Introduction to Quantum Algorithms

TL;DR

This paper introduces quantum algorithms that outperform classical ones in solving certain problems, discusses the limited known techniques for quantum speedup, and explores whether more such algorithms can be discovered.

Contribution

It provides an overview of existing quantum algorithms and highlights the challenges in discovering new techniques for quantum speedup.

Findings

Few quantum speedup techniques are known.

Uncertainty whether more techniques exist or only a few problems benefit.

Quantum algorithms can significantly outperform classical algorithms for some problems.

Abstract

These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical algorithms. It is not clear yet whether the reason for this is that we do not have enough intuition to discover more techniques, or that there are only a few problems for which quantum computers can significantly speed up the solution.