Research question
Can a hybrid quantum–classical multimodal model predict binding affinity when the drug, target, or both were unseen during training?
Condensed abstract
The study compares QVGAT-DPI with a specification-based implementation of Q-BAFNet under cold-start drug–target affinity protocols. QVGAT-DPI combines molecular graphs, BRICS fragments, molecular fingerprints, ChemBERTa drug representations, full-sequence ESM-2 protein representations, bidirectional cross-attention, and classically simulated residual variational quantum modules.
Key contribution
A residual hybrid architecture that adds quantum-derived corrections to classical attention and topology paths, evaluated with entity-level protocols for unseen drugs (S2), unseen targets (S3), and jointly unseen drugs and targets (S4).
Method overview
Drug inputs branch through graph-attention layers, an unordered BRICS-fragment set, a Morgan fingerprint, and ChemBERTa. Overlapping ESM-2 windows represent complete protein sequences. Bidirectional cross-attention models drug–protein interactions; six-qubit state-vector circuits supply gated residuals to attention and topology features before sample-specific fusion and regression.
QVGAT-DPI model journey
Baseline and current
The baseline stays fixed. Both figures use the same scales.
How one pair becomes an affinity estimate
Follow the drug and protein through five stages. Select any module for its role, or run the complete explanatory trace.
Illustrative inputs and motion · topology follows the published model
Pair
Cold-start status changes the evaluation split, not the input format. The example identities below are deliberately illustrative.
What does “unseen” actually mean?
Change the protocol above. Watch whole identities leave the training set.
Entire drug rows are held out. Test drugs never appear in training; target identities may overlap.
Counts belong only to this 6 × 6 schematic.Encode
Parallel encoders retain topology, fragments, fixed chemical descriptors, molecular language, and protein context.
Drug representations
Protein representation
Interact
Cross-attention exchanges token context in both directions; this is an interaction step, not simple concatenation.
Follow a query across the modalities
Choose an illustrative drug query. Ribbon thickness shows its normalized attention to six protein tokens.
A softmax demonstration, not an explanation of a real binding event. The published model exchanges context in both directions, as shown below.
Two conditioned paths · not a one-step concatenation
Residual quantum simulation
The same six-qubit feature-map pattern supports two gated residual additions to the classical backbone.
state-vector simulationno QPU
Fuse and predict
Sample-specific gates decide how much each branch contributes before the final regression head.
Cold-start evidence atlas
Select a dataset, protocol, and endpoint. Complete cells reveal paired fold differences; partial and unrun cells stay blank.
| Dataset | S2 · drug | S3 · target | S4 · both |
|---|---|---|---|
| DAVIS | |||
| KIBA |
Paired difference summary
Δ = QVGAT-DPI − Q-BAFNet · lower RMSE / higher CI is favorable
- Mean Δ
- Bootstrap 95% interval
- Exact p
- Holm-adjusted p
The average paired change favors QVGAT-DPI for RMSE. This was the only tested contrast that remained below 0.05 after Holm correction.
Incomplete paired grid
No inferential summary is shown for incomplete evidence.
S2 exact paired-fold records
| Fold | QVGAT CI | Q-BAFNet CI | Δ CI | QVGAT RMSE | Q-BAFNet RMSE | Δ RMSE |
|---|---|---|---|---|---|---|
| 0 | 0.710242 | 0.562881 | +0.147362 | 0.701621 | 0.844173 | −0.142552 |
| 1 | 0.692604 | 0.788627 | −0.096023 | 1.105588 | 1.234872 | −0.129284 |
| 2 | 0.687749 | 0.701508 | −0.013759 | 0.784225 | 1.043809 | −0.259584 |
| 3 | 0.743495 | 0.769435 | −0.025940 | 0.552421 | 0.652981 | −0.100561 |
| 4 | 0.699781 | 0.668143 | +0.031638 | 0.838288 | 0.814908 | +0.023380 |
| 5 | 0.810185 | 0.622598 | +0.187586 | 0.581790 | 0.711800 | −0.130010 |
| 6 | 0.649706 | 0.665326 | −0.015619 | 0.963913 | 0.953320 | +0.010593 |
| 7 | 0.537179 | 0.522140 | +0.015039 | 0.854242 | 0.901912 | −0.047671 |
| 8 | 0.658422 | 0.485214 | +0.173209 | 0.875684 | 0.907538 | −0.031854 |
| 9 | 0.746265 | 0.548541 | +0.197725 | 0.914771 | 1.048240 | −0.133469 |
S4 exact paired-fold records
| Fold | QVGAT CI | Q-BAFNet CI | Δ CI | QVGAT RMSE | Q-BAFNet RMSE | Δ RMSE |
|---|---|---|---|---|---|---|
| 0 | 0.644727 | 0.581463 | +0.063264 | 0.763919 | 1.234153 | −0.470234 |
| 1 | 0.747104 | 0.533431 | +0.213674 | 1.012555 | 1.224489 | −0.211934 |
| 2 | 0.681716 | 0.451359 | +0.230358 | 0.683005 | 0.687608 | −0.004603 |
| 3 | 0.792597 | 0.784040 | +0.008557 | 0.495128 | 0.542057 | −0.046929 |
| 4 | 0.632119 | 0.550019 | +0.082100 | 0.894987 | 0.785183 | +0.109805 |
| 5 | 0.747814 | 0.769903 | −0.022089 | 0.541370 | 1.195126 | −0.653756 |
| 6 | 0.625748 | 0.500051 | +0.125697 | 0.917209 | 0.963249 | −0.046040 |
| 7 | 0.563100 | 0.490686 | +0.072414 | 0.895364 | 0.794230 | +0.101134 |
| 8 | 0.659683 | 0.509071 | +0.150612 | 0.885351 | 0.937594 | −0.052243 |
| 9 | 0.682263 | 0.734587 | −0.052324 | 1.163495 | 1.239225 | −0.075730 |
All complete-protocol statistical summaries
| Protocol | Endpoint | Mean Δ | Bootstrap 95% interval | Exact p | Holm p |
|---|---|---|---|---|---|
| S2 | CI | +0.060122 | −0.000480 to +0.123441 | 0.09960938 | 0.19921875 |
| S2 | RMSE | −0.094101 | −0.144692 to −0.045941 | 0.00976562 | 0.03906250 |
| S4 | CI | +0.087226 | +0.032326 to +0.142750 | 0.01953125 | 0.05859375 |
| S4 | RMSE | −0.135053 | −0.294289 to −0.005012 | 0.11914062 | 0.19921875 |
Dataset and evaluation
Data
The pilot uses the DAVIS and KIBA drug–target affinity benchmarks. Only DAVIS S2 and S4 produced complete ten-fold paired result sets; DAVIS S3 and all KIBA protocol cells remained partial or unrun.
