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Questions tagged [kernel-methods]

Kernel methods are a class of machine learning algorithms for pattern analysis (e.g. SVMs). Any linear model can be turned into a non-linear model by applying the kernel trick to the model, i.e. replacing its features with a kernel function. Quantum computers are expected to improve existing classical kernel-based ML methods through their ability to efficiently access and manipulate data in large quantum feature spaces, which is classically intractable.

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6 votes
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Is a "kernel" just the quantum equivalent of classical SVMs?

I'm confused about the relationship between kernel methods and SVM methods used in quantum machine learning. Sometimes the two seem to be used interchangeably, but often I'll see them both in the same ...
Jay Muntz's user avatar
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4 votes
1 answer
152 views

Why is the quantum kernel $\kappa(x,x')=|\langle\phi(x)|\phi(x')\rangle|^2$ defined with a square?

I've always wondered why the quantum kernel method \begin{equation}\label{QKM1} \kappa (x,x')=|\langle \phi(x) |\phi(x') \rangle {{|}^{2}} \end{equation} must be a square. After reading “Supervised ...
Ren-Xin Zhao's user avatar
3 votes
1 answer
2k views

How does the ZZ Feature Map influence the measurement?

I've been look at this Notebook from qiskit and trying to understand whats happening, but can't quite figure it out. From my understanding, rotations around the Z ...
Ricardo's user avatar
  • 189
3 votes
1 answer
79 views

Data input limitations (size) for QML

I have done quite a few Google/paper searches but did not found an answer. I would like to test the possibility of speeding up/ improving the accuracy of an existing unsupervised machine learning (...
Bill's user avatar
  • 31
3 votes
1 answer
141 views

Advantage of density matrix over vector to form quantum kernel

In Maria Schuld, Supervised quantum machine learning models are kernel methods, Section III.A, on page 6, the third paragraph from the bottom states While from a quantum physics perspective it seems ...
Hans's user avatar
  • 217
2 votes
2 answers
312 views

Quantum SVM with large feature set

I am trying to practice QSVM from the following tutorial Introduction into Quantum Support Vector Machines The author has used 2 feature_dimension with 2 component PCA ...
Protima Rani Paul's user avatar
1 vote
1 answer
87 views

Quantum neural networks and quantum kernels deal with nonlinearities

I'm trying to understand quantum neural networks from reading Alchieri et al.'s review paper. The following paragraph describes the differences between classical and quantum neural networks: Also, ...
Medulla Oblongata's user avatar
1 vote
1 answer
259 views

Kernel ridge regression with qiskit's FeatureMap shows nonlinear patterns outside [0,1] range

I'm implementing a kernel ridge regressor using qiskit's FeatureMap and QuantumKernel to compute the alpha parameters of the solution. If I try to fit my model with non-normalized features I obtain ...
akatief's user avatar
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1 vote
0 answers
43 views

How can I pass multiple embeddings in my function?

I have a problem with my code. I would like to try multiple embeddings in my kernel (I'm using the adjoint method). My idea is to pass them to the function and use them depending on what I pass. ...
BootBootBoot's user avatar
0 votes
1 answer
191 views

QuantumKernel.construct_circuit:How to automatically build a quantum kernel circuit according to the QISKIT file?

This link https://qiskit.org/documentation/machine-learning/stubs/qiskit_machine_learning.kernels.QuantumKernel.construct_circuit.html#qiskit_machine_learning.kernels.QuantumKernel.construct_circuit ...
Ren-Xin Zhao's user avatar
0 votes
0 answers
59 views

Quantum Kernel Method: If the input is the QK provided by the variable qiskit, is it still true?

The puzzle is from Case 1: https://qiskit.org/documentation/machine-learning/tutorials/03_quantum_kernel.html Case 2: https://qiskit.org/documentation/machine-learning/tutorials/...
Ren-Xin Zhao's user avatar
0 votes
0 answers
78 views

Quantum Kernel Machine Learning loss function and the plot of kernel?

When I was doing quantum machine learning, after building the quantum kernel, I drew the graph of the loss function changing with the iteration function and the graph of the quantum kernel, but I ...
Mistico013's user avatar