Quantum Kernels, Noise, and Examples

Quantum kernels are useful for small-sample supervised learning, clustering, dimensionality reduction, and anomaly detection. Noise components evaluate the effects of channel noise and readout error on a model. This page also includes runnable example entry points.

Quantum kernels

import torch
from unitarylab.library.qml.kernels import OverlapKernel, kernel_matrix
 
x = torch.tensor([
    [0.0, 0.2],
    [0.3, -0.1],
    [0.8, 0.4],
], dtype=torch.float64)
 
kernel = OverlapKernel(num_qubits=2)
gram = kernel_matrix(x, kernel=kernel)
print(gram)

The training Gram matrix must be square. For prediction, the second dimension of the cross-kernel matrix must correspond to the training samples. Finite shots or numerical error may make the matrix not exactly symmetric positive semidefinite; symmetrize it and use closest_psd_matrix() when correction is needed.

Noise and readout error

from unitarylab.library.qml.noise import (
    DepolarizingChannel,
    NoiseModel,
    ReadoutErrorModel,
    mitigate_readout_probabilities,
)
 
noise = NoiseModel()
noise.add(DepolarizingChannel(probability=0.01), wires=(0, 1))

Built-in channels include BitFlipChannel, PhaseFlipChannel, AmplitudeDampingChannel, and DepolarizingChannel. NoiseModel associates channels with circuit locations or gate conditions. ReadoutErrorModel describes measurement confusion; mitigate_readout_probabilities() corrects probabilities using a calibration model.

Probability parameters must be within valid ranges. Error mitigation may produce small negative components or amplify statistical noise; check normalization and physical bounds. Noise models do not replace calibration on a real device. Report a noise-free baseline, shots, and random seed when comparing models.

PyTorch integration example

import torch
from unitarylab.library.qml.examples.classification import build_classifier
 
module = build_classifier("reuploading", seed=0)
x = torch.zeros((2, 4), dtype=torch.float64)
logits = module(x)
print(logits.shape)

Example subpackages provide these entry points:

Examples help validate installation and workflows; they do not define optimal hyperparameters for a particular dataset. For production training, create a separate validation set, record experiment settings, and increase data and circuit sizes gradually.

Common errors

• Feature count does not match the encoding layer: scale, select, or pad features first.
• PyTorch input and model parameter dtype/device differ: convert them consistently before training.
• Classification labels are not integer class indices, or the class count does not match the output dimension.
• Too few shots cause large fluctuations in kernel matrices and gradients.
• Selecting kernels, noise strengths, or model hyperparameters on the test set causes data leakage.

Related pages

• QML Overview and Backends
• Data, Circuit Layers, and Models
• Training, Execution, and Evaluation