Evolving Quantum Circuits: ISOMA-Driven Synthesis of Toffoli Gates

This paper presents the application of the improved Self-Organizing Migrating Algorithm (iSOMA) to the synthesis and optimization of quantum circuits. We develop a comprehensive method to evolve candidate quantum circuits with minimal cost by integrating iSOMA with circuit evaluators in Qiskit. Experimental evaluation across 100 independent runs demonstrates a 90% success rate in synthesizing Toffoli gates, with an 80% circuit uniqueness rate indicating diverse solution exploration. The algorithm achieves a median cost of 0.000 and determinism = 8/8 for successful runs, confirming its effectiveness for quantum circuit synthesis. This research is important for future 6G networks and beyond, as quantum computing has the potential to be more efficient, especially in the physical layer of the Radio Access Network (RAN), where quantum-supported optimization mechanisms are able to process a large number of tasks faster. The proposed synthesis of Toffoli gates controlled by iSOMA technology contributes to quantum computing by supporting the efficient design of quantum circuits, which is a prerequisite for the deployment of quantum-native functions, such as the Quantum Fourier Transform, in future communications and wireless infrastructures.