Quantum computing offers a promising alternative to conventional computation due to the theoretical capacity to solve many important problems with exponentially less complexity. Since every quantum operation is inherently reversible, the desired function is often realized in reversible logic and then mapped to quantum gates. We consider the realization of reversible circuits using a new class of quantum gates. Our method uses a mapping that grows at a very low linear rate with respect to the number of controls. Results show that, particularly for medium to large circuits, our method yields substantially smaller quantum gate counts than do prior approaches.

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.