A Theory for Valiant's Matchcircuits (Extended Abstract)

Angsheng Li; Mingji Xia

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arXiv · 0802.2860

A Theory for Valiant's Matchcircuits (Extended Abstract)

Angsheng Li·Mingji Xia

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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).

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Angsheng Li, Mingji Xia. 2008-02-20. A Theory for Valiant's Matchcircuits (Extended Abstract). https://arxiv.org/abs/0802.2860

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