={2008},
	publisher={Springer}
}
@inproceedings{lokshtanov2010saving,
	title={Saving space by algebraization},
	author={Lokshtanov, Daniel and Nederlof, Jesper},
	booktitle={Proceedings of the forty-second ACM symposium on Theory of computing},
	pages={321--330},
	year={2010},
	organization={ACM}
}

@inproceedings{koivisto2009partitioning,
	title={Partitioning into sets of bounded cardinality},
	author={Koivisto, Mikko},
	booktitle={International Workshop on Parameterized and Exact Computation},
	pages={258--263},
	year={2009},
	organization={Springer}
}

@article{nederlof2008inclusion,
	title={Inclusion exclusion for hard problems},
	author={Nederlof, Jesper},
	journal={Master's thesis, Utrecht University (August 2008)},
	year={2008}
}
@inproceedings{amini2009counting,
	title={Counting subgraphs via homomorphisms},
	author={Amini, Omid and Fomin, Fedor V and Saurabh, Saket},
	booktitle={International Colloquium on Automata, Languages, and Programming},
	pages={71--82},
	year={2009},
	organization={Springer}
}
@inproceedings{nederlof2009fast,
	title={Fast polynomial-space algorithms using m{\"o}bius inversion: Improving on steiner tree and related problems},
	author={Nederlof, Jesper},
	booktitle={International Colloquium on Automata, Languages, and Programming},
	pages={713--725},
	year={2009},
	organization={Springer}
}
@book{anderson1999lapack,
	title={LAPACK Users' guide},
	author={Anderson, Edward and Bai, Zhaojun and Bischof, Christian and Blackford, L Susan and Demmel, James and Dongarra, Jack and Du Croz, Jeremy and Greenbaum, Anne and Hammarling, Sven and McKenney, Alan and others},
	year={1999},
	publisher={SIAM}
}

@inproceedings{aaronson2011computational,
  title={The computational complexity of linear optics},
  author={Aaronson, Scott and Arkhipov, Alex},
  booktitle={Proceedings of the forty-third annual ACM symposium on Theory of computing},
  pages={333--342},
  year={2011},
  organization={ACM}
}

@inproceedings{clifford2018classical,
  title={The Classical Complexity of Boson Sampling},
  author={Clifford, Peter and Clifford, Rapha{\"e}l},
  booktitle={Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms},
  pages={146--155},
  year={2018},
  organization={SIAM}
}

@misc{DLMF,
	key = "{\relax DLMF}",
	title = "{\it NIST Digital Library of Mathematical Functions}",
	howpublished = "http://dlmf.nist.gov/, Release 1.0.18 of 2018-03-27",
	url = "http://dlmf.nist.gov/",
	note = "F.~W.~J. Olver, A.~B. {Olde Daalhuis}, D.~W. Lozier, B.~I. Schneider,
	R.~F. Boisvert, C.~W. Clark, B.~R. Miller and B.~V. Saunders, eds."}


@article{cygan2015faster,
  title={Faster exponential-time algorithms in graphs of bounded average degree},
    author={Cygan, Marek and Pilipczuk, Marcin},
      journal={Information and Computation},
        volume={243},
	  pages={75--85},
	    year={2015},
	      publisher={Elsevier}
	      }


@inproceedings{bjorklund2012counting,
  title={Counting perfect matchings as fast as Ryser},
    author={Bj{\"o}rklund, Andreas},
      booktitle={Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms},
        pages={914--921},
	  year={2012},
	    organization={SIAM}
	    }


@book{barvinok2016combinatorics,
  title={Combinatorics and complexity of partition functions},
    author={Barvinok, Alexander},
      volume={274},
        year={2016},
	  publisher={Springer}
	  }

@book{ryser1963combinatorial,
  title={Combinatorial mathematics},
    author={Ryser, Herbert John},
      number={14},
        year={1963},
	  publisher={Mathematical Association of America; distributed by Wiley [New York}
	  }
@book{aaronson2013quantum,
  title={Quantum computing since Democritus},
  author={Aaronson, Scott},
  year={2013},
  publisher={Cambridge University Press}
}


@article{lvovsky2014squeezed,
  title={Squeezed light},
  author={Lvovsky, AI},
  journal={arXiv preprint arXiv:1401.4118},
  year={2014}
}

@inproceedings{husfeldt2011invitation,
  title={Invitation to algorithmic uses of inclusion--exclusion},
  author={Husfeldt, Thore},
  booktitle={International Colloquium on Automata, Languages, and Programming},
  pages={42--59},
  year={2011},
  organization={Springer}
}

