A dynamic programming approach to multi-objective logic synthesis of quantum circuits

Quantum computing is an emerging technology that harnesses the laws of quantum mechanics to solve some problems much faster than classical computers. Quantum-logic synthesis refers to converting a given quantum gate into a set of gates that can be implemented in quantum technologies and primarily focuses on decreasing the number of CNOT gates. Of the most well-known quantum-logic synthesis methods are cosine-sine decomposition (CSD) and quantum Shannon decomposition (QSD), each with their distinct advantages. This study aims to present a multi-objective quantum-logic synthesis to optimize three evaluation criteria of the synthesized circuit, namely, the number of CNOT gates, the total number of gates, and the depth simultaneously. The proposed method involves constructing a solution space by exploring various combinations of CSD and QSD. Then, utilizing a bottom-up approach of multi-objective dynamic programming (MODP), a method is presented to search only a specific part of the entire solution space to find circuits with Pareto-optimal costs, i.e., the Pareto-optimal front. The results obtained from this method demonstrate a balance between the evaluation criteria. Furthermore, many Pareto-optimal solutions are generated that can be considered based on the applications' or the quantum technology requirements.