Information technology is vital in handling critical infrastructures, such as power grids, water supplies, healthcare, transportation networks, and infrastructures in space. Quantum computing has potential to revolutionise critical infrastructures by enabling faster optimisation, simulation, and data analysis for complex systems. The adoption of quantum technologies demands the reconsideration of cybersecurity protocols to mitigate quantum-era threats. Along with the technological progress in quantum computing, there is a risk of cyberattacks leading to research questions, asking: what new quantum computing algorithms are being designed to secure critical infrastructures; how they compare to conventional methods; how quantum computing algorithms are being designed to enhance the reliability of critical infrastructures; and what quantum computing methods are emerging for ensuring the stability and accuracy of computations critical to infrastructure management? This work focuses on answering these research questions by presenting a scoping review conducted by considering 420 research articles. The scoping review shows the possibilities that can be achieved by implementing various algorithms and methods for cybersecurity. The study encircles many categories, such as optimisation, security, networking, algorithms, protocols, communication, power systems, and space science, and shows that quantum computing can enhance their protection. This study discusses techniques for the cybersecurity of critical infrastructures in quantum computing and presents results on infrastructure analysis. We targeted various research phrases regarding the research questions mentioned about algorithms and methods for cybersecurity of critical infrastructure in quantum computing. This work calls for the reader to consider the various ways to protect critical infrastructures from different threats, including cyberattacks.