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Quantum Evolution Kernel for Node-Attributed Graphs
Manuel Padovani, Alessandra Di Pierro, Claudia Daffara
TL;DR
Node-attributed graph kernels need to account for continuous node features, but encoding multiple such attributes in analog quantum graph kernels remains challenging and largely unexplored. The paper introduces a neutral-atom quantum kernel with separate node-feature encoding and evaluates it on MNIST. Wasserstein distance is the most effective tested metric, while the kernel remains competitive with selected classical graph kernels in the low-data regime.
Problem
Encoding multiple continuous node attributes in analog quantum graph kernels remains a challenging and mostly unexplored problem.
Source: §1 · p. 2Method
The method encodes graph structure and local node features in a neutral-atom quantum evolution, then uses measurement-derived distributions to define a classification kernel.
Source: §5 · pp. 10–11Results
On MNIST, Wasserstein was the most effective tested metric, and the quantum kernel was competitive with selected classical graph kernels in the low-data regime but did not surpass the combined WL kernel or GCN mean performance.
Source: §5 · p. 11Takeaways & Limitations
For this digit-recognition task, Wasserstein offers a practical advantage over Jensen-Shannon because it bypasses binning.
Source: §5 · p. 11Simulation constraints meant that only a small subset of the filtered dataset was used for training and evaluation.
Source: §2.6 · p. 7
Abstract
from arXiv · showhide
We present a novel approach to embed node-attributed graphs onto neutral-atom quantum computers, and propose an application to digit recognition. Our approach extends PASQAL's quantum evolution kernel (QEK) by introducing a node-level feature encoding based on three-level quantum states. To this purpose, we present a prototype showing how the resulting embedding can be leveraged to extract correlation-based information for classification tasks. The entire quantum process is simulated using Pasqal's Pulser library, which inevitably imposes constraints on the size of the experimental datasets. We compare our method with classical baselines to evaluate its potential. We show that, for the digit recognition task, our method achieves a higher mean accuracy than the more commonly used Jensen-Shannon distance-based methods by utilizing the Wasserstein distance.
1 Introduction
Classical graph kernels often omit continuous node features, while encoding multiple continuous attributes in analog quantum graph kernels remains largely unexplored. This work examines a neutral-atom quantum-kernel approach that separately encodes node features and evaluates it on MNIST.
1 Introduction
- Encoding multiple continuous node attributes in analog quantum graph kernels remains a challenging and mostly unexplored problem.Classical structural kernels typically ignore continuous node features, which matter in node-attributed graphs.Source: §1 · pp. 1–2
- The study assesses whether multi-attribute continuous encoding is architecturally feasible on analog hardware and provides a baseline for future large-scale implementations.The paper focuses on quantum kernels for neutral-atom computers in the low-data regime.Source: §1 · p. 2
1.1 Contribution
- Local Raman pulses separately encode node features in a three-level system per atom, extending a neutral-atom graph-kernel approach.The system uses two hyperfine ground states alongside the Rydberg state.Source: §1.1 · p. 2
- The proposed kernel uses Wasserstein distance on measurement-derived probability distributions rather than the Jensen-Shannon metric.The authors report that Jensen-Shannon is less effective on the digit-recognition task.Source: §1.1 · p. 2
- The approach is evaluated on MNIST against classical graph machine-learning baselines.Source: §1.1 · p. 2
2 Method
The method maps graph structure to neutral-atom positions and node features to local rotations, then builds graph similarities from measurement distributions. The experiments apply this pipeline to MNIST digit graphs using simulated quantum evolution.
