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On the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates

  • Dmitry V. Zakablukov EMAIL logo
Published/Copyright: March 22, 2017

Abstract

The paper is concerned with the problem of complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates. For a reversible circuit implementing a map f:Z2nZ2n we define the Shannon complexity function L(n, q) as a function of n and the number q of additional inputs in the circuit. We prove the lower estimate L(n,q)2n(n2)3log2(n+q)n3 for the complexity of a reversible circuit and derive the upper estimate L(n, 0) ⩽ 48n2n(1 + o(1)) / log2n if there are no additional inputs. The asymptotic upper estimate for the complexity is shown to be L(n, q0) ≲ 2n with q0n2no(n) additional inputs.


Originally published in Diskretnaya Matematika (2016) 28, №2, 12–26 (in Russian).


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Received: 2014-4-24
Published Online: 2017-3-22
Published in Print: 2017-2-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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