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.

[DSGuala]

I wouldn't mind getting a bit more information about what we will discuss. For example, we can include a verb in each item of the list:

1. Define how images can be encoded in quantum states
2. Introduce low-depth image circuits to generate these states
3. ...

(just examples, no need to use those)

[fkiwit]

I like this idea! Added in the latest commit.

[DSGuala]

We can link the datasets page in here somewhere https://pennylane.ai/datasets/collection/low-depth-image-circuits

[fkiwit]

I think that's a good spot to reference the dataset, also added :)

[daniela-angulo]

not properly formatted, :math: and so on

[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

[daniela-angulo]

Suggested change

	# practical quantum machine learning approaches.
	#
	######################################################################
	# References
	# ----------
	# practical quantum machine learning approaches.
	#
	#
	# References
	# ----------

[daniela-angulo]

for some reason, the References section is rendering without the underscore line. I am suggesting a few things to fix it

[daniela-angulo]

Suggested change

	# Conclusion
	# ~~~~~~~~~~
	#
	# | In this notebook we have demonstrated the use of low-depth quantum circuits to load and
	# subsequently classify (a subset of) the MNIST dataset.
	# | By filtering to specific target labels, constructing parametrized circuits from the provided
	# layouts, and evaluating their states and fidelities, we have gained hands-on experience with
	# quantum machine learning workflows on real data encodings.
	# Conclusion
	# ~~~~~~~~~~
	#
	# In this notebook we have demonstrated the use of low-depth quantum circuits to load and
	# subsequently classify (a subset of) the MNIST dataset.
	# By filtering to specific target labels, constructing parametrized circuits from the provided
	# layouts, and evaluating their states and fidelities, we have gained hands-on experience with
	# quantum machine learning workflows on real data encodings.