Task scheduling in cloud computing is a major challenge due to its NP-hard problem, and classical heuristics are not efficient in convergence and getting stuck in local optima [11]. Objective of this paper proposes a novel integration of principles of Quantum Computing into cloud resource management, and a novel Quantum Inspired Evolutionary Algorithm (QIEA)[2] is proposed to solve the task scheduling problem in cloud environments. To establish this we propose the methodology, unlike classical Genetic Algorithm (GA), Ant Colony Optimization (ACO), and QIEA uses a Q-bit to maintain a high level of population diversity. A novel Quantum Rotation Gate is proposed as a main search operator to update the probability amplitudes of scheduling solutions to converge to a global optimum. As a results in this paper, it highlighted the simulation results show that QIEA reduces Makespan and Energy Consumption significantly compared to classical heuristics in previous works, and QIEA converges in a significantly reduced number of iterations. So basically, this paper conclude Quantum Computing and cloud resource management is a novel and promising integration of principles that would lead to a superior architecture of future decentralized and high-performance computing environments.