Ant colony optimization is one of the potential solutions to tackle intractable NP-Hard discrete combinatorial optimization problems. The metaphor of ant colony can be thought of as the evolution of the best path from a given graph as a globally optimal solution, which is unaffected by earlier local convergence to achieve improved optimization efficiency. Earlier Quantum Ant Colony Optimization research work was primarily based on Quantum-inspired Evolutionary Algorithms, which deals with customizing and improving the quantum rotation gate through upgraded formation of the lookup table of rotation angle. Instead of relying on evolutionary algorithms, we have proposed a discrete-time quantum algorithm based on adaptive quantum circuit for pheromone updation. The algorithm encodes all possible paths in the exhaustive search space as input to the ORACLE. Iterative model of exploration and exploitation of all possible paths by quantum ants results in global optimal path convergence through probabilistic measurement of selected path. Our novel approach attempts to accelerate the search space exploitation in a significant manner to obtain the best optimal path as a solution through quantum arallelization achieving polynomial time speed-up over its classical counter part.

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一种用于蚁群优化的新型量子算法

蚁群优化是解决棘手的 NP-Hard 离散组合优化问题的潜在解决方案之一。蚁群的比喻可以被认为是从给定的图作为全局最优解的最佳路径的进化，它不受早期局部收敛的影响，以提高优化效率。早期的量子蚁群优化研究工作主要基于Quantum-inspired Evolutionary Algorithms，通过旋转角度查找表的升级形成来定制和改进量子旋转门。我们不依赖于进化算法，而是提出了一种基于自适应量子电路的离散时间量子算法，用于信息素更新。该算法将穷举搜索空间中的所有可能路径编码为 ORACLE 的输入。量子蚂蚁探索和利用所有可能路径的迭代模型通过对选定路径的概率测量导致全局最优路径收敛。我们的新方法试图以显着的方式加速搜索空间开发，以获得最佳最优路径作为解决方案，通过量子并行化实现多项式时间加速超过其经典对应部分。