Enhancing Graph Neural Networks with Quantum Computed Encodings

TL;DR

This paper introduces quantum-inspired positional encodings for graph transformers, leveraging quantum correlations to improve model expressiveness and performance on standard benchmarks.

Contribution

It proposes novel quantum-inspired encodings for graph transformers and demonstrates their theoretical and empirical advantages over classical methods.

Findings

Quantum features can be more expressive for certain graphs.

Performance improvements on standard benchmarks.

Quantum-inspired encodings enhance graph transformer capabilities.

Abstract

Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings. In this work, we propose novel families of positional encodings tailored for graph transformers. These encodings leverage the long-range correlations inherent in quantum systems, which arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to potentially enhance the performance of transformers in handling graph data.