A Theory for Valiant's Matchcircuits (Extended Abstract)

Angsheng Li (1) , Mingji Xia (1)

1 LCS - State Key Laboratory of Computer Science [Beijing]

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).

Mots clés: Pfaffian; Matchgate; Matchcircuit

Domaines: Complexité [cs.CC]

Angsheng Li, Mingji Xia. A Theory for Valiant's Matchcircuits (Extended Abstract). STACS 2008, Feb 2008, Bordeaux, France. pp.491-502. ⟨hal-00232969⟩