On Synthesis of Reversible Circuits with Small Number of Additional Inputs Consisting of NOT, CNOT and 2-CNOT Gates

Dmitry V. Zakablukov

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arXiv · 1802.02346

On Synthesis of Reversible Circuits with Small Number of Additional Inputs Consisting of NOT, CNOT and 2-CNOT Gates

Dmitry V. Zakablukov

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Abstract

The paper discusses the gate complexity of reversible circuits with the small number of additional inputs consisting of NOT, CNOT and 2-CNOT gates. We study Shannon's gate complexity function $L(n, q)$ for a reversible circuit implementing a Boolean transformation $f\colon \mathbb Z_2^n \to \mathbb Z_2^n$ with $q \leqslant O(n^2)$ additional inputs. The general bound $L(n,q) \asymp n2^n \mathop / \log_2 n$ is proved for this case.

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BibTeX RIS

Dmitry V. Zakablukov. 2018-02-07. On Synthesis of Reversible Circuits with Small Number of Additional Inputs Consisting of NOT, CNOT and 2-CNOT Gates. https://arxiv.org/abs/1802.02346

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