Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and defect prediction, involve complex optimization, search, or classification, making them candidates for quantum enhancement. In this paper, we introduce Quantum-Based Software Engineering (QBSE) as a new research direction for applying quantum computing to classical software engineering problems. We outline its scope, clarify its distinction from quantum software engineering (QSE), and identify key problem types that may benefit from quantum optimization, search, and learning techniques. We also summarize existing research efforts that remain fragmented. Finally, we outline a preliminary research agenda that may help guide the future development of QBSE, providing a structured and meaningful direction within software engineering.