Improving Qiskit strategies for circuit synthesis using the Reed-Muller spectrum

Reversible computing and quantum computing have gained increasing attention due to their potential to overcome some of the fundamental limitations of classical computing, particularly regarding energy efficiency and computational power. In this paper, we compare the synthesis process using the well-known Qiskit framework developed by IBM and an approach based on Reed-Muller spectra. We show that some approaches are efficient for small values and others are better for the general use case. The synthesis results are presented using four strategies: unitary matrices, linear function synthesis, permutation synthesis, and Reed-Muller spectra. Our analysis shows that, on average, our proposal surpasses the Qiskit synthesis algorithms when considering the gate count metric. Additionally, a post-synthesis evaluation is performed using our proposed method, which employs a Reed-Muller–based representation to assess its effectiveness.