SiriusQuantum/qm7b-quantum-relabeled

QM7b — Quantum-Relabeled Dataset

A quantum-relabeled edition of QM7b (Montavon et al. 2013, arXiv:1305.7074) — 7,211 small organic molecules with 14 computed quantum-chemistry properties (atomization energies, polarizabilities, HOMO/LUMO eigenvalues, ionization potentials, electron affinities, excitation energies) at PBE0 / ZINDO / GW / SCS levels of theory.

Each molecule carries its packed heavy-atom Coulomb-matrix features, the 14 original DFT-computed property targets, a derived HOMO–LUMO gap at GW level, and a quantum-native label y_q produced by a Heisenberg-model quantum kernel on a 7-qubit simulator. The kernel matrix K_q and the per-sample 1-RDM observables are precomputed and shipped alongside, so downstream consumers can train against quantum-geometric structure without running any quantum circuit themselves.

Produced by ReLab (Sirius Quantum), shipped in QParquet v1.0.

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Headline result

On the 6,041-molecule subset of QM7b with exactly 7 heavy atoms (C, N, O, S, Cl), N_train = 300 / N_test = 100 stratified by HOMO–LUMO-gap quartile, the quantum kernel exposes a label channel that classical kernels on the same Coulomb features cannot represent.

Quantum-kernel separation on a structural label channel

measurement	value	interpretation
accuracy of quantum-kernel SVC on a quantum-native label channel	0.95	quantum kernel fits its own geometric label direction
accuracy of classical-RBF SVC on the same labels	0.51 (chance)	classical RBF cannot represent that direction
prediction-accuracy advantage of quantum kernel over classical RBF on the label channel	+0.44	head-to-head separation on a structural label channel (Huang et al. 2021)
kernel-space geometric difference g(K_Q, K_RBF)	14.32 (sample-size reference √N = 17.32)	quantum and classical kernels are structurally distinct (Schuld 2024; Huang 2021 Fig. 1)
sample-complexity ratio s_classical / s_quantum derived from kernel-target alignment	~1,500×	quantum kernel needs ~1,500× less data to reach the same alignment on y_q

Shuffled-label null (n = 30 permutations of training labels, fixed test labels):

measurement	real	null (mean ± std)	z-score
quantum SVC accuracy	0.95	0.488 ± 0.068	+6.76
classical SVC accuracy	0.51	0.499 ± 0.058	+0.19
accuracy advantage	+0.44	−0.011 ± 0.088	+5.13

The quantum SVC accuracy is 6.8 σ above shuffled chance; the head-to-head advantage is 5.1 σ above the shuffled null. The classical SVC is at chance whether the training labels are shuffled or not, confirming y_q is genuinely quantum-geometric and not a memorisation artifact.

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Context — original-task regression (reportable, not the dataset's claim)

This dataset's value is the quantum-native label channel and the precomputed quantum kernel matrix. Original-task regression is included for context only and is not the dataset's claim: classical SoTA on QM7b properties uses learned representations (sGDML, SchNet, PaiNN) at MAE ≈ 0.05–0.1 eV with the full training set, well beyond what kernel ridge regression on packed Coulomb features can reach. The kernel matrix shipped here is built for quantum-geometric structure, not for absolute-property regression; consumers running regression should bring their own ML stack on top of the features and the quantum-native label channel.

For completeness, kernel ridge regression test-set MAE on the 14 original DFT properties + the derived HOMO–LUMO gap, with the quantum kernel K_q and classical-RBF kernel K_c on the same 28-dimensional packed Coulomb features (4× feature compression at 7 qubits):

target index	observed range	classical-RBF MAE	quantum-kernel MAE
T00 (atomization energy, PBE0)	−2213 to −410	119.25	408.31
T01 (polarizability, PBE0)	3.4 to 39.7	3.156	3.340
T02 (polarizability, SCS)	0.05 to 3.35	0.205	0.161
T03 (HOMO, GW)	−16.0 to −7.5	0.985	2.303
T04 (LUMO, GW)	−2.3 to +4.2	1.187	1.012
T05 (IP, ZINDO)	1.5 to 36.8	1.632	1.608
T06 (EA, ZINDO)	6.9 to 15.7	0.964	2.176
T07 (E1, ZINDO)	−4.0 to +2.9	1.322	1.103
T08 (Emax, ZINDO)	−10.95 to −5.12	0.613	1.572
T09 (Imax, ZINDO)	−3.81 to +0.41	0.621	0.527
T10 (HOMO, ZINDO)	−14.1 to −7.0	0.659	2.060
T11 (LUMO, ZINDO)	−1.84 to +1.96	0.405	0.370
T12 (uncertain — see column-mapping note)	2.53 to 17.17	0.741	2.851
T13 (uncertain — see column-mapping note)	2.43 to 16.46	0.599	3.049
gap_GW (LUMO_GW − HOMO_GW)	7.34 to 15.24	1.844	2.648

Pattern: the quantum kernel matches or beats classical RBF on six properties (T02 SCS polarizability, T04 LUMO_GW, T05 IP_ZINDO, T07 first ZINDO excitation, T09 Imax intensity, T11 LUMO_ZINDO) and underperforms on absolute-energy targets (atomization, HOMO eigenvalues, electron affinity, gap). Classical wins on arbitrary regression tasks out of the box (Schuld 2024); the dataset's quantum-relabeled value lives in the structural label channel above, not here.

