Synthesis of reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs

Dmitry V. Zakablukov

doi:10.1515/dma-2022-0037

Article

Synthesis of reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs

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Published/Copyright: December 6, 2022

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From the journal Discrete Mathematics and Applications Volume 32 Issue 6

Abstract

Reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs are considered. For such circuits implementing maps f : Z2n → Z2n , we study the Shannon complexity function L(n, q) under the condition that the number of additional inputs is q = O(n²). For this range of q, it is shown that L(n, q) ≍ n2ⁿ / log₂ n. The growth order L(n, q) ≍ n2ⁿ / log₂ (n + q) for all q ≲ n2^{n−⌈n/ϕ(n)⌉}, where ϕ(n) → ∞ and n / ϕ(n) − log₂ n → ∞ as n → ∞, is evaluated.

Keywords: reversible circuits; circuit complexity; computations with memory

Funding source: Originally published in Diskretnaya Matematika (2021) 33,№1, 46–53 (in Russian).

Award Identifier / Grant number: 16-01-00196 A

Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00196 A).

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Received: 2021-05-18

Published Online: 2022-12-06

Published in Print: 2022-12-16

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Articles in the same Issue

https://doi.org/10.1515/dma-2022-0037

Keywords for this article

reversible circuits; circuit complexity; computations with memory