An Introduction to Quantum Computing, Without the Physics

TL;DR

This paper provides a rigorous, physics-free introduction to quantum computing for mathematicians, covering core concepts, differences from classical computing, and illustrating with algorithms and software examples.

Contribution

It offers a formal, physics-agnostic framework for understanding quantum computing, including detailed explanations of key algorithms and practical implementation insights.

Findings

Analysis of quantum computing characteristics

Description of Simon's and Grover's algorithms

Implementation examples using open-source software

Abstract

This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics, stressing the differences with classical computers, and finally describe two well-known algorithms (Simon's algorithm and Grover's algorithm) using the formalism developed in previous sections. This paper does not touch on the physics of the devices, and therefore does not require any notion of quantum mechanics. Numerical examples on an implementation of Grover's algorithm using open-source software are provided.