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In this paper, we investigate the synthesis of ternary reversible circuits in the absence of ancilla bits. We demonstrated that 2-qudit ternary Swap, NOT and 1-controlled-NOT gates are universal for realization of arbitrary ternary n-qudit reversible circuits without ancilla qudits, and all even ternary n-qudit reversible circuits can be constructed by ternary NOT and ternary 1-controlled-NOT gates without ancilla qudits. The realization approach is constructive. This result is significantly different from the binary case.
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Yang et al. (2006) studied this question.
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