Quantum computing is envisaged as an evolving paradigm for solving computationally complex optimization problems with a large-number factorization and exhaustive search. Recently, there has been a proliferation growth of the size of multi-dimensional datasets, the input-output space dimensionality, and data structures. Hence, the conventional machine learning approaches in data training and processing face a huge limited computing capabilities to support the sixthgeneration (6G) networks with highly dynamic applications and services. Under this regard, the fast developing quantum computing with machine learning (QML) for 6G networks is investigated. QML algorithms can significantly enhanced the processing efficiency and exponentially computational speed-up for effective quantum data representation and superposition framework, highly capable of guaranteeing high data storage and secured communications. We present the state-of-the-art in quantum computing and provide comprehensive overviews through machine learning approaches for their applications in the 6G networks. Furthermore, we introduce quantum-inspired machine learning applications for 6G networks, considering their enabling technologies and potential challenges. Finally, some dominating research issues and future research directions for the quantum-inspired machine learning in 6G networks are elaborated.