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The quantum machine learning (QML) paradigms and their synergies with network slicing can be envisioned to be a disruptive technology on the cusp of entering to era of sixth-generation (6G), where the mobile communication systems are underpinned in the form of advanced tenancy-based digital use-cases to meet different service requirements. To overcome the challenges of massive slices such as handling the increased dynamism, heterogeneity, amount of data, extended training time, and variety of security levels for slice instances, the power of quantum computing pursuing a distributed computation and learning can be deemed as a promising prerequisite. In this intent, we propose a cloud-native federated learning framework based on quantum deep reinforcement learning (QDRL) where distributed decision agents deployed as micro-services at the edge and cloud through Kubernetes infrastructure then are connected dynamically to the radio access network (RAN). Specifically, the decision agents leverage the remold of classical deep reinforcement learning (DRL) algorithm into variational quantum circuits (VQCs) to obtain the optimal cooperative control on slice resources. The initial numerical results show that the proposed federated QDRL (FQDRL) scheme provides comparable performance than benchmark solutions and reveals the quantum advantage in parameter reduction. To the best of our knowledge, this is the first exploratory study considering an FQDRL approach for 6G communication network.