Quantum invariants for the graph isomorphism problem

TL;DR

This paper introduces a quantum computing algorithm that creates a new invariant for the graph isomorphism problem, outperforming many existing invariants in distinguishing non-isomorphic graphs.

Contribution

It presents a novel quantum algorithm that defines an invariant for graph isomorphism, enhancing the ability to differentiate non-isomorphic graphs.

Findings

The quantum invariant distinguishes more non-isomorphic graphs than previous invariants.

The algorithm's correctness is proven and its improved distinguishing power is explained.

It advances quantum approaches to the graph isomorphism problem.

Abstract

Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to integer factorisation. The best known proved algorithm to solve this problem in general, was proposed by L\'aszl\'o Babai and Eugene Luks in 1983. Recently, there has been some research in the topic by using quantum computing, that also leads the present piece of research. In fact, we present a quantum computing algorithm that defines an invariant over Graph Isomorphism characterisation. This quantum algorithm is able to distinguish more non-isomorphic graphs than most of the known invariants so far. The proof of correctness and some hints illustrating the extent and reason of the improvement are also included in this paper.