License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2023.7
URN: urn:nbn:de:0030-drops-183177
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18317/
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Ambainis, Andris ; Kokainis, Martins ; Vihrovs, Jevgēnijs

Improved Algorithm and Lower Bound for Variable Time Quantum Search

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LIPIcs-TQC-2023-7.pdf (0.8 MB)

Abstract

We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity O(√Tlog n) where T = ∑_{i = 1}ⁿ t_i² with t_i denoting the time to check the i^th item. Our second result is a quantum lower bound of Ω(√{Tlog T}). Both the algorithm and the lower bound improve over previously known results by a factor of √{log T} but the algorithm is also substantially simpler than the previously known quantum algorithms.

BibTeX - Entry

@InProceedings{ambainis_et_al:LIPIcs.TQC.2023.7,
  author =	{Ambainis, Andris and Kokainis, Martins and Vihrovs, Jevg\={e}nijs},
  title =	{{Improved Algorithm and Lower Bound for Variable Time Quantum Search}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18317},
  URN =		{urn:nbn:de:0030-drops-183177},
  doi =		{10.4230/LIPIcs.TQC.2023.7},
  annote =	{Keywords: quantum search, amplitude amplification}
}

Keywords: quantum search, amplitude amplification
Collection: 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)
Issue Date: 2023
Date of publication: 18.07.2023

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