Attributed-graphs kernel implementation using local detuning of neutral-atoms Rydberg Hamiltonian

Abstract

We extend the quantum-feature kernel framework, which relies on measurements of graph-dependent observables, along three directions. First, leveraging neutral-atom quantum processing units (QPUs), we introduce a scheme that incorporates attributed graphs by embedding edge features into atomic positions and node features into local detuning fields of a Rydberg Hamiltonian. We demonstrate both theoretically and empirically that local detuning enhances kernel expressiveness. Second, in addition to the existing quantum evolution kernel (QEK), which uses global observables, we propose the generalized-distance quantum-correlation (GDQC) kernel, based on local observables. While the two kernels show comparable performance, we show that GDQC can achieve higher expressiveness. Third, instead of restricting to observables at single time steps, we combine information from multiple stages of the quantum evolution via pooling operations. Using extensive simulations on two molecular benchmark datasets, MUTAG and PTC\_FM, we find: (a) QEK and GDQC perform competitively with leading classical algorithms; and (b) pooling further improves performance, enabling quantum-feature kernels to surpass classical baselines. These results show that node-feature embedding and kernel designs based on local observables advance quantum-enhanced graph machine learning on neutral-atom devices.

16 pages, 4 figures

References in corpus (8)

• Geometric deep learning: going beyond Euclidean data
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Biological network comparison using graphlet degree distribution
• Observation of collective excitation of two individual atoms in the Rydberg blockade regime
• Quantum simulation and computing with Rydberg-interacting qubits
• A Survey of Graph Neural Networks for Social Recommender Systems
• Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays
• Quantum Feature Maps for Graph Machine Learning on a Neutral Atom Quantum Processor