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The upcoming fifth generation (5G) of wireless networks is expected to lay a foundation of intelligent networks with the provision of some isolated artificial intelligence (AI) operations. However, fully intelligent network orchestration and management for providing innovative services will only be realized in Beyond 5G (B5G) networks. To this end, we envisage that the sixth generation (6G) of wireless networks will be driven by on-demand self-reconfiguration to ensure a many-fold increase in the network performance and service types. The increasingly stringent performance requirements of emerging networks may finally trigger the deployment of some interesting new technologies, such as large intelligent surfaces, electromagnetic-orbital angular momentum, visible light communications, and cell-free communications, to name a few. Our vision for 6G is a massively connected complex network capable of rapidly responding to the users' service calls through real-time learning of the network state as described by the network edge (e.g., base-station locations and cache contents), air interface (e.g., radio spectrum and propagation channel), and the user-side (e.g., battery-life and locations). The multi-state, multi-dimensional nature of the network state, requiring the real-time knowledge, can be viewed as a quantum uncertainty problem. In this regard, the emerging paradigms of machine learning (ML), quantum computing (QC), and quantum ML (QML) and their synergies with communication networks can be considered as core 6G enablers. Considering these potentials, starting with the 5G target services and enabling technologies, we provide a comprehensive review of the related state of the art in the domains of ML (including deep learning), QC, and QML and identify their potential benefits, issues, and use cases for their applications in the B5G networks. Subsequently, we propose a novel QC-assisted and QML-based framework for 6G communication networks while articulating its challenges and potential enabling technologies at the network infrastructure, network edge, air interface, and user end. Finally, some promising future research directions for the quantum- and QML-assisted B5G networks are identified and discussed.