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Estimation of the depth of reversible circuits consisting of NOT, CNOT and 2-CNOT gates

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Abstract

The paper discusses the asymptotic depth of a reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The reversible circuit depth function D(n, q) is introduced for a circuit implementing a mapping f: Z n2 → Z n2 as a function of n and the number q of additional inputs. It is proved that for the case of implementation of a permutation from A(Z n2 ) with a reversible circuit having no additional inputs the depth is bounded as D(n, 0) ≳ 2n/(3log2 n). It is also proved that for the case of transformation f: Z n2 → Z n2 with a reversible circuit having q 0 ~ 2n additional inputs the depth is bounded as D(n,q 0) ≲ 3n.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Faculty of Informatics and control Systems, ul. Baumanskaya 2-ya, 5/1, Moscow, 105005, Russia

    D. V. Zakablukov

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  1. D. V. Zakablukov
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Correspondence to D. V. Zakablukov.

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Original Russian Text © D.V. Zakablukov. 2016. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2016. Vol. 71, No. 3, pp. 3-12.

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Zakablukov, D.V. Estimation of the depth of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. Moscow Univ. Math. Bull. 71, 89–97 (2016). https://doi.org/10.3103/S0027132216030013

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