Protocol
The planned comparison used ten deterministic folds per cold-start protocol. Completed, fold-matched QVGAT-DPI and paper-specification Q-BAFNet results were summarized with paired differences, bootstrap confidence intervals, exact p-values, and Holm correction across the primary CI and RMSE endpoints.
Main results
For complete DAVIS S2, the mean QVGAT-DPI minus Q-BAFNet difference was +0.060122 for CI and −0.094101 for RMSE; only the RMSE result remained below 0.05 after Holm correction (p = 0.0391). DAVIS S4 favored QVGAT-DPI in mean CI and RMSE differences, but neither endpoint remained below 0.05 after correction. Neither complete protocol met the prespecified dual-endpoint superiority rule.
Baseline comparison
Against the local paper-specification Q-BAFNet comparator, QVGAT-DPI had favorable mean differences on both primary endpoints in complete DAVIS S2 and S4. Multiplicity-adjusted support was limited to S2 RMSE. Q-BAFNet is a hybrid comparator, not a classical baseline or an exact reproduction claim.
Limitations and failure modes
- All quantum circuits were state-vector simulations; no quantum processing unit was used, and the study does not establish quantum advantage.
- The experimental grid was incomplete: only DAVIS S2 and S4 reached ten paired folds, so partial DAVIS S3 and KIBA runs are not confirmatory evidence.
- The reported comparison does not isolate a causal contribution from the residual quantum modules.
- Benchmark affinity prediction does not establish prospective biological, experimental, or clinical utility.
Reproducibility
A CPU-only audit of the 20 reported DAVIS S2/S4 paired fold records and four tested contrasts.
Reported statistics recomputedChecked locally 2026-09-05 · bundle v1.0.0
- Paper-associated code
- Zenodo record 21805175 This external archive is separate from the small check below. Its full environment was not executed here.
- Inputs for this check
- The existing sourced fold transcription, including published delta columns. No molecule files, checkpoints, or training data are required.
- Prerequisites
- Python 3.10+ · standard library only · CPU · no network or large dataset download. A notebook environment is optional.
Run the small check
- Download and extract the complete bundle.
- Open a terminal in the extracted folder and run
python check.py. - Recompute paired means, enumerate all 1,024 sign assignments per contrast for exact two-sided p-values, then apply step-down Holm across all four endpoints.
Includes Python, an equivalent notebook, source JSON, expected output, and SHA-256 provenance. The notebook runs from the extracted folder.
Expected output and individual files
Holm-adjusted p: S2 CI 0.19921875; S2 RMSE 0.0390625; S4 CI 0.05859375; S4 RMSE 0.19921875. Only S2 RMSE is below 0.05.
What this does not establish
No model training or bootstrap interval is recomputed. Incomplete DAVIS S3 and KIBA cells remain incomplete or unrun. This does not establish a dual-endpoint win or quantum advantage.
These checks use the portfolio’s existing sourced records. External archive links could not be freshly rechecked during package preparation. A passing check is not a full-paper replication.
The decisions behind the method
Why identity-disjoint splits, paired deltas, and an explicitly incomplete evidence grid matter more than an impressive model diagram.
Read the research noteVerification sources
Cite this work
Arman Salehi, Ghazal Salehi, Ashkan Heydarian, Hamid Reza Goudarzi (2026). Comparative study of hybrid quantum-classical models for cold-start drug–target affinity prediction: a partial pilot analysis. Scientific Reports. https://doi.org/10.1038/s41598-026-69754-2
BibTeX
@article{salehi2026qvgat,
title = {Comparative study of hybrid quantum-classical models for cold-start drug–target affinity prediction: a partial pilot analysis},
author = {Arman Salehi and Ghazal Salehi and Ashkan Heydarian and Hamid Reza Goudarzi},
year = {2026},
doi = {10.1038/s41598-026-69754-2},
journal = {Scientific Reports},
publisher = {Springer Nature}
}Publication record last verified 2026-09-01.
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