Fuzzy Reward-based Reinforcement Learning for Clifford Circuit Synthesis

Quantum operator synthesis is a key task in quantum transpilers, enabling the translation of high-level algorithms into hardware-executable gate sequences by decomposing arbitrary operators into native gates while optimizing for efficiency and constraints. Recently, reinforcement learning (RL) has emerged as a promising approach for quantum circuit synthesis, particularly for Clifford operators. However, the crisp-reward functions used in current RL frameworks may fail to capture the subtleties of complex quantum circuit synthesis tasks, leading to suboptimal designs. In this paper, this gap is addressed by integrating a fuzzy reward into an RL algorithm to synthesize Clifford operators. The fuzzy reward is computed by a fuzzy rule-based system, designed from the analysis of the error rate in current IBM quantum devices. The experiments show that our fuzzy reward accelerates convergence, achieving the same performance in terms of depth and controlled-X (CX) depth as the crisp-reward algorithm, but with fewer training steps. This highlights the efficiency of fuzzy rewards and their potential to improve the synthesis capabilities of RL systems.