References¶
- 1
Andreas Björklund and Thore Husfeldt. Exact algorithms for exact satisfiability and number of perfect matchings. Algorithmica, 52(2):226–249, 2008.
- 2
Raymond Kan. From moments of sum to moments of product. Journal of Multivariate Analysis, 99(3):542–554, 2008.
- 3
Mikko Koivisto. Partitioning into sets of bounded cardinality. In International Workshop on Parameterized and Exact Computation, 258–263. Springer, 2009.
- 4
Jesper Nederlof. Fast polynomial-space algorithms using möbius inversion: improving on steiner tree and related problems. In International Colloquium on Automata, Languages, and Programming, 713–725. Springer, 2009.
- 5
Andreas Björklund. Counting perfect matchings as fast as ryser. In Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms, 914–921. SIAM, 2012.
- 6
Andreas Björklund, Brajesh Gupt, and Nicolás Quesada. A faster hafnian formula for complex matrices and its benchmarking on a supercomputer. Journal of Experimental Algorithmics (JEA), 24(1):11, 2019.
- 7
Marek Cygan and Marcin Pilipczuk. Faster exponential-time algorithms in graphs of bounded average degree. Information and Computation, 243:75–85, 2015.
- 8
Herbert John Ryser. Combinatorial mathematics. Number 14. Mathematical Association of America; distributed by Wiley [New York], 1963.
- 9
Grzegorz Rempala and Jacek Wesolowski. Symmetric functionals on random matrices and random matchings problems. Volume 147. Springer Science & Business Media, 2007.
- 10
Donald E. Knuth. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Addison-Wesley, 3 edition, 1998.
- 11
Leslie G Valiant. The complexity of computing the permanent. Theoretical computer science, 8(2):189–201, 1979.
- 12
Alexander Barvinok. Approximating permanents and hafnians. arXiv preprint arXiv:1601.07518, 2016.
- 13
Piotr Sankowski. Alternative algorithms for counting all matchings in graphs. In Helmut Alt and Michel Habib, editors, STACS 2003, 427–438. Berlin, Heidelberg, 2003. Springer Berlin Heidelberg.
- 14
Alexander Barvinok. Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor. Random Structures & Algorithms, 14(1):29–61, 1999.
- 15
Mark Rudelson, Alex Samorodnitsky, Ofer Zeitouni, and others. Hafnians, perfect matchings and gaussian matrices. The Annals of Probability, 44(4):2858–2888, 2016.
- 16
Nicolás Quesada, Juan Miguel Arrazola, and Nathan Killoran. Gaussian boson sampling using threshold detectors. Physical Review A, 98(6):062322, 2018.
- 17
Alexander I Barvinok. Two algorithmic results for the traveling salesman problem. Mathematics of Operations Research, 21(1):65–84, 1996.
- 18
S Berkowitz and FJ Garner. The calculation of multidimensional Hermite polynomials and Gram-Charlier coefficients. Math. Comput., 24(111):537–545, 1970.
- 19
Alessio Serafini. Quantum Continuous Variables: A Primer of Theoretical Methods. CRC Press, 2017.
- 20
Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J Cerf, Timothy C Ralph, Jeffrey H Shapiro, and Seth Lloyd. Gaussian quantum information. Reviews of Modern Physics, 84(2):621, 2012.
- 21
Bernard Picinbono. Second-order complex random vectors and normal distributions. IEEE Transactions on Signal Processing, 44(10):2637–2640, 1996.
- 22
R Simon, N Mukunda, and Biswadeb Dutta. Quantum-noise matrix for multimode systems: $U(n)$ invariance, squeezing, and normal forms. Physical Review A, 49(3):1567, 1994.
- 23
Nicolás Quesada. Franck-condon factors by counting perfect matchings of graphs with loops. The Journal of chemical physics, 150(16):164113, 2019.
- 24
N. Quesada, L. G. Helt, J. Izaac, J. M. Arrazola, R. Shahrokhshahi, C. R. Myers, and K. K. Sabapathy. Simulating realistic non-gaussian state preparation. Phys. Rev. A, 100:022341, 2019.
- 25
Craig S Hamilton, Regina Kruse, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Gaussian boson sampling. Physical review letters, 119(17):170501, 2017.
- 26
VV Dodonov, OV Man’ko, and VI Man’ko. Multidimensional hermite polynomials and photon distribution for polymode mixed light. Physical Review A, 50(1):813, 1994.
- 27
Nicolás Quesada and Juan Miguel Arrazola. Exact simulation of gaussian boson sampling in polynomial space and exponential time. Physical Review Research, 2(2):023005, 2020.
- 28
Saleh Rahimi-Keshari, Austin P Lund, and Timothy C Ralph. What can quantum optics say about computational complexity theory? Physical review letters, 114(6):060501, 2015.
- 29
Soran Jahangiri, Juan Miguel Arrazola, Nicolás Quesada, and Nathan Killoran. Point processes with gaussian boson sampling. Physical Review E, 101(2):022134, 2020.
- 30
Alexander Barvinok. Combinatorics and complexity of partition functions. Volume 274. Springer, 2016.
- 31
Eduardo R Caianiello. On quantum field theory—i: explicit solution of dyson’s equation in electrodynamics without use of feynman graphs. Il Nuovo Cimento (1943-1954), 10(12):1634–1652, 1953.
- 32
Settimo Termini. Imagination and Rigor: Essays on Eduardo R. Caianiello’s Scientific Heritage. Springer, 2006.
- 33
Maurice M Mizrahi. Generalized hermite polynomials. Journal of Computational and Applied Mathematics, 1(3):137–140, 1975.
- 34
Pieter Kok and Samuel L Braunstein. Multi-dimensional hermite polynomials in quantum optics. Journal of Physics A: Mathematical and General, 34(31):6185, 2001.
- 35
Kurt Bernardo Wolf. Canonical transforms. i. complex linear transforms. Journal of Mathematical Physics, 15(8):1295–1301, 1974.
- 36
Kramer P, M Moshinsky, and T.H Seligman. Complex extensions of canonical transformations and quantum mechanics. In E.M. Loebl, editor, Group Theory and Its Applications, pages 250–300. Academic, New York, 1975.
- 37
EV Doktorov, IA Malkin, and VI Man’ko. Dynamical symmetry of vibronic transitions in polyatomic molecules and the franck-condon principle. Journal of Molecular Spectroscopy, 64(2):302–326, 1977.
Downloads