An elementary derivation of the Deutsch-Jozsa algorithm

TL;DR

This paper presents a simplified derivation of the Deutsch-Jozsa algorithm, making it accessible for students using only basic quantum mechanics and linear algebra, thus enhancing understanding of quantum speedup.

Contribution

It offers an elementary formulation of the Deutsch-Jozsa algorithm, removing complex steps to facilitate learning for students with foundational quantum knowledge.

Findings

Simplified derivation accessible to students

Enhanced understanding of quantum speedup

Educational tool for quantum computing concepts

Abstract

Quantum computing takes fully advantage of the superposition principle to increase greatly (even exponentially) the speed of calculations, relative to the classical approach. The Deutsch-Jozsa algorithm is the simplest quantum algorithm illustrating this power. Unfortunately, the standard derivation involves several ingenious steps which usually leave students feeling that they could never have figured out the algorithm by themselves. We present here a different formulation of the problem which allows students to derive the algorithm using only basic knowledge of quantum mechanics and linear algebra.