Add demo on loading classical data with low-depth circuits

[fkiwit]

Title:
Add demo on loading classical data with low-depth circuits

Summary:
This pull request adds a new demonstration on how to efficiently load classical image data into quantum states using low-depth quantum circuits, based on the paper "Typical Machine Learning Datasets as Low‑Depth Quantum Circuits". The demo uses the MNIST dataset and shows how to train a variational quantum classifier on the encoded data. This demo leverages the new qml.data module for dataset loading.

Relevant references:

• "Typical Machine Learning Datasets as Low‑Depth Quantum Circuits" (2025) [1]
• "A flexible representation of quantum images for polynomial preparation, image compression, and processing operations" [2, 3]
• "A Multi-Channel Representation for images on quantum computers using the RGBα color space" [4, 5]
• "Efficient MPS representations and quantum circuits from the Fourier modes of classical image data" [6]

Possible Drawbacks:
The dataset required for this demo is large (~1GB), which might be a consideration for users with limited bandwidth or storage.

Related GitHub Issues:
None

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If you are writing a demonstration, please answer these questions to facilitate the marketing process.

• GOALS — Why are we working on this now?

Promote the new qml.data feature for loading datasets and show a PennyLane implementation of a recent paper on efficient data loading for QML.

• AUDIENCE — Who is this for?

QML researchers, students, and practitioners interested in efficient data loading techniques and their application to image classification tasks.

• KEYWORDS — What words should be included in the marketing post?

Quantum Machine Learning, Quantum Datasets, Image Loading, Low-depth circuits, Variational Quantum Classifier, MNIST, PennyLane, qml.data

• Which of the following types of documentation is most similar to your file?
  (more details here)

• Tutorial
• Demo
• How-to

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[DSGuala]

Made an initial skim and left comments. Overall a very nice/complete first draft.

Still pending from my side:

• In depth review of the text for clarity
• In depth review of the code for efficiency and output

But basically I think 1 or two more rounds of review and this should be ready to go.

[daniela-angulo]

not properly formatted, :math: and so on

[fkiwit]

ah true, thanks for checking! I think Diego made a change and it should be fixed now

[daniela-angulo]

Suggested change

	# shows minor blurring. By selecting a deeper circuit the quality of the reconstructed images could be
	# shows minor blurring. By selecting a deeper, circuit the quality of the reconstructed images could be

[fkiwit]

Thanks for catching this, but I think the original version was right. Deeper is just an adjective modifying circuit.