A Quantum Algorithm for the Sub-Graph Isomorphism Problem

TL;DR

This paper introduces a quantum variational algorithm for the sub-graph isomorphism problem, leveraging a new adjacency matrix representation and an efficient Ansatz, capable of handling graphs with up to 16 vertices and scalable to larger instances.

Contribution

It presents a novel quantum algorithm with a new adjacency matrix encoding and an efficient Ansatz for sub-graph isomorphism, demonstrating promising simulation results.

Findings

Successfully simulated graphs up to 16 vertices

Scalable approach due to logarithmic qubit requirements

Potential applicability to realistic problem instances

Abstract

We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number of qubits that scales logarithmically with the number of vertices of the graphs; and (2) on a new Ansatz that can efficiently probe the permutation space. Simulations are then presented to showcase the approach on graphs up to 16 vertices, whereas, given the logarithmic scaling, the approach could be applied to realistic sub-graph isomorphism problem instances in the medium term.