---
license: cc-by-4.0
pretty_name: "BBBP — Quantum-Relabeled (Blood-Brain Barrier Penetration)"
tags:
  - quantum-ml
  - quantum-kernel
  - quantum-native
  - kernel-matrix
  - graph_hamiltonian-encoding
  - relab
  - sirius-quantum
  - drug-discovery
  - ADMET
  - blood-brain-barrier
  - BBBP
  - BBB
  - molecular
  - cheminformatics
  - SMILES
  - pharma
  - MoleculeNet
  - small-molecule
  - CNS
task_categories:
  - feature-extraction
  - tabular-classification
size_categories:
  - n<1K
modalities:
  - tabular
source_datasets:
  - tdcommons/BBB_Martins
---

# BBBP — Quantum-Relabeled (Blood-Brain Barrier Penetration)

Quantum kernel matrix for the MoleculeNet BBBP (Blood-Brain Barrier Penetration) drug-discovery dataset. 85 small-molecule compounds, computed via a 25-qubit Heisenberg graph Hamiltonian circuit. Drop-in precomputed kernel for sklearn methods, pre-training signal for molecular foundation models.

Produced by [ReLab](https://github.com/Sirius-Quantum) — the quantum kernel
engine from Sirius Quantum. Each row of this dataset is the kernel slice
`K[i, :] = |⟨ψ(x_i) | ψ(x_j)⟩|²` for compound `i` against all others, a quantum
analog of a precomputed similarity matrix.

## What this is

Blood-brain barrier penetration (BBBP) is a critical ADMET property for CNS drug discovery — a candidate compound must cross the BBB to act in the brain. The MoleculeNet BBBP dataset (Martins et al., curated by TDC) contains drug compounds labeled by whether they penetrate the BBB in experimental assays. This is a binary classification benchmark widely used in cheminformatics, with established baselines from ChemBERTa, MolFormer, MAMMAL, Random Forest on Morgan fingerprints, and graph neural networks.

This dataset replaces (or augments) the classical feature representation of those
compounds with a **quantum kernel matrix**: for every pair of compounds (i, j), the
value `K[i, j]` is the quantum-state fidelity `|⟨ψ(x_i) | ψ(x_j)⟩|²` after each
compound has been encoded into a 25-qubit `graph_hamiltonian` circuit. The full
matrix is the quantum analog of a precomputed similarity matrix — drop it into any
sklearn kernel method.

## How it was relabeled

1. **Parse**: each compound's SMILES string is parsed via RDKit
2. **Encode**: the molecular graph is mapped to a graph_hamiltonian quantum circuit at
   25 qubits (Heisenberg-family Hamiltonian over the bond topology;
   arXiv:[2407.14055](https://arxiv.org/abs/2407.14055))
3. **Simulate**: the statevector |ψ(x)⟩ is computed on [Zilver](https://github.com/Sirius-Quantum/zilver)
   (Apache 2.0, Apple Silicon MLX/Metal)
4. **Kernel**: pairwise fidelity `K[i, j] = |⟨ψ(x_i) | ψ(x_j)⟩|²` populates the
   matrix
5. **Quantum-native targets**: optional `y_q` labels from the centered top
   eigenvector of K (Rayleigh-quotient relabeling) — algorithmic labels that
   capture quantum structure, not experimental outcomes

The result: every row of this dataset is one compound's quantum-similarity
profile against all the others, encoded in a representation no classical
fingerprint can produce.

## Encoding

| Property | Value |
|---|---|
| Encoding | `graph_hamiltonian` |
| Qubits | 25 |
| Feature dim | 30 |
| Compression | 1x |
| n_samples | 85 |
| Source dataset | `tdcommons/BBB_Martins` |

## Dataset Schema

Each row `i` contains the full kernel row `K[i, :]` as a list of floats.

| Column | Type | Description |
|---|---|---|
| `row_idx` | int | Sample index i |
| `kernel_row` | list[float] | K[i, j] for j = 0..n_samples-1 |

```python
from datasets import load_dataset
import numpy as np

ds = load_dataset("SiriusQuantum/bbbp-quantum-relabeled", split="train")

# Reconstruct kernel matrix
K = np.array(ds["kernel_row"])   # shape (n_samples, n_samples)
```


## QQ Benchmark — Quantum Community Baseline

First published quantum kernel benchmark on this dataset. Future methods
(QAOA, VQE, Ising, variational circuits) compare against this baseline.

| Metric | Value |
|---|---|
| Method | `graph_hamiltonian` |
| Qubits | 25 |
| Compression | 1x |
| KTA | 0.1199 |
| dim(g) | N/A |
| Kernel matrix shape | (85, 85) |

**Claim:** first published quantum kernel benchmark on `tdcommons/BBB_Martins`.
Encoding: graph_hamiltonian. n_qubits: 25. Compression: 1x.


## Kernel Quality

| Metric | Value | Interpretation |
|---|---|---|
| KTA | 0.1199 | kernel-target alignment (> 0 → discriminative) |
| dim(g) | N/A | DLA algebra dimension (Ragone 2024) |

## Use

How to leverage this kernel matrix:

- **Precomputed kernel for sklearn**: drop into `SVC(kernel='precomputed')`, `KernelRidge`, `SpectralClustering`, any kernel method — no further computation needed
- **Pre-training signal for molecular foundation models**: orthogonal to the SMILES masked-LM signal used by ChemBERTa / MolFormer; use as an additional training target
- **Classical vs quantum structural comparison**: reproduce the quality table above against your own classical fingerprint baseline (Morgan FP + RBF, etc.)
- **Few-shot benchmark substrate**: train a kernel classifier on a small fraction, evaluate generalization with held-out rows

## Methodology

1. Features extracted from `tdcommons/BBB_Martins`
2. Encoding: `graph_hamiltonian` → statevector |psi(x)> via numpy/Zilver/JAX backend
3. Kernel: K[i,j] = |<psi(x_i)|psi(x_j)>|^2 (fidelity)
4. Validated: KTA, concentration check (Thanasilp 2022), dim(g) (Ragone 2024)

## Citation

```bibtex
@software{relab2026,
  title  = {ReLab: Quantum-Native Re-Labeling Engine},
  author = {Sirius Quantum Solutions LTD},
  year   = {2026},
  url    = {https://github.com/Sirius-Quantum}
}
```