This paper presents a methodology to transfer self-timed circuit specifications into sequential quantum Boolean circuits (SQBCs) and composable SQBCs (CQBCs). State graphs (SGs) are used to describe the behaviors of self-timed circuits and then are translated into SQBCs based on Toffoli gates. The concept of IP (Intellectual Property) reuse is applied to the constructed SQBCs to produce reusable and composable quantum Boolean circuits (CQBCs). Therefore, these reusable CQBCs as basic modular components can be exploited to construct more complicated quantum Boolean circuits. A set of self-timed components is successfully and automatically synthesized into CQBCs by our methodology. These CQBCs can be used as building blocks to compose control-path components of self-timed systems.