## 1 Introduction
### Research Status  
According to literature studies, scheduling algorithms are mainly proposed based on heterogeneous computing systems. It has received widespread attention from the academic community for its ability to perform large-scale scientific computing, information processing, and data services at low cost and high efficiency. Scheduling algorithms can be categorized in a variety of ways, such as task scheduling procedures, types of goals, or mathematical models and research methodologies. Examples include random and non-random scheduling, static and dynamic scheduling, and scheduling with no deadline constraints and with deadline constraints [2]. Traditional scheduling algorithms are mainly list-based scheduling algorithms, clustering-based scheduling algorithms, and task replication-based scheduling algorithms. Heterogeneous earliest finish time (HEFT) [3] and dynamic level scheduling (DLS) [4; 5] are the most representative. While traditional scheduling works well for smaller tasks and data handling, the rapid development of 5G and artificial intelligence makes traditional scheduling no longer applicable. Scheduling algorithms based on artificial intelligence are constantly being proposed. For example, to generate a predictive scheduling scheme for the early detection of faulty machines, [PERSON] et al. [6] proposed an algorithm based on ant colony optimization. To improve task allocation schemes, [PERSON] et al. [7] used deep reinforcement learning. [PERSON] [8] introduced machine learning to heterogeneous computing systems, aiming to accelerate platform execution through neural networks and multilayer perceptron. Although AI-based scheduling algorithms have been extensively researched and applied in various scenarios, their drawbacks include not accurately reflecting the internal connections in the task graph and longer model training time. Due to the limitations of traditional scheduling algorithms and AI-based scheduling algorithms, combinatorial optimization algorithms have gained a lot of attention. This is because the strengths of several algorithms are used to complement one another. Among them, due to genetic algorithms' mature technology and ease of operation, they are widely used in multi-objective optimization, detection accuracy improvement, job shop scheduling, and cloud computing task scheduling [9; 10; 11; 12]. In recent years, the problem that genetic algorithms tend to stick to locally optimal solutions and converge slowly has been investigated using quantum computing. Quantum genetic algorithm (QGA) is an improvement of traditional genetic algorithms that uses qubits, quantum coherence, quantum rotation gate, and more. For example, [PERSON] et al. [13] used chaotic sequences to update the quantum rotation gate. [PERSON] et al. [14] improved genetic algorithms based on revolving door refinement to improve scheduling efficiency in distributed systems. [PERSON] et al. [15] improved the efficiency of bi-objective load balancing scheduling based on the quantum genetic algorithm. [PERSON] et al. [16] improved quantum genetic algorithms using random key distribution to improve scheduling efficiency in a multi-processor environment. To speed up the convergence of the algorithm, [PERSON] et al. [17] improved the population structure of the QGA based on small-world theory to improve the algorithm's performance. [PERSON] et al. [18] improved the QGA by using mutative scale chaos optimization, which accelerated the algorithm's convergence speed and improved solution accuracy. [PERSON] et al. [19] used cellular automaton to update the population in the quantum genetic algorithm. This improved the convergence and accuracy of the algorithm for multi-objective functions. [PERSON] et al. [20] introduced multi-subpopulations to improve the encoding stage of the QGA, which improved the algorithm's performance in optimizing benchmark functions. [PERSON] et al.