CHARME: A chain-based reinforcement learning approach for the minor embedding problem

TL;DR

CHARME is a novel reinforcement learning-based method that improves the efficiency and quality of minor embedding for quantum annealing, outperforming existing algorithms in qubit usage and solution quality.

Contribution

This paper introduces CHARME, a reinforcement learning approach with a graph neural network for the minor embedding problem, addressing scalability and solution quality issues.

Findings

CHARME outperforms Minorminer and ATOM in qubit efficiency.

CHARME surpasses OCT in solution quality and runtime.

Exploration strategy improves training efficiency and solution quality.

Abstract

Quantum annealing (QA) has great potential to solve combinatorial optimization problems efficiently. However, the effectiveness of QA algorithms is heavily based on the embedding of problem instances, represented as logical graphs, into the quantum processing unit (QPU) whose topology is in the form of a limited connectivity graph, known as the minor embedding problem. Because the minor embedding problem is an NP-hard problem~\mbox{\cite{Goodrich2018}}, existing methods for the minor embedding problem suffer from scalability issues when faced with larger problem sizes. In this paper, we propose a novel approach utilizing Reinforcement Learning (RL) techniques to address the minor embedding problem, named CHARME. CHARME includes three key components: a Graph Neural Network (GNN) architecture for policy modeling, a state transition algorithm that ensures solution validity, and an order exploration strategy for effective training. Through comprehensive experiments on synthetic and real-world instances, we demonstrate the efficiency of our proposed order exploration strategy as well as our proposed RL framework, CHARME. In particular, CHARME yields superior solutions in terms of qubit usage compared to fast embedding methods such as Minorminer and ATOM. Moreover, our method surpasses the OCT-based approach, known for its slower runtime but high-quality solutions, in several cases. In addition, our proposed exploration enhances the efficiency of the training of the CHARME framework by providing better solutions compared to the greedy strategy.