A faster hafnian formula for complex matrices and its benchmarking on a supercomputer
(2019) In ACM Journal of Experimental Algorithmics 24(1).- Abstract
We introduce new and simple algorithms for the calculation of the number of perfect matchings of complex weighted, undirected graphs with and without loops. Our compact formulas for the hafnian and loop hafnian of n × n complex matrices run in O(n32n/2) time, are embarrassingly parallelizable and, to the best of our knowledge, are the fastest exact algorithms to compute these quantities. Despite our highly optimized algorithm, numerical benchmarks on the Titan supercomputer with matrices up to size 56 × 56 indicate that one would require the 288,000 CPUs of this machine for about 6 weeks to compute the hafnian of a 100 × 100 matrix.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/48be8e16-9833-4b7a-89a4-2be02de7014b
- author
- Björklund, Andreas LU ; Gupt, Brajesh and Quesada, Nicolás
- organization
- publishing date
- 2019-06
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Gaussian boson sampling, Hafnian, Perfect matching
- in
- ACM Journal of Experimental Algorithmics
- volume
- 24
- issue
- 1
- article number
- 1.11
- pages
- 17 pages
- publisher
- Association for Computing Machinery (ACM)
- external identifiers
-
- scopus:85067788588
- ISSN
- 1084-6654
- DOI
- 10.1145/3325111
- language
- English
- LU publication?
- yes
- id
- 48be8e16-9833-4b7a-89a4-2be02de7014b
- date added to LUP
- 2019-07-05 13:44:40
- date last changed
- 2022-04-26 02:54:27
@article{48be8e16-9833-4b7a-89a4-2be02de7014b, abstract = {{<p>We introduce new and simple algorithms for the calculation of the number of perfect matchings of complex weighted, undirected graphs with and without loops. Our compact formulas for the hafnian and loop hafnian of n × n complex matrices run in O(n<sup>3</sup>2<sup>n/2</sup>) time, are embarrassingly parallelizable and, to the best of our knowledge, are the fastest exact algorithms to compute these quantities. Despite our highly optimized algorithm, numerical benchmarks on the Titan supercomputer with matrices up to size 56 × 56 indicate that one would require the 288,000 CPUs of this machine for about 6 weeks to compute the hafnian of a 100 × 100 matrix.</p>}}, author = {{Björklund, Andreas and Gupt, Brajesh and Quesada, Nicolás}}, issn = {{1084-6654}}, keywords = {{Gaussian boson sampling; Hafnian; Perfect matching}}, language = {{eng}}, number = {{1}}, publisher = {{Association for Computing Machinery (ACM)}}, series = {{ACM Journal of Experimental Algorithmics}}, title = {{A faster hafnian formula for complex matrices and its benchmarking on a supercomputer}}, url = {{http://dx.doi.org/10.1145/3325111}}, doi = {{10.1145/3325111}}, volume = {{24}}, year = {{2019}}, }