The swift expansion of cloud computing has heightened the demand for energy-efficient and high-performance resource allocation solutions across extensive systems. This research presents an innovative hybrid framework that combines a Quantum Tensor-based Deep Neural Network (QT-DNN) with Binary Bird Swarm Optimization (BBSO) to enhance resource allocation while preserving Quality of Service (QoS). In contrast to conventional approaches, the QT-DNN accurately predicts task-resource mappings using tensor-based task representation, significantly minimizing computing overhead. The BBSO allocates resources dynamically, optimizing energy efficiency and task distribution. Experimental results from extensive simulations indicate the efficacy of the suggested strategy; the proposed approach demonstrates the highest level of accuracy, reaching 98.1%. This surpasses the GA-SVM model, which achieves an accuracy of 96.3%, and the ART model, which achieves an accuracy of 95.4%. The proposed method performs better in terms of response time with 1.598 as compared to existing methods Energy-Focused Dynamic Task Scheduling (EFDTS) and Federated Energy-efficient Scheduler for Task Allocation in Large-scale environments (FESTAL) with 2.31 and 2.04, moreover, the proposed method performs better in terms of makespan with 12 as compared to Round Robin (RR) and Recurrent Attention-based Summarization Algorithm (RASA) with 20 and 14. The hybrid method establishes a new standard for sustainable and efficient administration of cloud computing resources by explicitly addressing scalability and real-time performance.