@article{hosoya1971topological,
  title={Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons},
  author={Hosoya, Haruo},
  journal={Bulletin of the Chemical Society of Japan},
  volume={44},
  number={9},
  pages={2332--2339},
  year={1971},
  publisher={The Chemical Society of Japan}
}
@article{neville2017classical,
  title={Classical boson sampling algorithms with superior performance to near-term experiments},
    author={Neville, Alex and Sparrow, Chris and Clifford, Rapha{\"e}l and Johnston, Eric and Birchall, Patrick M and Montanaro, Ashley and Laing, Anthony},
      journal={Nature Physics},
        volume={13},
	  number={12},
	    pages={1153},
	      year={2017},
	        publisher={Nature Publishing Group}
		}


@article{hamilton2017gaussian,
  title={Gaussian Boson Sampling},
    author={Hamilton, Craig S and Kruse, Regina and Sansoni, Linda and Barkhofen, Sonja and Silberhorn, Christine and Jex, Igor},
      journal={Physical review letters},
        volume={119},
	  number={17},
	    pages={170501},
	      year={2017},
	        publisher={APS}
		}

@article{wu2016computing,
  title={Computing permanents for boson sampling on Tianhe-2 supercomputer},
    author={Wu, Junjie and Liu, Yong and Zhang, Baida and Jin, Xianmin and Wang, Yang and Wang, Huiquan and Yang, Xuejun},
      journal={arXiv preprint arXiv:1606.05836},
        year={2016}
	}


@article{kruse2018detailed,
  title={A detailed study of Gaussian Boson Sampling},
    author={Kruse, Regina and Hamilton, Craig S and Sansoni, Linda and Barkhofen, Sonja and Silberhorn, Christine and Jex, Igor},
      journal={arXiv preprint arXiv:1801.07488},
        year={2018}
	}
@article{2016arXiv160107518B,
	title={Approximating permanents and hafnians},
	author={Barvinok, Alexander},
	journal={arXiv preprint arXiv:1601.07518},
	year={2016}
}
@article{2014arXiv1409.3905R,
	title={Hafnians, perfect matchings and Gaussian matrices},
	author={Rudelson, Mark and Samorodnitsky, Alex and Zeitouni, Ofer and others},
	journal={The Annals of Probability},
	volume={44},
	number={4},
	pages={2858--2888},
	year={2016},
	publisher={Institute of Mathematical Statistics}
}

@inproceedings{Chien:2004:DAC:982792.982903,
 author = {Chien, Steve},
 title = {A Determinant-based Algorithm for Counting Perfect Matchings in a General Graph},
 booktitle = {Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms},
 series = {SODA '04},
 year = {2004},
 isbn = {0-89871-558-X},
 location = {New Orleans, Louisiana},
 pages = {728--735},
 numpages = {8},
 url = {http://dl.acm.org/citation.cfm?id=982792.982903},
 acmid = {982903},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA},
} 

@InProceedings{10.1007/3-540-36494-3_38,
author="Sankowski, Piotr",
editor="Alt, Helmut
and Habib, Michel",
title="Alternative Algorithms for Counting All Matchings in Graphs",
booktitle="STACS 2003",
year="2003",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="427--438",
isbn="978-3-540-36494-8"
}

@book{minc1984permanents,
  title={Permanents},
  author={Minc, H.},
  isbn={9780521302265},
  lccn={85121118},
  series={Encyclopedia of Mathematics an},
  url={https://books.google.ca/books?id=gnT2LCvciqUC},
  year={1984},
  publisher={Cambridge University Press}
}

@article{BarvinokIntro,
author = {Alexander Barvinok},
title = {Polynomial Time Algorithms to Approximate Permanents and Mixed Discriminants Within a Simply Exponential Factor},
journal = {Random Structures \& Algorithms},
volume = {14},
number = {1},
pages = {29-61},
keywords = {permanent, mixed discriminant, randomized algorithms, approximation algorithms}
}

@book{ryser_1963, 
title={Combinatorial Mathematics}, 
DOI={10.5948/UPO9781614440147}, 
publisher={Mathematical Association of America}, 
author={Ryser, Herbert John}, 
year={1963}}

@Article{Glynn2013,
author="Glynn, David G.",
title="Permanent formulae from the Veronesean",
journal="Designs, Codes and Cryptography",
year="2013",
month="Jul",
day="01",
volume="68",
number="1",
pages="39--47",
issn="1573-7586",
doi="10.1007/s10623-012-9618-1",
url="https://doi.org/10.1007/s10623-012-9618-1"
}

