  In this work, we propose novel families of positional encodings tailored to
graph neural networks obtained with quantum computers. These encodings leverage
the long-range correlations inherent in quantum systems that 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 enhance the performance of
transformers in handling graph data.
