Quantum computing is set to transform the field of materials science, offering computational methods that could far surpass conventional approaches for tackling intricate material design challenges. This review introduces the foundational principles of rapidly growing quantum computing and its application trends in the design and analysis of nanomaterials. We explain how quantum speedup, achieved through quantum algorithms utilizing qubit superposition and entanglement, is applied to material design. Additionally, the principles and research trends of quantum variational methods, including the Variational Quantum Eigensolver (VQE), which has recently gained attention as a quantum algorithm simulation technique, will be discussed. By combining new techniques based on quantum algorithms with the quantum speed-up, the quantum computing is expected to offer new insights into data-intensive materials research and provide innovative methodologies for the development of new functional materials. With the advancement of quantum algorithms, the field of materials science could enter a new era, enabling more precise and efficient approaches in materials design and functional analysis.