Quantum computing has transformed computational paradigms through its unique principles and algorithms. This paper provides a systematic overview of quantum algorithms, their application-based classification, and their industrial relevance. It surveys the broader areas of the field from a chronological perspective and highlights significant advances. The study also identifies emerging trends and key research directions in quantum algorithm development.

Using the ab-initio calculations based on density functional theory, we have investigated the structural, electronic and magnetic properties of Ti-substituted Zn3P2 compound. One and two Ti atom replacements in the unit cell of Zn3P2, which contain eight molecules per formula unit (40 atoms), are considered in the study. Our results show that the ferromagnetic phase is favored for the single Ti atom substitution, as the total energy corresponding to the ferromagnetic phase is lower than that of the nonmagnetic phase. A considerable value of the magnetic moment at the Ti site is obtained from our calculations.

A potential energy surface (PES) scan is central to numerous problems in quantum chemistry, including identifying reaction mechanisms, reaction kinetics, transition states, activation barrier, etc. This work details the potential energy surface scan of the dihedral angle of the molecule n-butane using various open-source/freeware computational quantum chemistry software, including CP2K, GAMESS, NWChem, ORCA, Psi4, and PySCF. The input preparation, adopted methodology, execution flow, and results are discussed in detail, equipping readers with the necessary hands-on knowledge of computational tools to perform electronic structure calculations through a dihedral scan.