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A faster hafnian fo...
A faster hafnian formula for complex matrices and its benchmarking on a supercomputer
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- Björklund, Andreas (författare)
- Lund University,Lunds universitet,Institutionen för datavetenskap,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Computer Science,Departments at LTH,Faculty of Engineering, LTH
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- Gupt, Brajesh (författare)
- Xanadu
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- Quesada, Nicolás (författare)
- Xanadu
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(creator_code:org_t)
- 2019-06-11
- 2019
- Engelska 17 s.
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Ingår i: ACM Journal of Experimental Algorithmics. - : Association for Computing Machinery (ACM). - 1084-6654. ; 24:1
- Relaterad länk:
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http://dx.doi.org/10...
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http://arxiv.org/pdf...
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https://lup.lub.lu.s...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
Nyckelord
- Gaussian boson sampling
- Hafnian
- Perfect matching
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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