A typology of quantum algorithms

TL;DR

This paper classifies approximately 130 quantum algorithms based on their mathematical problems, applications, and subroutines to reveal trends, promising fields, and key primitives for quantum advantage.

Contribution

It provides a comprehensive taxonomy of quantum algorithms, highlighting their core features and guiding future research and implementation efforts.

Findings

Identifies key algorithmic primitives for quantum advantage.

Reveals trends and promising fields in quantum algorithm development.

Classifies algorithms based on problems, applications, and subroutines.

Abstract

We draw the current landscape of quantum algorithms, by classifying about 130 quantum algorithms, according to the fundamental mathematical problems they solve, their real-world applications, the main subroutines they employ, and several other relevant criteria. The primary objectives include revealing trends of algorithms, identifying promising fields for implementations in the NISQ era, and identifying the key algorithmic primitives that power quantum advantage.