@article{BaxFranklin,
author="Bax, E. and Fraklin, J.",
title="A finite-difference sieve to compute the permanent",
journal="Caltech-CS-TR-96-04, California Institute of Technology",
year="1996"
}

@article{Balasubramanian,
author="Balasubramanian, K.",
title="Combinatorics and Diagonals of Matrices",
journal="Ph.D. Thesis, Department of Statistics, Loyola College, Madras, India, T073, Indian Statistical Institute, Calcutta",
year="1980"
}


@article{kan2008moments,
  title={From moments of sum to moments of product},
  author={Kan, Raymond},
  journal={Journal of Multivariate Analysis},
  volume={99},
  number={3},
  pages={542--554},
  year={2008},
  publisher={Academic Press}
}

@book{TAOCP,
title={The Art of Computer Programming, Vol. 2: Seminumerical Algorithms},
author={Donald E. Knuth},
publisher={Addison-Wesley}, 
year={1998},
edition={3}
}

@article{barvinok1999polynomial,
  title={Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor},
  author={Barvinok, Alexander},
  journal={Random Structures \& Algorithms},
  volume={14},
  number={1},
  pages={29--61},
  year={1999},
  publisher={Wiley Online Library}
}


@article{rudelson2016hafnians,
  title={Hafnians, perfect matchings and Gaussian matrices},
  author={Rudelson, Mark and Samorodnitsky, Alex and Zeitouni, Ofer and others},
  journal={The Annals of Probability},
  volume={44},
  number={4},
  pages={2858--2888},
  year={2016},
  publisher={Institute of Mathematical Statistics}
}


@article{simon1994quantum,
  title={Quantum-noise matrix for multimode systems: {$U(n)$} invariance, squeezing, and normal forms},
  author={Simon, R and Mukunda, N and Dutta, Biswadeb},
  journal={Physical Review A},
  volume={49},
  number={3},
  pages={1567},
  year={1994},
  publisher={APS}
}

@article{picinbono1996second,
  title={Second-order complex random vectors and normal distributions},
  author={Picinbono, Bernard},
  journal={IEEE Transactions on Signal Processing},
  volume={44},
  number={10},
  pages={2637--2640},
  year={1996},
  publisher={IEEE}
}

@article{weedbrook2012gaussian,
  title={Gaussian quantum information},
  author={Weedbrook, Christian and Pirandola, Stefano and Garc{\'\i}a-Patr{\'o}n, Ra{\'u}l and Cerf, Nicolas J and Ralph, Timothy C and Shapiro, Jeffrey H and Lloyd, Seth},
  journal={Reviews of Modern Physics},
  volume={84},
  number={2},
  pages={621},
  year={2012},
  publisher={APS}
}

@INPROCEEDINGS{quesada2019classical,
  author = {Nicol\'as Quesada},
  pages = {152},
  booktitle = "Proceedings of the 26th Central European Workshop in Quantum Optics",
  title = "The Classical Complexity of Gaussian Boson Sampling",
  venue = {Paderborn, Germany},
  year = {2019},
  url = {https://cewqo2019.uni-paderborn.de/abstracts/26815_abstract.pdf}
}

@article{quesada2018gaussian,
  title={Gaussian boson sampling using threshold detectors},
    author={Quesada, Nicol{\'a}s and Arrazola, Juan Miguel and Killoran, Nathan},
      journal={Physical Review A},
        volume={98},
	  number={6},
	    pages={062322},
	      year={2018},
	        publisher={APS}
		}

@book{serafini2017quantum,
  title={Quantum Continuous Variables: A Primer of Theoretical Methods},
    author={Serafini, Alessio},
      year={2017},
        publisher={CRC Press}
	}


@article{quesada2019franck,
  title={Franck-Condon factors by counting perfect matchings of graphs with loops},
    author={Quesada, Nicol{\'a}s},
      journal={The Journal of chemical physics},
        volume={150},
	  number={16},
	    pages={164113},
	      year={2019},
	        publisher={AIP Publishing}
		}

@article{quesada2019simulating,
  title={Simulating realistic non-Gaussian state preparation},
    author={Quesada, N and Helt, LG and Izaac, J and Arrazola, JM and Shahrokhshahi, R and Myers, CR and Sabapathy, KK},
      journal={arXiv preprint arXiv:1905.07011},
        year={2019}
	}
