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DOI: 10.4230/LIPIcs.TQC.2018.5
URN: urn:nbn:de:0030-drops-92527
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9252/
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Helm, Alexander ; May, Alexander

Subset Sum Quantumly in 1.17^n

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LIPIcs-TQC-2018-5.pdf (0.6 MB)


Abstract

We study the quantum complexity of solving the subset sum problem, where the elements a_1, ..., a_n are randomly chosen from Z_{2^{l(n)}} and t = sum_i a_i in Z_{2^{l(n)}} is a sum of n/2 elements. In 2013, Bernstein, Jeffery, Lange and Meurer constructed a quantum subset sum algorithm with heuristic time complexity 2^{0.241n}, by enhancing the classical subset sum algorithm of Howgrave-Graham and Joux with a quantum random walk technique. We improve on this by defining a quantum random walk for the classical subset sum algorithm of Becker, Coron and Joux. The new algorithm only needs heuristic running time and memory 2^{0.226n}, for almost all random subset sum instances.

BibTeX - Entry

@InProceedings{helm_et_al:LIPIcs:2018:9252,
  author =	{Alexander Helm and Alexander May},
  title =	{{Subset Sum Quantumly in 1.17^n}},
  booktitle =	{13th Conference on the Theory of Quantum Computation,  Communication and Cryptography (TQC 2018)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-080-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{111},
  editor =	{Stacey Jeffery},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9252},
  URN =		{urn:nbn:de:0030-drops-92527},
  doi =		{10.4230/LIPIcs.TQC.2018.5},
  annote =	{Keywords: Subset sum, Quantum walk, Representation technique}
}

Keywords: Subset sum, Quantum walk, Representation technique
Seminar: 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)
Issue Date: 2018
Date of publication: 11.07.2018


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