Quantum calculi and formalisms are useful tools for ensuring security and computational capabilities in blockchain and cryptography. They aid in designing and analysing new cryptographic protocols for blockchain, determining the behaviour of quantum operations in blockchain‐based smart contracts, assessing the feasibility and security of quantum algorithms in blockchain applications, and building a quantum‐safe blockchain system. A comprehensive review of the applications of quantum calculi and formalisms in computer security and network security, along with a bibliographic analysis is presented. It is unique in that it combines bibliometric analyses with a technical review of the domain of quantum calculi and formalism. Bibliometric and biographic analysis in the field helps identify research trends, assess the influence of research, determine collaboration patterns, evaluate journals, and examine publication behaviours, among other things. It performs bibliographic and bibliometric analysis using a dataset collected from Scopus and Web of Science through different queries. The obtained results help identify important institutions, authors, organisations, collaboration networks, keywords, and more. The provided open challenges and future vision pave the way for further research in the direction of quantum calculi and formalism applications in computer security and network security.