Add demo on loading classical data with low-depth circuits (#1554)

**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

----
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](https://www.notion.so/xanaduai/Different-kinds-of-documentation-69200645fe59442991c71f9e7d8a77f8))
    
- [ ] Tutorial
- [x] Demo
- [ ] How-to

---------

Co-authored-by: Diego <67476785+DSGuala@users.noreply.github.com>
Co-authored-by: Daniela Angulo <42325731+daniela-angulo@users.noreply.github.com>
Co-authored-by: Diego <diego_guala@hotmail.com>

Author: 3 people

_static/demo_thumbnails/large_demo_thumbnails/pennylane-demo-loading-data-low-depth-large-thumbnail.png

@@ -0,0 +1,122 @@
+{
+  "title": "Loading classical data with low-depth circuits",
+  "authors": [
+    {
+      "username": "flokiwit"
+    },
+    {
+      "username": "bernhard"
+    },
+    {
+      "username": "criofrio"
+    }
+  ],
+  "executable_stable": true,
+  "executable_latest": true,
+  "dateOfPublication": "2025-12-04T00:00:00+00:00",
+  "dateOfLastModification": "2025-12-04T00:00:00+00:00",
+  "categories": [
+    "Quantum Machine Learning"
+  ],
+  "tags": [],
+  "previewImages": [
+    {
+      "type": "thumbnail",
+      "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/pennylane-demo-loading-data-low-depth-thumbnail.png"
+    },
+    {
+      "type": "large_thumbnail",
+      "uri": "/_static/demo_thumbnails/opengraph_demo_thumbnails/pennylane-demo-loading-data-low-depth-open-graph.png"
+    }
+  ],
+  "seoDescription": "This demo shows how to efficiently encode classical image data into quantum states using low-depth circuits, and train a variational quantum classifier on a low-depth MNIST dataset.",
+  "doi": "",
+  "references": [
+      {
+          "id": "kiwit2025",
+          "type": "article",
+          "title": "Typical Machine Learning Datasets as Low-Depth Quantum Circuits",
+          "authors": "Kiwit, F.J., Jobst, B., Luckow, A., Pollmann, F., Riofrío, C.A.",
+          "year": "2025",
+          "journal": "Quantum Sci. Technol.",
+          "doi": "10.1088/2058-9565/ae0123",
+          "url": "https://doi.org/10.1088/2058-9565/ae0123"
+      },
+      {
+          "id": "le2011a",
+          "type": "article",
+          "title": "A flexible representation of quantum images for polynomial preparation, image compression, and processing operations",
+          "authors": "Le, P.Q., Dong, F., Hirota, K.",
+          "year": "2011",
+          "journal": "Quantum Inf. Process",
+          "doi": "10.1007/s11128-010-0177-y",
+          "url": "https://doi.org/10.1007/s11128-010-0177-y"
+      },
+      {
+          "id": "le2011b",
+          "type": "other",
+          "title": "A Flexible Representation and Invertible Transformations for Images on Quantum Computers",
+          "authors": "Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.",
+          "year": "2011",
+          "booktitle": "New Advances in Intelligent Signal Processing. Studies in Computational Intelligence, vol 372",
+          "publisher": "Springer, Berlin, Heidelberg",
+          "doi": "10.1007/978-3-642-11739-8_9",
+          "url": "https://doi.org/10.1007/978-3-642-11739-8_9"
+      },
+      {
+          "id": "sun2011",
+          "type": "other",
+          "title": "A Multi-Channel Representation for Images on Quantum Computers Using the RGBα Color Space",
+          "authors": "Sun, B. et al.",
+          "year": "2011",
+          "booktitle": "2011 IEEE 7th International Symposium on Intelligent Signal Processing, Floriana, Malta",
+          "pages": "1–6",
+          "doi": "10.1109/WISP.2011.6051718",
+          "url": "https://doi.org/10.1109/WISP.2011.6051718"
+      },
+      {
+          "id": "sun2013",
+          "type": "article",
+          "title": "An RGB Multi-Channel Representation for Images on Quantum Computers",
+          "authors": "Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.",
+          "year": "2013",
+          "journal": "J. Adv. Comput. Intell. Intell. Inform.",
+          "volume": "17",
+          "number": "3",
+          "pages": "404–417",
+          "doi": "10.20965/jaciii.2013.p0404",
+          "url": "https://doi.org/10.20965/jaciii.2013.p0404"
+      },
+      {
+          "id": "jobst2024",
+          "type": "article",
+          "title": "Efficient MPS representations and quantum circuits from the Fourier modes of classical image data",
+          "authors": "Jobst, B., Shen, K., Riofrío, C.A., Shishenina, E., Pollmann, F.",
+          "year": "2024",
+          "journal": "Quantum",
+          "volume": "8",
+          "pages": "1544",
+          "doi": "10.22331/q-2024-12-03-1544",
+          "url": "https://doi.org/10.22331/q-2024-12-03-1544"
+      }
+  ],
+  "basedOnPapers": ["10.1088/2058-9565/ae0123"],
+  "referencedByPapers": [],
+  "relatedContent": [
+        {
+            "type": "demonstration",
+            "id": "tutorial_constant_depth_mps_prep",
+            "weight": 1.0
+        },
+        {
+            "type": "demonstration",
+            "id": "tutorial_adversarial_attacks_QML",
+            "weight": 1.0
+        },
+        {
+            "type": "demonstration",
+            "id": "tutorial_initial_state_preparation",
+            "weight": 0.8
+        }
+    ]
+}

_static/demo_thumbnails/opengraph_demo_thumbnails/pennylane-demo-loading-data-low-depth-open-graph.png

@@ -0,0 +1,2 @@
+autoray==0.8
+tqdm==4.67.1