Quantum random walk is the quantum counterpart of a classical random walk. The classical random walk concept has long been used as a computational framework for designing classical algorithms for complex problems. Quantum analogues of random walk provide speed-up in computational power for various algorithms such as element distinctness, spatial search, graph connectivity, etc. Quantum walks have emerged to be a universal computational model over the last decade. Quantum walk formulations applied in graph theory have shown quadratic and polynomial time in graph traversal as opposed to the exponential time taken by classical algorithms. Quantum walk models have also found use in designing quantum computers. Inspired by these facts, this article presents a substantial systematic literature review and analysis of various quantum walk formulations and their strengths and limitations w.r.t. application domains used in literature up-to-date by researchers in various fields. The analysis provided in this article may help upcoming researchers to gain new insights towards the application of quantum walk formulation in varied domains. Various performance metrics, physical implementation set-ups, coin operators, and simulators used to analyze classical and quantum walk dynamics on graphs have been described. Finally, the article discusses existing open problems and notable future directions related to quantum walk application for potential researchers.

量子随机游走是经典随机游走的量子对应物。长期以来，经典随机游走概念一直被用作设计复杂问题经典算法的计算框架。随机游走的量子类似物为各种算法（例如元素差异性、空间搜索、图连通性等）提供计算能力的加速. 在过去的十年中，量子行走已经成为一种通用的计算模型。图论中应用的量子行走公式在图遍历中显示出二次和多项式时间，而不是经典算法所用的指数时间。量子行走模型也可用于设计量子计算机。受这些事实的启发，本文对各种量子行走公式及其优势和局限性进行了大量系统的文献回顾和分析，这些应用领域是各个领域研究人员最新使用的文献。本文提供的分析可能有助于即将到来的研究人员获得有关量子行走公式在不同领域应用的新见解。各种性能指标、物理实现设置、硬币运营商、已经描述了用于分析图上经典和量子行走动力学的模拟器。最后，本文为潜在研究人员讨论了与量子行走应用相关的现有开放问题和值得注意的未来方向。