# Quantum independent set problem and non-abelian adiabatic mixing

## TL;DR

This paper introduces a quantum algorithm leveraging non-abelian adiabatic mixing to efficiently solve certain independent set problems in graph theory, showing potential advantages over classical methods through analysis and simulations.

## Contribution

The paper presents a novel quantum algorithm based on non-abelian adiabatic mixing for independent set problems, with analysis and numerical validation on different graph types.

## Key findings

- Quantum algorithm outperforms classical algorithms on tested graph types.
- Non-abelian adiabatic mixing aids exploration of near-degenerate ground states.
- Potential general applicability of the technique to other quantum optimization problems.

## Abstract

We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different types of graphs, with the number of edges proportional to the number of vertices or its square. The theoretical advantages of our quantum algorithm over classical algorithms are discussed. Non-abelian adiabatic mixing can be a general technique to aid exploration in a landscape of near-degenerate ground states.