IEICE TRANSACTIONS on Fundamentals
Function Design for Minimum Multiple-Control Toffoli Circuits of Reversible Adder/Subtractor Blocks and Arithmetic Logic Units
Summary :
In this paper, we propose a design of reversible adder/subtractor blocks and arithmetic logic units (ALUs). The main concept of our approach is different from that of the existing related studies; we emphasize the function design. Our approach of investigating the reversible functions includes (a) the embedding of irreversible functions into incompletely-specified reversible functions, (b) the operation assignment, and (c) the permutation of function outputs. We give some extensions of these techniques for further improvements in the design of reversible functions. The resulting reversible circuits are smaller than that of the existing design in terms of the number of multiple-control Toffoli gates. To evaluate the quantum cost of the obtained circuits, we convert the circuits to reduced quantum circuits for experiments. The results also show the superiority of our realization of adder/subtractor blocks and ALUs in quantum cost.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2231-2243
- Publication Date
- 2018/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.2231
- Type of Manuscript
- Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
- Category
Authors
Md Belayet ALI
Iwate University
Takashi HIRAYAMA
Iwate University
Katsuhisa YAMANAKA
Iwate University
Yasuaki NISHITANI
Iwate University
Keyword
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Md Belayet ALI, Takashi HIRAYAMA, Katsuhisa YAMANAKA, Yasuaki NISHITANI, "Function Design for Minimum Multiple-Control Toffoli Circuits of Reversible Adder/Subtractor Blocks and Arithmetic Logic Units" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2231-2243, December 2018, doi: 10.1587/transfun.E101.A.2231.
Abstract: In this paper, we propose a design of reversible adder/subtractor blocks and arithmetic logic units (ALUs). The main concept of our approach is different from that of the existing related studies; we emphasize the function design. Our approach of investigating the reversible functions includes (a) the embedding of irreversible functions into incompletely-specified reversible functions, (b) the operation assignment, and (c) the permutation of function outputs. We give some extensions of these techniques for further improvements in the design of reversible functions. The resulting reversible circuits are smaller than that of the existing design in terms of the number of multiple-control Toffoli gates. To evaluate the quantum cost of the obtained circuits, we convert the circuits to reduced quantum circuits for experiments. The results also show the superiority of our realization of adder/subtractor blocks and ALUs in quantum cost.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2231/_p
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@ARTICLE{e101-a_12_2231,
author={Md Belayet ALI, Takashi HIRAYAMA, Katsuhisa YAMANAKA, Yasuaki NISHITANI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Function Design for Minimum Multiple-Control Toffoli Circuits of Reversible Adder/Subtractor Blocks and Arithmetic Logic Units},
year={2018},
volume={E101-A},
number={12},
pages={2231-2243},
abstract={In this paper, we propose a design of reversible adder/subtractor blocks and arithmetic logic units (ALUs). The main concept of our approach is different from that of the existing related studies; we emphasize the function design. Our approach of investigating the reversible functions includes (a) the embedding of irreversible functions into incompletely-specified reversible functions, (b) the operation assignment, and (c) the permutation of function outputs. We give some extensions of these techniques for further improvements in the design of reversible functions. The resulting reversible circuits are smaller than that of the existing design in terms of the number of multiple-control Toffoli gates. To evaluate the quantum cost of the obtained circuits, we convert the circuits to reduced quantum circuits for experiments. The results also show the superiority of our realization of adder/subtractor blocks and ALUs in quantum cost.},
keywords={},
doi={10.1587/transfun.E101.A.2231},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Function Design for Minimum Multiple-Control Toffoli Circuits of Reversible Adder/Subtractor Blocks and Arithmetic Logic Units
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2231
EP - 2243
AU - Md Belayet ALI
AU - Takashi HIRAYAMA
AU - Katsuhisa YAMANAKA
AU - Yasuaki NISHITANI
PY - 2018
DO - 10.1587/transfun.E101.A.2231
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - In this paper, we propose a design of reversible adder/subtractor blocks and arithmetic logic units (ALUs). The main concept of our approach is different from that of the existing related studies; we emphasize the function design. Our approach of investigating the reversible functions includes (a) the embedding of irreversible functions into incompletely-specified reversible functions, (b) the operation assignment, and (c) the permutation of function outputs. We give some extensions of these techniques for further improvements in the design of reversible functions. The resulting reversible circuits are smaller than that of the existing design in terms of the number of multiple-control Toffoli gates. To evaluate the quantum cost of the obtained circuits, we convert the circuits to reduced quantum circuits for experiments. The results also show the superiority of our realization of adder/subtractor blocks and ALUs in quantum cost.
ER -
English
