Reversible logic has applications in various research areas, including signal processing, cryptography and quantum computation. In this article, direct NCT-based synthesis of a given k -cycle in a cycle-based synthesis scenario is examined. To this end, a set of seven building blocks is proposed that reveals the potential of direct synthesis of a given permutation to reduce both quantum cost and average runtime. To synthesize a given large cycle, we propose a decomposition algorithm to extract the suggested building blocks from the input specification. Then, a synthesis method is introduced that uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested that uses the proposed cycle-based synthesis method in conjunction with one of the recent NCT-based synthesis approaches which is based on Reed-Muller (RM) spectra. The time complexity and the effectiveness of the proposed synthesis approach are analyzed in detail. Our analyses show that the proposed hybrid framework leads to a better quantum cost in the worst-case scenario compared to the previously presented methods. The proposed framework always converges and typically synthesizes a given specification very fast compared to the available synthesis algorithms. Besides, the quantum costs of benchmark functions are improved about 20% on average (55% in the best case).
Reversible logic has applications in various research areas, including signal processing, cryptography and quantum computation. In this article, direct NCT-based synthesis of a given k -cycle in a cycle-based synthesis scenario is examined. To this end, a set of seven building blocks is proposed that reveals the potential of direct synthesis of a given permutation to reduce both quantum cost and average runtime. To synthesize a given large cycle, we propose a decomposition algorithm to extract the suggested building blocks from the input specification. Then, a synthesis method is introduced that uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested that uses the proposed cycle-based synthesis method in conjunction with one of the recent NCT-based synthesis approaches which is based on Reed-Muller (RM) spectra. The time complexity and the effectiveness of the proposed synthesis approach are analyzed in detail. Our analyses show that the proposed hybrid framework leads to a better quantum cost in the worst-case scenario compared to the previously presented methods. The proposed framework always converges and typically synthesizes a given specification very fast compared to the available synthesis algorithms. Besides, the quantum costs of benchmark functions are improved about 20% on average (55% in the best case).
Several algorithms have been proposed for the synthesis of reversible circuits. In this paper, a cycle-based synthesis algorithm for reversible logic, based on the NCT library, has been proposed. In other words, direct implementation of a single 3-cycle, a pair of 3-cycles and a pair of 2-cycles have been explored and used to propose an efficient Toffoli-based synthesis algorithm for reversible circuits. The synthesis algorithm decomposes a given large cycle into a set of single 3-cycles, pairs of 3-cycles and pair of 2-cycles and synthesizes the resulted cycles directly. Our experimental results show that the proposed synthesis algorithm can outperform the available 2-cycle-based approach about 34% on average. In addition, several discussions for the generalization of the proposed method to the 2m-cycles are given.
Several algorithms have been proposed for the synthesis of reversible circuits. In this paper, a cycle-based synthesis algorithm for reversible logic, based on the NCT library, has been proposed. In other words, direct implementation of a single 3-cycle, a pair of 3-cycles and a pair of 2-cycles have been explored and used to propose an efficient Toffoli-based synthesis algorithm for reversible circuits. The synthesis algorithm decomposes a given large cycle into a set of single 3-cycles, pairs of 3-cycles and pair of 2-cycles and synthesizes the resulted cycles directly. Our experimental results show that the proposed synthesis algorithm can outperform the available 2-cycle-based approach about 34% on average. In addition, several discussions for the generalization of the proposed method to the 2m-cycles are given.
Reversible computing and quantum computing have gained increasing attention due to their potential to overcome some of the fundamental limitations of classical computing, particularly regarding energy efficiency and computational power. In this paper, we compare the synthesis process using the well-known Qiskit framework developed by IBM and an approach based on Reed-Muller spectra. We show that some approaches are efficient for small values and others are better for the general use case. The synthesis results are presented using four strategies: unitary matrices, linear function synthesis, permutation synthesis, and Reed-Muller spectra. Our analysis shows that, on average, our proposal surpasses the Qiskit synthesis algorithms when considering the gate count metric. Additionally, a post-synthesis evaluation is performed using our proposed method, which employs a Reed-Muller–based representation to assess its effectiveness.
The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which is a subset of the symmetric group, where the NCT library is considered as the generators of the permutation group.
Reversible logic circuits have been historically motivated by theoretical research in low-power, and recently attracted interest as components of the quantum algorithm, optical computing and nanotechnology. However due to the intrinsic property of reversible logic, traditional irreversible logic design and synthesis methods cannot be carried out. Thus a new set of algorithms are developed correctly to synthesize reversible logic circuit. This paper presents a comprehensive literature review with comparative study on heuristic based reversible logic synthesis. It reviews a range of heuristic based reversible logic synthesis techniques reported by researchers (BDD-based, cycle-based, search-based, non-search-based, rule-based, transformation-based, and ESOP-based). All techniques are described in detail and summarized in a table based on their features, limitation, library used and their consideration metric. Benchmark comparison of gate count and quantum cost are analysed for each synthesis technique. Comparing the synthesis algorithm outputs over the years, it can be observed that different approach has been used for the synthesis of reversible circuit. However, the improvements are not significant. Quantum cost and gate count has improved over the years, but arguments and debates are still on certain issues such as the issue of garbage outputs that remain the same. This paper provides the information of all heuristic based synthesis of reversible logic method proposed over the years. All techniques are explained in detail and thus informative for new reversible logic researchers and bridging the knowledge gap in this area.
Reversible logic circuits have been historically motivated by theoretical research in low-power, and recently attracted interest as components of the quantum algorithm, optical computing and nanotechnology. However due to the intrinsic property of reversible logic, traditional irreversible logic design and synthesis methods cannot be carried out. Thus a new set of algorithms are developed correctly to synthesize reversible logic circuit. This paper presents a comprehensive literature review with comparative study on heuristic based reversible logic synthesis. It reviews a range of heuristic based reversible logic synthesis techniques reported by researchers (BDD-based, cycle-based, search-based, non-search-based, rule-based, transformation-based, and ESOP-based). All techniques are described in detail and summarized in a table based on their features, limitation, library used and their consideration metric. Benchmark comparison of gate count and quantum cost are analysed for each synthesis technique. Comparing the synthesis algorithm outputs over the years, it can be observed that different approach has been used for the synthesis of reversible circuit. However, the improvements are not significant. Quantum cost and gate count has improved over the years, but arguments and debates are still on certain issues such as the issue of garbage outputs that remain the same. This paper provides the information of all heuristic based synthesis of reversible logic method proposed over the years. All techniques are explained in detail and thus informative for new reversible logic researchers and bridging the knowledge gap in this area.