micro-mass-amplitude-kernel

Amplitude quantum kernel Gram matrix for the micro-mass mass spectrometry dataset, produced by Sirius Quantum.

K[i,j] = |⟨ψ(x_i)|ψ(x_j)⟩|² — Hilbert-Schmidt fidelity in quantum feature space.

Compression Benchmark

At 162x fewer dimensions, the amplitude kernel achieves 92.2% accuracy versus 93.6% with full features. Qualifies under the oracle sketching criterion (Zhao et al. 2026, arXiv:2604.07639): compression ratio > 10x with comparable accuracy.

	Method	Features	Accuracy
Classical baseline	SVM-linear	1300	93.6%
Quantum kernel	SVM-amplitude	8 qubits	92.2%
Delta		162x compression	-1.4%

Claim: 8-qubit amplitude kernel achieves 92.2% on 10-class mass spectrometry identification at 162x compression, within 1.4% of SVM-linear on all 1300 features.

QQ Benchmark: Quantum Community Baseline

First published quantum kernel benchmark on micro-mass. Future quantum methods (QAOA, VQE, variational circuits, tensor networks) compare against this baseline.

Property	Value
Method	amplitude / 8q / SVM / oracle-sketching
Encoding	Amplitude (Hilbert-Schmidt fidelity)
Qubits	8
Compression	162x (1300 features to 8 qubits)
Kernel	K(x,x') = |⟨ψ(x)|ψ(x')⟩|²
CV protocol	StratifiedKFold(n_splits=5, shuffle=True, seed=42)
QQ score	92.2% accuracy (10-class)

Dataset Schema

Each row i contains the full kernel row K[i, :] as a list of floats. Reconstruct the full (360, 360) Gram matrix as shown below.

Column	Type	Description
row_idx	int	Sample index i
kernel_row	list[float]	K[i, j] for j = 0..359

Usage

from datasets import load_dataset
import numpy as np
from sklearn.svm import SVC

ds = load_dataset("SiriusQuantum/micro-mass-amplitude-kernel", split="train")

# Reconstruct kernel matrix
K = np.array(ds["kernel_row"])   # shape (360, 360)

# Train SVM on precomputed kernel
svm = SVC(kernel="precomputed", C=1.0)
svm.fit(K[train_idx][:, train_idx], y[train_idx])
preds = svm.predict(K[test_idx][:, train_idx])

Scientific Basis

Encoding: Amplitude (Lloyd, Schuld 2020, arXiv:2001.03622)

• K(x,x') = |⟨ψ(x)|ψ(x')⟩|² (Hilbert-Schmidt fidelity kernel)
• Theoretically optimal when classes are separated in Hilbert space
• Scale-invariant: StandardScaler output feeds directly, no aliasing

Compression claim basis: Oracle Sketching (Zhao et al. 2026, arXiv:2604.07639)

• Polylogarithmic quantum machines match exponentially larger classical machines
• Criterion: compression ratio > 10x with comparable accuracy (<=5% loss)
• micro-mass: 162x compression, 1.4% accuracy loss. Both criteria satisfied.

Reproduce

Kernel matrix was produced with the ReLab engine, a quantum-native data layer for physical AI.

import relab

# One call. Quantum kernel matrix from 1300 features compressed to 8 qubits.
K = relab.kernel(X, n_qubits=8, encoding="amplitude")

SDK not yet public. Contact Sirius Quantum for early access.

Citation

If you use this kernel, cite Sirius Quantum:

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

Key references:

@article{lloyd2020quantum,
  title   = {Quantum embeddings for machine learning},
  author  = {Lloyd, Seth and Schuld, Maria and others},
  journal = {arXiv:2001.03622},
  year    = {2020}
}

@article{zhao2026sketching,
  title   = {Quantum oracle sketching},
  author  = {Zhao et al.},
  journal = {arXiv:2604.07639},
  year    = {2026}
}