Quantum computing from a mathematical perspective: a description of the quantum circuit model

TL;DR

This paper provides a rigorous mathematical overview of quantum computing, focusing on the quantum circuit model, aimed at mathematicians to bridge the language gap with physics and computer science.

Contribution

It offers an essentially self-contained, rigorous mathematical description of quantum computing principles, facilitating mathematicians' understanding of the quantum circuit model.

Findings

Clear mathematical framework for quantum circuits

Bridges gap between mathematics and quantum computing

Accessible introduction for mathematicians

Abstract

This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing discipline and find themselves taken aback by the language gap between mathematics and the pioneering fields on the matter: computer science and quantum physics. A first version of this paper was originally published at arXiv in October 2018. Minor corrections added on Spring 2025.