A Symmetry-Based Taxonomy of Quantum Algorithms

TL;DR

This paper introduces a taxonomy for quantum algorithms based on the symmetries of quantum state spaces, oracles, and circuits, providing a new framework for understanding their classification, behavior, and complexity.

Contribution

It presents a novel symmetry-based classification scheme for quantum algorithms, linking physical symmetries to algorithmic properties and practical quantum computing benefits.

Findings

Algorithms are classified by their symmetry groups and invariants.

Symmetry-based classification reveals connections to conservation laws in physics.

Practical benefits include improved scalability and reliability in quantum computation.

Abstract

We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups and invariants, we define distinct algorithm classes whose behavior, verification, and complexity can be characterized by the symmetries they preserve or exploit. This symmetry-centric classification not only reflects the deep connection between symmetries and conservation laws in physics, but also yields practical benefits for scalable and reliable quantum computation.