QEC (quantum error correcting) code is a fundamental in realizing the challenge in realizing the potential of quantum calculations. In recent years, cyclic, skew-constacyclic, constacyclic codes over non-chain rings have emerged as useful tools for construction of new quantum codes. This paper summarizes recent advancements in constructing and analyzing these codes for quantum error correction (QEC). We explore the theoretical foundations, practical applications and limitations of these codes in QEC. We generalized some results on those codes and constructed some new results which might have future scopes of research in this exciting area.