Quantum Algorithms from a Linear Algebra Perspective

The field of quantum computing has gained much attention in recent years due to further advances in the development of quantum computers and the recognition that this new paradigm will greatly endanger many modern encryption practices. This paper gives analysis of some of these algorithms, notably Grover’s database search algorithm, and Shor’s factoring and discrete log algorithms, from the perspective of linear algebra. The consequences these have for modern cryptography are discussed, and a brief overview of the current state of the field is given. Without assuming a physics background, this paper aims to provide a self-contained and mathematically rigorous explanation of quantum algorithms for an undergraduate audience