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

被引：21

作者：

Björklund A. ^{[1
]}

Gupt B. ^{[2
]}

Quesada N. ^{[2
]}

机构：

[1] Department of Computer Science, Lund University

[2] Xanadu, Toronto

来源：

ACM Journal of Experimental Algorithmics | 2019年 / 24卷 / 01期

关键词：

Gaussian boson sampling; Hafnian; Perfect matching;

D O I：

10.1145/3325111

中图分类号：

学科分类号：

摘要：

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. © 2019 Association for Computing Machinery.

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