Quantum-Logic Synthesis Using Improved Block-Based Approach

Quantum-logic synthesis refers to generating a quantum circuit for a given arbitrary quantum gate according to a specific universal gate library implementable in quantum technologies. Previously, an approach called block-based quantum decomposition (BQD) has been proposed to synthesize quantum circuits by using a combination of two well-known quantum circuit synthesis methods, namely, quantum Shannon decomposition (QSD) and cosine-sine decomposition (CSD). In this paper, an improved block-based quantum decomposition (IBQD) is proposed. IBQD is a parametric approach and explores a larger space than CSD, QSD, and BQD to obtain best results for various synthesis cost metrics. IBQD cost functions for synthesis are calculated in terms of different synthesis cost metrics with respect to the parameters of the proposed approach. Furthermore, in order to find optimum results according to these functions, IBQD synthesis approach is defined as a constrained-optimization model. The results show that IBQD can lead to the minimum total gate cost among all the proposed approaches for the specific case of 4-qubit quantum circuit synthesis. Moreover, for the first time, the depth costs of the CSD, QSD, BQD, and IBQD synthesis approaches are evaluated and it is shown that IBQD makes a trade-off between the total gates and depth costs for the synthesized quantum circuits.