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.2019.6
URN: urn:nbn:de:0030-drops-103984
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10398/
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DeLorenzo, Kai ; Kimmel, Shelby ; Witter, R. Teal

Applications of the Quantum Algorithm for st-Connectivity

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LIPIcs-TQC-2019-6.pdf (0.5 MB)

Abstract

We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show that our algorithm for cycle detection has improved performance under the promise of large circuit rank or a small number of edges. We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.

BibTeX - Entry

@InProceedings{delorenzo_et_al:LIPIcs:2019:10398,
  author =	{Kai DeLorenzo and Shelby Kimmel and R. Teal Witter},
  title =	{{Applications of the Quantum Algorithm for st-Connectivity}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{Wim van Dam and Laura Mancinska},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10398},
  URN =		{urn:nbn:de:0030-drops-103984},
  doi =		{10.4230/LIPIcs.TQC.2019.6},
  annote =	{Keywords: graphs, algorithms, query complexity, quantum algorithms, span programs}
}

Keywords: graphs, algorithms, query complexity, quantum algorithms, span programs
Collection: 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)
Issue Date: 2019
Date of publication: 31.05.2019

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