License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2018.5
URN: urn:nbn:de:0030-drops-92527
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9252/
Helm, Alexander ;
May, Alexander
Subset Sum Quantumly in 1.17^n
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}
}
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Keywords: |
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Subset sum, Quantum walk, Representation technique |
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Collection: |
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13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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16.07.2018 |
