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DOI: 10.4230/LIPIcs.STACS.2008.1368
URN: urn:nbn:de:0030-drops-13686
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1368/
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Li, Angsheng ; Xia, Mingji

A Theory for Valiant's Matchcircuits (Extended Abstract)

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Abstract

The computational function of a matchgate is represented by its character matrix. In this article, we show that all nonsingular character matrices are closed under matrix inverse operation, so that for every $k$, the nonsingular character matrices of $k$-bit matchgates form a group, extending the recent work of Cai and Choudhary (2006) of the same result for the case of $k=2$, and that the single and the two-bit matchgates are universal for matchcircuits, answering a question of Valiant (2002).

BibTeX - Entry

@InProceedings{li_et_al:LIPIcs:2008:1368,
  author =	{Angsheng Li and Mingji Xia},
  title =	{{A Theory for Valiant's Matchcircuits (Extended Abstract)}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{491--205},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1368},
  URN =		{urn:nbn:de:0030-drops-13686},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2008.1368},
  annote =	{Keywords: Pfaffian, Matchgate, Matchcircuit}
}

Keywords: Pfaffian, Matchgate, Matchcircuit
Seminar: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008


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