Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Electronics Letters

Mixed polarity reversible Peres gates

C. Moraga

Published Jun 27, 2014• 14 citations
Publisher

Abstract

Reversible Peres gates with more than two all over binary‐valued control signals are discussed. Methods are disclosed for the low‐cost realisation of this kind of Peres gates without requiring ancillary lines. It is shown that Peres gates with n control signals may be obtained with a quantum cost of 2 n + 1 − n − 2, using Feynman gates and controlled gates realising the κ th root of NOT, where κ = 2 n −1 . Proper distribution of the controlled gates and their inverses allows driving the reversible Peres gate with control signals of different polarities.

DOI
10.1049/el.2014.0443

Related papers

Mixed polarity reversible Peres gates

Claudio Moraga

Reversible Peres gates with more than two all over binary-valued control signals are discussed. Methods are disclosed for the low cost realization of this kind of Peres gates without requiring ancillary lines. Proper distribution of the controlled gates and their inverses allow driving the reversible Peres gate with control signals of different polarities.

arXiv:1503.07356•Mar 25, 2015•0 citations

Low quantum cost realization of generalized peres and toffoli gates with multiple-control signals

Marek Szyprowski, Paweł Kerntopf

Multiple-control Toffoli gates are basic building blocks for reversible and quantum circuits. 3-bit Peres gate can be considered as a pair of 3-bit and 2-bit Toffoli gates, which can be implemented with fewer elementary quantum gates (what defines a metric called quantum cost) than the total number of elementary quantum gates required by each of Toffoli gates implemented separately. Due to this property, Peres gates are often used for quantum cost reduction of reversible circuits. This paper introduces a generalization of the Peres gate with n > 2 control signals. For such generalized gates corresponding quantum circuits are presented. The realizations have quantum cost of n2and require no ancillary signals. The proposed designs are built from elementary quantum gates, which consist of NOT, controlled NOT, controlled `square-roots-of-NOT' (known as controlled V/V+gates) and controlled `higher roots-of-NOT' (up to 2n-1-roots-of-NOT). The obtained quantum circuits are not entangled. The proposed designs are used to construct Toffoli gates of n control signals with quantum cost of 2n2- 2n + 1 and using no ancillary signals. This is an improvement in comparison with 2n+1- 3 and 48n2+ O(n), which are quantum costs of the known designs of the multiple-control Toffoli gate without ancillary signals.

IEEE International Conference on Nanotechnology (IEEE-NANO)•Aug 1, 2013•24 citations

Dual Toffoli and Peres-reversible gates

Claudio Moraga

The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.

arXiv:2011.01746•Nov 1, 2020•0 citations

Ternary Toffoli-type Reversible Gates: Control Alternatives and Quantum Models

Claudio Moraga

Toffoli-type reversible gates are analyzed. Peres-type ternary gates are introduced for the first time. Conjunctive, disjunctive, majority, XOR types and hybrid control strategies are disclosed. Barenco-type of quantum models for these cases are developed.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2021•2 citations

Lowering the Quantum Gate Cost of Reversible Circuits

D. Michael Miller, Zahra Sasanian

One approach to determining a quantum circuit is to first synthesize a circuit composed of binary reversible gates and to then map that circuit to an equivalent quantum gate realization. This paper considers the mapping phase with the goal of reducing the number of quantum gates required. Our method is based on novel line labeling and gate moving procedures. Results are presented for the quantum library: NOT, controlled-NOT, and the square-root-of-NOT gates (V and V+). The approach is applicable to other quantum gate libraries.

IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)•Aug 1, 2010•29 citations

Lower cost quantum gate realizations of multiple-control Toffoli gates

D. Michael Miller

A systematic method is presented for realizing multiple-control Toffoli gates using elementary quantum gates. Results are presented showing that for the NOT, controlled-NOT and the two square root of NOT gates, the method produces circuits as good and in certain cases better than those known to date. A major feature of the work reported here is that in addition to the previously studied cases of one and the maximum required ancillary lines, the presented method covers all cases in between. The approach is general and can be directly applied to other sets of elementary gates.

IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM)•Aug 1, 2009•15 citations
Reversible Peres gates with more than two all over binary‐valued control signals are discussed. Methods are disclosed for the low‐cost realisation of this kind of Peres gates without requiring ancillary lines. It is shown that Peres gates with n control signals may be obtained with a quantum cost of 2 n + 1 − n − 2, using Feynman gates and controlled gates realising the κ th root of NOT, where κ = 2 n −1 . Proper distribution of the controlled gates and their inverses allows driving the reversible Peres gate with control signals of different polarities.
Multiple-control Toffoli gates are basic building blocks for reversible and quantum circuits. 3-bit Peres gate can be considered as a pair of 3-bit and 2-bit Toffoli gates, which can be implemented with fewer elementary quantum gates (what defines a metric called quantum cost) than the total number of elementary quantum gates required by each of Toffoli gates implemented separately. Due to this property, Peres gates are often used for quantum cost reduction of reversible circuits. This paper introduces a generalization of the Peres gate with n > 2 control signals. For such generalized gates corresponding quantum circuits are presented. The realizations have quantum cost of n2and require no ancillary signals. The proposed designs are built from elementary quantum gates, which consist of NOT, controlled NOT, controlled `square-roots-of-NOT' (known as controlled V/V+gates) and controlled `higher roots-of-NOT' (up to 2n-1-roots-of-NOT). The obtained quantum circuits are not entangled. The proposed designs are used to construct Toffoli gates of n control signals with quantum cost of 2n2- 2n + 1 and using no ancillary signals. This is an improvement in comparison with 2n+1- 3 and 48n2+ O(n), which are quantum costs of the known designs of the multiple-control Toffoli gate without ancillary signals.
The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.
One approach to determining a quantum circuit is to first synthesize a circuit composed of binary reversible gates and to then map that circuit to an equivalent quantum gate realization. This paper considers the mapping phase with the goal of reducing the number of quantum gates required. Our method is based on novel line labeling and gate moving procedures. Results are presented for the quantum library: NOT, controlled-NOT, and the square-root-of-NOT gates (V and V+). The approach is applicable to other quantum gate libraries.
A systematic method is presented for realizing multiple-control Toffoli gates using elementary quantum gates. Results are presented showing that for the NOT, controlled-NOT and the two square root of NOT gates, the method produces circuits as good and in certain cases better than those known to date. A major feature of the work reported here is that in addition to the previously studied cases of one and the maximum required ancillary lines, the presented method covers all cases in between. The approach is general and can be directly applied to other sets of elementary gates.