Reversible Circuit Synthesis Using a Cycle-Based Approach

Reversible logic has applications in various research areas including signal processing, cryptography and quantum computation. In this paper, 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 which uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested which 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).