• Corpus ID: 44093237

A faster hafnian formula for complex matrices and its benchmarking on the Titan supercomputer

@article{Bjrklund2018AFH,
  title={A faster hafnian formula for complex matrices and its benchmarking on the Titan supercomputer},
  author={Andreas Bj{\"o}rklund and Brajesh Gupt and Nicol{\'a}s Quesada},
  journal={ArXiv},
  year={2018},
  volume={abs/1805.12498}
}
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 \times n $ complex matrices run in $O(n^3 2^{n/2})$ 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… 

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