Fractal coding techniques are time-consuming and complex. The proposed Grover’s quantum search algorithm (QSA) reduces the computational complexity in searching mechanism and achieves square root speedup over classical algorithms in an unsorted database. The quantum fidelity can be calculated to reduce minimum matching error between a given range block and its corresponding domain block. The proposed system is implemented for texture, satellite, and grayscale images for different sizes of range and domain blocks. The results are compared and displayed to reduce the complexity in the searching mechanism. The comparative analysis of existing methods and proposed algorithm has been carried out using performance parameters as compression ratio (CR), computational complexity and PSNR.