A Theory for Valiant's Matchcircuits (Extended Abstract)

Authors Angsheng Li, Mingji Xia

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Angsheng Li
Mingji Xia

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Angsheng Li and Mingji Xia. A Theory for Valiant's Matchcircuits (Extended Abstract). In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 491-502, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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).
  • Pfaffian
  • Matchgate
  • Matchcircuit


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