An n-bit Toffoli gate quantum circuit based on the realisation proposed by Barenco et al., where some of the Toffoli gates in their construction are replaced with Peres gates, is presented. This results in a significant cost reduction. The main contribution of this presentation is a quantum circuit which simulates the (m+1)-bit Toffoli gate with 32m−120 elementary quantum gates and one garbage bit which is passed unchanged.
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Maslov et al. (2003) studied this question.
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