2.1 Pulses and Evolution
- Rydberg interactions encode graph structure: atoms are positioned so connected nodes fall within the blockade threshold and unconnected nodes remain beyond it.Below the threshold, doubly excited Rydberg states become energetically disfavored, creating the blockade effect used to entangle nearby atoms.Source: §2.1 · p. 3
2.2 Mapping Node-Feature Graphs to Neutral Atoms
- Graph topology is encoded through atom positions, while node features are normalized and mapped to rotations of the atom’s |g⟩ and |h⟩ levels.Edge features can instead be mapped to interatomic distances, but their experimental impact is not evaluated.Source: §2.2 · p. 3
2.3 Distributions From Measurements
- Measurements yield size-invariant excitation and correlation distributions for each encoded feature pair.The excitation distribution uses bit-string Hamming weights; the correlation distribution uses pairwise connected correlations.Source: §2.3 · p. 4
2.4 Distribution-based Quantum Kernel
- The kernel compares output distributions using distances, including Wasserstein W1, which avoids binning but has higher time complexity than Jensen-Shannon distance.For one-dimensional distributions, W1 yields a positive-semidefinite kernel; weighted combinations aggregate kernels across distributions.Source: §2.4 · p. 5
- A support vector classifier uses the resulting kernel, with γ, regularization C, and distribution weights selected through nested cross-validation.The retained parameter triplet maximizes macro-averaged F1.Source: §2.4 · pp. 5–6
2.5 Graph Embedding
- Pulser simulation and graph-embedding filters constrain the experiments: graphs must have at most nine nodes, acceptable distance error, and limited spatial extent.The embedding uses a force-directed spring model and applies device topology and minimum-distance constraints.Source: §2.5 · p. 6
2.6 Experiments
- MNIST images are converted into graphs with pixel-coordinate and edge-angle features, and the quantum process is evaluated on only a small subset because of simulation constraints.After graph filtering, approximately 80% of the dataset remains; evaluation uses multiple training sizes and a fixed balanced test set.Source: §2.6 · pp. 7–8
- 240.1 ns maximized validation F1 in Bayesian optimization on a 200-sample MNIST subset.The caption reports low F1 for short evolution times and a sharp drop at long times.Source: §2.6 · pp. 7–8, Figure 2 · p. 8
3 Results
The Wasserstein-based quantum kernel achieves the highest mean accuracy among the tested distance metrics. Against classical baselines, it performs below the GCN, comparably to the positional WL variant, and above the angle-only and featureless WL kernels.
3.1 Comparison of Distance Metrics
- Wasserstein achieves the highest mean accuracy across all training sizes, with comparable results from both aggregation strategies.The study consequently uses sum aggregation for comparison with classical baselines.Source: §3.1 · p. 9, Figure 3 · p. 9
- Jensen-Shannon performs slightly worse, while using 30 bins drops performance versus 10; Hellinger and L2 perform poorly as training-set size increases.Wasserstein without node-level features performs better than Hellinger and L2 but worse than all tested cases with local features.Source: §3.1 · p. 9
3.2 Comparison with Classical Baselines
- The quantum kernel performs comparably to the positional WL variant and outperforms angle-only and featureless WL kernels, while the GCN achieves the highest accuracy.The quantum kernel uses Wasserstein distance with sum aggregation.Source: §3.2 · pp. 9–10, Figure 4 · p. 10
4 Related Work
The work builds on quantum evolution kernels that encode graph structure through neutral-atom evolution and on attributed-graph extensions that encode features using local detuning. It instead uses local Raman pulses and three-level atoms to encode node features separately from graph topology, alongside a Wasserstein metric.
4 Related Work
- QEK embeds graph structure through successive mixing and natural-evolution layers, then constructs distributions from Rydberg excitations.The attributed-graph extension encodes node features in local detuning fields and uses a local-correlation-matrix kernel; both approaches use two-level states and Rydberg lasers.Source: §4 · p. 10
- Local Raman pulses couple hyperfine ground states, creating a three-level system that separates node-feature encoding from graph topology.The approach also uses Wasserstein distance rather than the Jensen-Shannon distance used in QEK.Source: §4 · p. 10
5 Conclusion
The paper proposes a quantum kernel for node-attributed graphs that encodes structural and local feature information into quantum evolution and uses measurement distributions for classification. On MNIST, Wasserstein distance was the most effective tested metric, while the simple circuit did not surpass the mean performance of the WL combined classical kernel or the GCN.
5 Conclusion
- The proposed quantum kernel encodes structural and local feature information into quantum evolution, then uses measurement distributions to define a classification kernel.Source: §5 · pp. 10–11
- On MNIST, Wasserstein distance was the most effective tested metric, but the simple circuit did not surpass the mean performance of the WL combined classical kernel or the GCN.The version without node-level features performed worse; more elaborate encodings and longer evolution times are suggested as directions for improvement.Source: §5 · p. 11
- The optimizable weights ωk could indicate which graph-feature distributions are most relevant to classification.Source: §5 · p. 11
- On real analog hardware, graph encoding scales as O(|V|), while correlation estimation takes O(log |V|/ϵ^2); classical O(|V|^2) correlation-matrix post-processing remains a scaling concern.The authors state that demonstrating a strict computational or learning advantage over classical graph methods remains an open challenge.Source: §5 · p. 11