The word quantum has recently become an interesting topic for experts worldwide. With its innovative solutions to improve network management, security, and computational efficiency, quantum computing has the potential to revolutionize smart city architectural design. Although it's still in its early stages, the incorporation of quantum computing into smart city infrastructures holds great potential for improvements in several areas, such as energy systems, transportation, and healthcare. The purpose of this study is to outline the state-of-the-art and future directions for quantum computing technology in smart city applications. With an emphasis on their usefulness and advantages in urban settings, we provide an extensive overview of the current quantum computing frameworks, along with a thorough analysis of quantum algorithms, network architectures, and communication protocols designed for smart cities are some of the study's major contributions. We also examine realistic deployment scenarios that tackle both the future directions of research and the current technological hurdles. Furthermore, our study also addresses the adoption and deployment of quantum computing solutions in smart cities by offering urban planners and technologists strategic insights and foundational knowledge through an in-depth analysis. In addition, our study provides reference guidance on integrating the solutions proposed in recent papers into a unified architectural framework for quantum computing technologies. © This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.