A Theory for Valiant's Matchcircuits (Extended Abstract)

Details A Theory for Valiant's Matchcircuits (Extended Abstract) A Theory for Valiant's Matchcircuits (Extended Abstract)

2008-02-20

arxiv.org/abs/0802.2860v1

Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (

Computer Science

Computational Complexity

Scientific paper

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).

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