It is envisioned that 6G, unlike its predecessor 5G, will depart from connected machines and connected people to connected intelligence. The main goal of 6G networks is to support massive connectivity for time-sensitive and computation-sensitive services in mission-critical applications. The creation of real-time optimization (RTO) enabled by the fast growing data analytic and machine learning will seize the opportunities for 6G wireless networks to support such immersive services such as virtual reality (VR), augmented reality (AR), mixed reality (MR), and tactile Internet. Recently, with the rapid development of quantum computers, quantum-inspired optimization and machine learning algorithms have been exploited as efficient solutions for future wireless networks. In this article, we provide a comprehensive view on the new concept of quantum-inspired RTO and its application to the optimal resource allocation for 6G wireless networks. Our main contributions are to introduce some of the initial research results and introduce the potentiality of quantum-inspired RTO on some 6G emerging technologies. Not only do we review the fundamental principles; we also explore the challenges and opportunities of this exciting research direction.