Clique detection using symmetry-restricted quantum circuits

TL;DR

This paper demonstrates how permutation-invariant quantum circuits can effectively solve the clique detection problem by leveraging the problem's inherent symmetry, outperforming other quantum approaches.

Contribution

It introduces a permutation-invariant quantum circuit approach tailored for the clique problem, highlighting the importance of symmetry in quantum machine learning.

Findings

Permutation-invariant circuits outperform cyclic-invariant and standard ansatz.

Symmetry plays a crucial role in the effectiveness of quantum algorithms for graph problems.

The approach leverages problem symmetry to improve quantum circuit performance.

Abstract

We show the application of permutation-invariant quantum circuits to the clique problem. The experiment asks to label a clique through identification of the nodes in a larger subgraph. The permutation-invariant quantum circuit outperforms a cyclic-invariant alternative as well as a standard quantum machine learning ansatz. We explain the behavior through the intrinsic symmetry of the problem, in the sense that the problem is symmetric under permutation of both the feature and the label.