Contextuality demo (#719)

Demo: Contextuality and inductive bias in quantum machine learning

This is a demo for my recent paper https://arxiv.org/abs/2302.01365 

In the demo we study the toy learning problem described in the paper,
and build and train a quantum model that encodes the relevant inductive
bias. The model is shown to outperform a 'generic' quantum model that
does not encode this bias.

The demo is not focused much on contextuality (because it would require
a lot of explanation), but rather focuses on the type of learning
problem (inspired from contextuality) that is presented in the paper.

JAX is used for vectorization and JIT compilation.

---------

Co-authored-by: Ivana Kurecic <[email protected]>
Co-authored-by: Guillermo Alonso-Linaje <[email protected]>

demonstrations/tutorial_contextuality.metadata.json

@@ -0,0 +1,83 @@
+{
+    "title": "Contextuality and inductive bias in QML",
+    "authors": [
+        {
+            "id": "joseph_bowles"
+        }
+    ],
+    "dateOfPublication": "2023-09-06T00:00:00+00:00",
+    "dateOfLastModification": "2023-09-06T00:00:00+00:00",
+    "categories": [
+        "Quantum Machine Learning"
+    ],
+    "tags": [],
+    "previewImages": [
+        {
+            "type": "thumbnail",
+            "uri": "/_images/thumbnail_tutorial_Contextuality.png"
+        },
+        {
+            "type": "large_thumbnail",
+            "uri": "/_static/large_demo_thumbnails/thumbnail_large_Contextuality.png"
+        }
+    ],
+    "seoDescription": "Train a problem-inspired ansatz on a contextuality-inspired dataset.",
+    "doi": "",
+    "canonicalURL": "/qml/demos/tutorial_contextuality",
+    "references": [
+        {
+            "id": "paper",
+            "type": "article",
+            "title": "Contextuality and inductive bias in quantum machine learning.",
+            "authors": "J. Bowles, V. J. Wright, M. Farkas, N. Killoran, M. Schuld",
+            "year": "2023",
+            "journal": "",
+            "url": "https://arxiv.org/abs/2302.01365"
+        },
+        {
+            "id": "contextuality",
+            "type": "article",
+            "title": "Contextuality for preparations, transformations, and unsharp measurements.",
+            "authors": "R. W. Spekkens",
+            "year": "2005",
+            "journal": "Phys. Rev. A 71",
+            "url": "https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.052108"
+        },
+        {
+            "id": "reptheory",
+            "type": "article",
+            "title": "Representation Theory for Geometric Quantum Machine Learning.",
+            "authors": "M. Ragone, P. Braccia, Q. T. Nguyen, L. Schatzki, P. J. Coles, F. Sauvage, M. Larocca, M. Cerezo",
+            "year": "2023",
+            "journal": "",
+            "url": "https://arxiv.org/abs/2210.07980"
+        },
+        {
+            "id": "equivariant",
+            "type": "article",
+            "title": "Theory for Equivariant Quantum Neural Networks.",
+            "authors": "Q. T. Nguyen, L. Schatzki, P. Braccia, M. Ragone, P. J. Coles, F. Sauvage, M. Larocca, M. Cerezo",
+            "year": "2022",
+            "journal": "",
+            "url": "https://arxiv.org/abs/2210.08566"
+        },
+        {
+            "id": "surrogates",
+            "type": "article",
+            "title": "Classical surrogates for quantum learning models.",
+            "authors": "F. J. Schreiber, J. Eiser, J. J. Meyer",
+            "year": "2022",
+            "journal": "",
+            "url": "https://arxiv.org/abs/2206.11740"
+        }
+    ],
+    "basedOnPapers": [],
+    "referencedByPapers": [],
+    "relatedContent": [
+        {
+            "type": "demonstration",
+            "id": "tutorial_geometric_qml",
+            "weight": 1.0
+        }
+    ]
+}