One of the main motivations for reversible computing is that quantum computing has as one of its foundations the reversibility of all gates, that is, quantum computing circuit models are reversible. An important problem in reversible computing that has been intensively studied for the last decades is the synthesis of reversible circuits. The extended abstract considers optimization rules aiming to a new algorithm for post-synthesis optimization of reversible circuits composed of generalized Toffoli gates.
One of the main motivations for reversible computing is that quantum computing has as one of its foundations the reversibility of all gates, that is, quantum computing circuit models are reversible. An important problem in reversible computing that has been intensively studied for the last decades is the synthesis of reversible circuits. The extended abstract considers optimization rules aiming to a new algorithm for post-synthesis optimization of reversible circuits composed of generalized Toffoli gates.
Reversible circuit synthesis is an important field in quantum computing, low-power design, and reversible circuit. The problem of reversible circuit synthesis is complicated and hard to solve because the input of the reversible circuit will experience a huge increase when extended to multi-bit. In this paper, a novel algorithm of reversible circuit synthesis is proposed. With the satisfied priority of positions, we can efficiently select the position which should be satisfied, and each selected gate is generated to benefit the overall situation. Therefore, the proposed algorithm is able to optimize the reversible circuit with fewer gates and can be implemented in regard to multibit reversible circuit synthesis. In addition, the gate set we used contains only Toffoli, spanning all wires. This Toffoli gate is liable to be transformed into another gate set and is helpful for algorithm design. The experiment shows that the proposed algorithm, with efficient and optimal results, is superior to others.
Optimal synthesis of reversible functions is a nontrivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results in a huge search space (16! ≈ 244functions). The output of such a search alone, counting only the space required to list Toffoli gates for every function, would require over 100 terabytes of storage. In this paper, we present two algorithms: one, that synthesizes an optimal circuit for any 4-bit reversible specification, and another that synthesizes all optimal implementations. We employ several techniques to make the problem tractable. We report results from several experiments, including synthesis of all optimal 4-bit permutations, synthesis of random 4-bit permutations, optimal synthesis of all 4-bit linear reversible circuits, and synthesis of existing benchmark functions; we compose a list of the hardest permutations to synthesize, and show distribution of optimal circuits. We further illustrate that our proposed approach may be extended to accommodate physical constraints via reporting LNN-optimal reversible circuits. Our results have important implications in the design and optimization of reversible and quantum circuits, testing circuit synthesis heuristics, and performing experiments in the area of quantum information processing.
Optimal synthesis of reversible circuits is a very hard task. In 2010, a method and a tool of practical usage for finding optimal circuits built from multi-control Toffoli gates for any 4-bit reversible specification were finally developed. In 2011 we published an extension to the algorithm, which allows to reduce the quantum cost of the resulting circuits. In this paper we present another extension to this approach. Namely, we have extended the reversible gate library to mixed-polarity multi-control Toffoli gates (i.e. with both positive and negative controls). Our experimental results for the known reversible benchmarks show that using mixed-polarity Toffoli gates gives significant savings in gate count. The paper presents standard computational experiments for circuit synthesis. These results have implications in testing synthesis algorithms for reversible mixed-polarity circuits and quantum circuits.
Optimal synthesis of reversible circuits is a very hard task. In 2010, a method and a tool of practical usage for finding optimal circuits built from multi-control Toffoli gates for any 4-bit reversible specification were finally developed. In 2011 we published an extension to the algorithm, which allows to reduce the quantum cost of the resulting circuits. In this paper we present another extension to this approach. Namely, we have extended the reversible gate library to mixed-polarity multi-control Toffoli gates (Le. with both positive and negative controls). Our experimental results for the known reversible benchmarks show that using mixed-polarity Toffoli gates gives significant savings in gate count. The paper presents standard computational experiments for circuit synthesis. These results have implications in testing synthesis algorithms for reversible mixed-polarity circuits and quantum circuits.
In quantum computing, the synthesis of reversible circuits is an important topic. Reversible circuit synthesis is particularly challenging because the complexity grows as the number of bits increases. To date, many reversible circuit synthesis algorithms have been proposed, but most are unable to find the optima within an acceptable time. Because traditional methods only consider partial interests, the resulting cost would be more gates. This paper proposes a novel method, called Bound Oriented Algorithm, which has the ability to find the optimal solution with a high hit rate, one greater than 75% on average. Moreover, with the prediction of the optima by bound, it can reduce excess calculation to further improve efficiency. In addition, a special library containing only Toffoli gates is used, which simplifies algorithm design and is more easily converted to a common library. The experiment result shows that the proposed method performs better than other methods in terms of solution quality and time cost.
Quantum information processing is of interest as it offers the potential for a new generation of very powerful computers supporting novel computational paradigms. Over the last couple of decades, different aspects of quantum computers ranging from quantum algorithms to quantum physical design have received growing attention. One of the most important research areas is the synthesis and post-synthesis optimization of reversible and quantum circuits. Many synthesis and optimization approaches can be found in the literature, yet, due to the complexity of the problem, finding approaches leading to optimal, or near optimal, results is still an open problem. The synthesized circuits are usually evaluated based on quantum cost models. Therefore, they are often technology mapped to circuits of more primitive gates. To this end, various technology mapping approaches have also been proposed in the past few years. Related work shows an existing gap in optimized technology mapping for reversible and quantum circuits. In this dissertation, an optimized technology mapping design flow is introduced for mapping reversible circuits to quantum circuits. The contributions of this dissertation are classified as follows: - New reversible circuit optimization methods. - Optimized reversible to quantum mapping approaches. - New quantum gate libraries and new cost models for reversible gates based on the new libraries. - Quantum circuit optimization approaches. The steps above, form an optimized flow for mapping reversible circuits to quantum circuits. At each step of the design flow optimized and consistent approaches are suggested with the goal of reducing the quantum cost of the synthesized reversible circuits. The evaluations show that the proposed mapping methodology leads to significant improvement in the quantum cost of the existing benchmark circuits.