Quantum Chemistry / ML
Kernel methods formolecular classification.
Predicting molecular properties from 2D graph structure alone — by mapping each molecule into a hybrid classical-quantum feature space and classifying with a quantum fidelity kernel.
Dat Chi (Ryan) Le · Abubakar (Sid) Iliyasu · Gyanateet Dutta
01 — The Problem
A molecule's properties live in its graph.
Predicting molecular properties from a 2D graph representation alone — with no 3D structure or simulation — depends entirely on how well the feature map φ(G) captures what actually matters about that molecule's structure.
02 — Method
Local structure, plus global quantum dynamics.
Classical features capture local structure — functional groups and bonding patterns via topology, graph indices, and spectral analysis. A continuous-time quantum walk (CTQW), sampled at multiple evolution times, adds 29 dimensions that capture global dynamics, including quantum interference effects that classical features miss entirely.
13D
Classical features: topology, indices, spectral
29D
Quantum features: continuous-time quantum walk
42D
Combined hybrid feature vector
5
Benchmark datasets: AIDS, MUTAG, PROTEINS, NCI1, PTC_MR
Classification runs on an SVM using a quantum fidelity kernel, K(i, j) = |⟨ψᵢ|ψⱼ⟩|², computed via a ZZ-style feature map and a hardware-efficient ansatz, built on the QURI Parts framework, with a 10-fold cross-validated grid search and benchmarked against classical Weisfeiler–Leman, shortest-path, and graphlet kernels.
03 — Results
82.6% average accuracy across five datasets.
The quantum kernel improved on 3 of 5 datasets over classical-only features, for a +1.5 point average lift and an overall 82.6% ± 4.5% accuracy.
Dataset sizes — AIDS: 2,000 · MUTAG: 188 · PROTEINS: 1,113 · NCI1: 4,110 · PTC_MR: 344 graphs
04 — Does the Quantum Feature Help?
On MUTAG, the hybrid beat both halves alone.
05 — Conclusions & Next Steps
Competitive with published results, and fast.
AIDS matched or exceeded literature benchmarks at 99.5%, and MUTAG landed within a point of state-of-the-art at 89.4% — all in about 3.6 seconds of total runtime with O(n²) kernel computation, scaling comfortably to NCI1's 4,110 graphs. Next: running on real quantum hardware (IBM Quantum, Rigetti), larger variational circuits, and extending toward drug discovery and materials science.