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A Theory for Valiant's Matchcircuits (Extended 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 , the nonsingular
character matrices of -bit matchgates form a group, extending the recent
work of Cai and Choudhary (2006) of the same result for the case of , and
that the single and the two-bit matchgates are universal for matchcircuits,
answering a question of Valiant (2002)