An overview of Shor's Algorithm and Distributed Algorithms in Quantum Computing

Abstract

In this paper, we consider two of the most important paradigms in quantum computing, namely, Shor's algorithm used to perform integer factorisation and distributed quantum computing algorithms. The algorithm proposed by Peter Shor in 1994 is one of the most important achievements in quantum computing, as it allows for polynomial factorisation of large integers and thus compromises today's encryption algorithms. Distributed quantum computing solves the scalability problem by linking several quantum computation devices with each other using classical and quantum means of communication. The following review focuses on the state-of-the-art developments in quantum computing and applications of such algorithms to cryptography and scalability problems.