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Column-mapping caveat — names array in source .mat is scrambled

The names field in the upstream qm7b.mat file is character-array corrupted by scipy.io.loadmat and is not human-readable as shipped. The 14 property indices in this datacard follow the canonical ordering from Montavon et al. 2013, Table 1 (arXiv:1305.7074).

Indices with unambiguous numeric ranges — T03 / T04 (HOMO / LUMO GW eigenvalues), T10 / T11 (HOMO / LUMO ZINDO) — are confidently labelled. T12 and T13 have positive ranges that do not match HOMO / LUMO PBE0 (eigenvalues should be negative for HOMO), so we mark them uncertain. Consumers needing exact column semantics should cross-reference Montavon 2013.

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What this dataset adds over a classical QM7b

field	classical QM7b	this dataset
Coulomb matrices + 14 property targets	✓	✓
packed heavy-atom features (28-D)	—	✓
K_q — precomputed quantum kernel matrix (N × N float32)	—	✓
y_q — quantum-native labels in {−1, +1}	—	✓
observables_1rdm — per-sample 1-RDM Pauli expectations	—	✓
derived gap_GW target	—	✓
validated schema + provenance metadata	—	✓

The added columns express geometric structure in a 7-qubit Hilbert space (a Heisenberg model on the molecular bond graph) that classical kernels on the same Coulomb features do not capture — the shuffled-null and head-to-head numbers above quantify how much.

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Schema (QParquet v1.0)

QParquet v1.0 ships a kernel-centric schema; classical features and targets remain joinable from the upstream QM7b source by input_id (SHA-1 of the packed Coulomb-matrix sub-vector, first 16 hex chars).

column	type	shape	description
row_idx	int64	(N,)	row index 0 … N−1, sorted on read
input_id	string	(N,)	stable per-sample identifier (SHA-1 of features_packed[i])
kernel_row	list	(N,) per row → (N, N) total	row of K_q — the quantum fidelity kernel matrix
labels_quantum	int8	(N, 1)	y_q ∈ {−1, +1} — quantum-native labels
observables_1rdm	list	(N, 21)	per-sample 1-RDM Pauli ⟨X_j⟩, ⟨Y_j⟩, ⟨Z_j⟩ for j ∈ [0, 7)
file-level qparquet_metadata	JSON (parquet key-value metadata)	—	encoding, n_qubits, backend, full evaluation report, per-property MAE table, shuffled-null z-scores, citations

Validation enforced at write time: K_q square, symmetric within atol = 1e-6, diagonal ≈ 1.0 within atol = 1e-3, input_ids unique, observables_1rdm shape (N, 3·n_qubits).

To recover the classical features and DFT property targets, join by input_id against the upstream QM7b .mat file (scipy.io.loadmat("qm7b.mat")); the hashing is deterministic on features_packed. The full classical view is not duplicated in this artifact — its value is the quantum-relabeled columns.

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Loading

import numpy as np
import pandas as pd
import pyarrow.parquet as pq
from sklearn.svm import SVC
from sklearn.kernel_ridge import KernelRidge

# QParquet v1.0 — read the kernel matrix and quantum labels
table = pq.read_table("qm7b_quantum.parquet")
df    = table.to_pandas()
K_q   = np.vstack(df["kernel_row"].to_numpy()).astype(np.float32)   # (N, N)
y_q   = np.vstack(df["labels_quantum"].to_numpy()).ravel().astype(np.int8)
input_ids = df["input_id"].tolist()

# File-level qparquet_metadata (encoding, evaluation, citations, …)
import json
meta = json.loads(table.schema.metadata[b"qparquet_metadata"].decode())

# Train on the quantum-native label channel
clf = SVC(kernel="precomputed", C=1.0).fit(K_q[:300], y_q[:300])
print(clf.score(K_q[300:, :300], y_q[300:]))

# Original-task regression: join with upstream QM7b for classical targets
# (download qm7b.mat from quantum-machine.org/data/qm7b.mat — link in metadata)

The dataset is a drop-in for scikit-learn precomputed-kernel pipelines: load K_q, train. No quantum hardware or simulator required at inference time.

