Graph representation learning for parameter transferability in quantum approximate optimization algorithm

Graph representation learning for parameter transferability in quantum approximate optimization algorithm

22 July 2024 | Jose Falla1 · Quinn Langfitt3 · Yuri Alexeev3 · Ilya Safro1,2
This paper explores the application of graph representation learning techniques to enhance the parameter transferability in the Quantum Approximate Optimization Algorithm (QAOA) for solving combinatorial optimization problems, particularly the MaxCut problem. The authors investigate how graph embedding models can predict optimal donor graphs for parameter transferability to target acceptor graphs, aiming to reduce the computational cost and improve the efficiency of QAOA parameter optimization. They apply five different graph embedding techniques—Graph2Vec, GL2Vec, wavelet characteristic, spectral feature (SF), and FEATHER—to a set of 30,000 40-node random graphs, optimizing QAOA parameters for a depth of $p=3$. The performance of these models is evaluated using approximation ratios, which measure the effectiveness of parameter transferability. The results show that Graph2Vec and GL2Vec, which rely on structural graph features, outperform other models in predicting good donor candidates, especially for similar MaxCut instances. The study also demonstrates that the transferred parameters maintain effectiveness even in noisy conditions, as simulated on IBM's Guadalupe and Auckland quantum processors, suggesting their potential for real-world quantum applications. The findings provide a framework for identifying classes of combinatorial optimization instances where optimal donor candidates can be predicted, significantly accelerating QAOA under both ideal and noisy conditions.This paper explores the application of graph representation learning techniques to enhance the parameter transferability in the Quantum Approximate Optimization Algorithm (QAOA) for solving combinatorial optimization problems, particularly the MaxCut problem. The authors investigate how graph embedding models can predict optimal donor graphs for parameter transferability to target acceptor graphs, aiming to reduce the computational cost and improve the efficiency of QAOA parameter optimization. They apply five different graph embedding techniques—Graph2Vec, GL2Vec, wavelet characteristic, spectral feature (SF), and FEATHER—to a set of 30,000 40-node random graphs, optimizing QAOA parameters for a depth of $p=3$. The performance of these models is evaluated using approximation ratios, which measure the effectiveness of parameter transferability. The results show that Graph2Vec and GL2Vec, which rely on structural graph features, outperform other models in predicting good donor candidates, especially for similar MaxCut instances. The study also demonstrates that the transferred parameters maintain effectiveness even in noisy conditions, as simulated on IBM's Guadalupe and Auckland quantum processors, suggesting their potential for real-world quantum applications. The findings provide a framework for identifying classes of combinatorial optimization instances where optimal donor candidates can be predicted, significantly accelerating QAOA under both ideal and noisy conditions.
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