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.

Accuracy
F1 Score
AIDS
99.5%
99.2%
MUTAG
89.4%
88.1%
PROTEINS
75.2%
74.4%
NCI1
74.8%
72.6%
PTC_MR
59.0%
56.5%

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.

WL + CTQW (hybrid)
89.4%
CTQW only
86.2%
Classical WL only
84.1%

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.