Speaker
Description
Graphs arise throughout molecular chemistry, social networks, and biology, but current quantum methods for graph learning often either ignore global graph geometry or depend on variational circuits that are difficult to train on near-term devices. We introduce QGSP (Quantum Graph Spectral Positioning), a parameter-free quantum graph embedding method that encodes graph structure into fixed-width quantum circuits through three complementary channels: a global spectral channel that maps diffusion-weighted Laplacian eigenvector coordinates to quantum amplitude states, a feature channel that encodes node attributes through deterministic rotation gates, and a local channel that encodes neighborhood topology on a dedicated register coupled to the global state via controlled entangling gates. The circuit uses seven qubits regardless of graph size, has no trainable quantum parameters, and runs in approximately 14 ms per node in classical statevector simulation. We evaluate QGSP on five standard TU benchmark datasets. As a feature augmentation method, QGSP improves 29 of 30 baseline–dataset pairs across six classical graph pipelines, with gains of up to 5.9 percentage points. As a standalone unsupervised embedding combined with an SVM classifier, QGSP-full achieves accuracy comparable to strong unsupervised baselines. Restricting the readout to a hardware-realizable sub-vector of single- and two-qubit Pauli expectation values matches the full-statevector readout across all five datasets. This result motivates a finite-shot device study and suggests that amplitude-encoded spectral coordinates provide a compact, training-free source of structural features for graph representation learning.
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Hybrid quantum-classical approaches for learning and optimization |