Quantum-enhanced Boolean Algebra (QBA) represents a novel approach to logical statement verification, utilizing quantum simulation to dramatically accelerate the process compared to classical methods. This paper explores the design of a QBA, detailing the underlying quantum algorithms and their potential to offer a significant speedup in verification. We present a comprehensive overview of the core mechanism, highlighting the advantages of quantum computation over traditional approaches. The research focuses on establishing a robust and scalable framework for QBA verification, demonstrating its potential to revolutionize the field of logical verification. The paper concludes with a discussion of future research directions and potential applications.