Evaluation and Improvement of Quantum Synthesis Algorithms based on a Thorough Set of Metrics

Existing synthesis-related cost functions are explored and five fundamental properties of an efficient quantum circuit implementation are introduced. In addition, a thorough set of metrics for quantum circuit synthesis are proposed and applied on some well-known synthesis algorithms. Our analysis reveals the requirement of proposing new synthesis algorithms to produce realizable circuits. A new heuristic is also introduced which improves the results of a commonly used synthesis algorithm in terms of the proposed synthesis-related metrics.