To produce K_q and y_q for new molecules with the ReLab SDK:

import relab

# Quantum kernel matrix
K_q = relab.kernel(features_scaled, domain="molecular", n_qubits=7)

# Quantum-derived labels
y_q = relab.fit(features_scaled, domain="molecular", n_qubits=7)

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Methodology

• Encoding: a Heisenberg model on the molecular bond graph (XX + YY + ZZ couplings, one qubit per heavy atom). Coulomb off-diagonals J_ij map to bond couplings; diagonals h_i = ½ Z_i^2.4 map to local fields. Reference: arXiv:2407.14055 (Heisenberg encoding for graph-structured data).
• Why this encoding for molecular data: Coulomb sub-matrix entries are physics-native pairwise couplings — encoding them as quantum entanglement preserves the topological inductive bias that sorted-eigenspectrum representations (Rupp et al. 2012) destroy. Validated on QM7 atomization-energy regression prior to this dataset.
• Feature scaling: MinMaxScaler to [−π, π] per Schuld, Sweke, Meyer 2021 Fourier-bandwidth constraint.
• Quantum-label construction: generalised Rayleigh quotient on K_q against the classical-RBF kernel K_c, threshold at the median back-projection (Huang et al. 2021 §IV). Test-set extension via quantum-kernel interpolation — K_q is the only kernel that can faithfully generalise the quantum label direction.
• Backend: Apple Silicon Metal GPU via the Zilver MLX simulator (open-source v0.3.2). Statevector-exact at 7 qubits. Cross-verified against a pure-NumPy reference at atol = 1e-4.

What this kernel is, in plain language

The kernel compresses 28-dimensional Coulomb features into a 7-qubit Hilbert space and measures molecular similarity as the fidelity of two Heisenberg-evolved states. At seven qubits, the kernel is classically tractable in practice — the full N × N matrix is computable in tens of seconds on a laptop. The claim is compression and quantum-geometric structure, not asymptotic classical hardness. The geometry the kernel measures is not reproduced by RBF, polynomial, or cosine kernels on the same Coulomb features; that distinctness is what the head-to-head and shuffled-null numbers above quantify.

For the asymptotic-hardness question see Tang's body of work on dequantisation (arXiv:1807.04271; arXiv:1910.06151) and the QSVT framework (Gilyén, Su, Low, Wiebe 2019). The plain Heisenberg fidelity kernel is BQP-complete worst-case (Janzing & Wocjan 2007) but admits no published Tang-style classical sampling algorithm; we do not make an asymptotic-hardness claim at seven qubits. The QSVT spectral-filter upgrade — block-encoding the bond Hamiltonian and applying a HOMO–LUMO gap-midpoint projector polynomial — is provably not dequantisable (Lin & Tong 2020; Martyn et al. 2021) and is on the ReLab roadmap; it is not the kernel shipped in this dataset.

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Reproduction

Headline run:

• N_train = 300, N_test = 100, stratified across HOMO–LUMO-gap quartiles
• RNG seed = 42
• Backend: Apple Silicon (Zilver MLX/Metal simulator; cross-verified against a NumPy reference at atol = 1e-4)
• K_q for the full N = 400 Gram matrix computed in 8.6 s on a MacBook (Apple M-series, Zilver MLX/Metal). The kernel matrix and quantum-native labels are precomputed and shipped in the QParquet artifact, so consumers can train against K_q without re-simulating.

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Citation

@dataset{relab_qm7b_quantum_2026,
  title  = {QM7b — Quantum-Relabeled (QParquet v1.0)},
  author = {ReLab (Sirius Quantum)},
  year   = {2026},
  source = {derived from Montavon et al. 2013, arXiv:1305.7074},
  note   = {Quantum kernel matrix and quantum-native labels via a Heisenberg model on the molecular bond graph (7 qubits, one per heavy atom).}
}

If you build on this dataset, please also cite the upstream QM7b source (Montavon 2013) and the ReLab engine that generated the quantum-relabeled columns.

References

• Montavon, Rupp, Gobre, Vazquez-Mayagoitia, Hansen, Tkatchenko, Müller, von Lilienfeld 2013 — arXiv:1305.7074 — QM7b dataset
• Rupp, Tkatchenko, Müller, von Lilienfeld 2012 — arXiv:1109.2618 — Coulomb-matrix representation
• Huang et al. 2021 — arXiv:2011.01938 §IV — head-to-head benchmark, geometric difference threshold, sample-complexity bound
• Schuld, Sweke, Meyer 2021 — arXiv:2008.08605 — Fourier-bandwidth scaling
• Schuld 2024 — arXiv:2403.07059 — geometric advantage g(K_Q, K_C)
• Zhao et al. 2026 — arXiv:2604.07639 — compression-match framework
• Gilyén, Su, Low, Wiebe 2019 — arXiv:1806.01838 — QSVT
• Janzing & Wocjan 2007 — arXiv:quant-ph/0610203 — BQP-completeness of Hamiltonian overlap
• arXiv:2407.14055 — graph-Hamiltonian encoding for structured data