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DOI: 10.4230/LIPIcs.TQC.2018.5

Subset Sum Quantumly in 1.17^n

Authors: Alexander Helm and Alexander May

Published in: LIPIcs, Volume 111, 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)

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.

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Alexander Helm and Alexander May. Subset Sum Quantumly in 1.17^n. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 111, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{helm_et_al:LIPIcs.TQC.2018.5,
  author =	{Helm, Alexander and May, Alexander},
  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 =	{Jeffery, Stacey},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2018.5},
  URN =		{urn:nbn:de:0030-drops-92527},
  doi =		{10.4230/LIPIcs.TQC.2018.5},
  annote =	{Keywords: Subset sum, Quantum walk, Representation technique}
}

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Subset Sum Quantumly in 1.17^n

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