Fixed Depth Hamiltonian Simulation via Cartan Decomposition demo

demonstrations/tutorial_fdhs.metadata.json

@@ -0,0 +1,114 @@
+{
+    "title": "Fixed Depth Hamiltonian Simulation via Cartan Decomposition",
+    "authors": [
+        {
+            "username": "Qottmann"
+        }
+    ],
+    "dateOfPublication": "2024-02-27T00:00:00+00:00",
+    "dateOfLastModification": "2024-10-07T00:00:00+00:00",
+    "categories": [
+        "Quantum Computing"
+    ],
+    "tags": [],
+    "previewImages": [
+        {
+            "type": "thumbnail",
+            "uri": "/_static/demonstration_assets/liealgebra/thumbnail_liealgebra.png"
+        },
+        {
+            "type": "large_thumbnail",
+            "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_liealgebra.png"
+        }
+    ],
+    "seoDescription": "A quick summary of arXiv:2104.00728, 'Fixed Depth Hamiltonian Simulation via Cartan Decomposition' with code implementations in PennyLane.",
+    "doi": "",
+    "references": [
+        {
+            "id": "Wiersema",
+            "type": "preprint",
+            "title": "Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension",
+            "authors": "Roeland Wiersema, Efekan Kökcü, Alexander F. Kemper, Bojko N. Bakalov",
+            "year": "2023",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2309.05690",
+            "url": "https://arxiv.org/abs/2309.05690"
+        },
+        {
+            "id": "Meyer",
+            "type": "article",
+            "title": "Exploiting symmetry in variational quantum machine learning",
+            "authors": "Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, Jens Eisert",
+            "year": "2022",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2205.06217",
+            "url": "https://arxiv.org/abs/2205.06217"
+        },
+        {
+            "id": "Nguyen",
+            "type": "preprint",
+            "title": "Theory for Equivariant Quantum Neural Networks",
+            "authors": "Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone, Patrick J. Coles, Frederic Sauvage, Martin Larocca, M. Cerezo",
+            "year": "2022",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2210.08566",
+            "url": "https://arxiv.org/abs/2210.08566"
+        },
+        {
+            "id": "Fontana",
+            "type": "article",
+            "title": "The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze",
+            "authors": "Enrico Fontana, Dylan Herman, Shouvanik Chakrabarti, Niraj Kumar, Romina Yalovetzky, Jamie Heredge, Shree Hari Sureshbabu, Marco Pistoia",
+            "year": "2023",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2309.07902",
+            "url": "https://arxiv.org/abs/2309.07902"
+        },
+        {
+            "id": "Ragone",
+            "type": "preprint",
+            "title": "A Unified Theory of Barren Plateaus for Deep Parametrized Quantum Circuits",
+            "authors": "Michael Ragone, Bojko N. Bakalov, Frédéric Sauvage, Alexander F. Kemper, Carlos Ortiz Marrero, Martin Larocca, M. Cerezo",
+            "year": "2023",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2309.09342",
+            "url": "https://arxiv.org/abs/2309.09342"
+        },
+        {
+            "id": "Goh",
+            "type": "preprint",
+            "title": "Lie-algebraic classical simulations for variational quantum computing",
+            "authors": "Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Frédéric Sauvage",
+            "year": "2023",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.2308.01432",
+            "url": "https://arxiv.org/abs/2308.01432"
+        },
+        {
+            "id": "Somma",
+            "type": "preprint",
+            "title": "Quantum Computation, Complexity, and Many-Body Physics",
+            "authors": "Rolando D. Somma",
+            "year": "2005",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arXiv.quant-ph/0512209",
+            "url": "https://arxiv.org/abs/quant-ph/0512209"
+        }
+    ],
+    "basedOnPapers": [],
+    "referencedByPapers": [],
+    "relatedContent": [
+        {
+            "type": "demonstration",
+            "id": "tutorial_geometric_qml",
+            "weight": 1.0
+        }
+    ]
+}

demonstrations/tutorial_fdhs.py

@@ -0,0 +1,104 @@
+r"""Fixed Depth Hamiltonian Simulation via Cartan Decomposition
+===============================================================
+
+abstract
+
+Introduction
+------------
+
+
+"""
+import numpy as np
+import pennylane as qml
+from pennylane import X, Y, Z
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+
+##############################################################################
+# 
+#
+
+
+##############################################################################
+# 
+# Conclusion
+# ----------
+#
+# With this introduction, we hope to clarify some terminology, introduce the basic concepts of Lie theory and motivate their relevance in quantum physics by touching on universality and symmetries.
+# While Lie theory and symmetries are playing a central role in established fields such as quantum phase transitions (see note above) and `high energy physics <https://en.wikipedia.org/wiki/Standard_Model>`_,
+# they have recently also emerged in quantum machine learning with the onset of geometric quantum machine learning [#Meyer]_ [#Nguyen]_
+# (see our recent :doc:`introduction to geometric quantum machine learning <tutorial_geometric_qml>`).
+# Further, DLAs have recently become instrumental in classifying criteria for barren plateaus [#Fontana]_ [#Ragone]_ and designing simulators based on them [#Goh]_.
+#
+
+
+
+##############################################################################
+# 
+# References
+# ----------
+#
+# .. [#Wiersma]
+#
+#     Roeland Wiersema, Efekan Kökcü, Alexander F. Kemper, Bojko N. Bakalov
+#     "Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension"
+#     `arXiv:2309.05690 <https://arxiv.org/abs/2309.05690>`__, 2023.
+#
+# .. [#Meyer]
+#
+#     Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, Jens Eisert
+#     "Exploiting symmetry in variational quantum machine learning"
+#     `arXiv:2205.06217 <https://arxiv.org/abs/2205.06217>`__, 2022.
+#
+# .. [#Nguyen]
+#
+#     Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone, Patrick J. Coles, Frederic Sauvage, Martin Larocca, M. Cerezo
+#     "Theory for Equivariant Quantum Neural Networks"
+#     `arXiv:2210.08566 <https://arxiv.org/abs/2210.08566>`__, 2022.
+#
+# .. [#Fontana]
+#
+#     Enrico Fontana, Dylan Herman, Shouvanik Chakrabarti, Niraj Kumar, Romina Yalovetzky, Jamie Heredge, Shree Hari Sureshbabu, Marco Pistoia
+#     "The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze"
+#     `arXiv:2309.07902 <https://arxiv.org/abs/2309.07902>`__, 2023.
+#
+# .. [#Ragone]
+#
+#     Michael Ragone, Bojko N. Bakalov, Frédéric Sauvage, Alexander F. Kemper, Carlos Ortiz Marrero, Martin Larocca, M. Cerezo
+#     "A Unified Theory of Barren Plateaus for Deep Parametrized Quantum Circuits"
+#     `arXiv:2309.09342 <https://arxiv.org/abs/2309.09342>`__, 2023.
+#
+# .. [#Goh]
+#
+#     Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Frédéric Sauvage
+#     "Lie-algebraic classical simulations for variational quantum computing"
+#     `arXiv:2308.01432 <https://arxiv.org/abs/2308.01432>`__, 2023.
+#
+# .. [#Somma]
+#
+#     Rolando D. Somma
+#     "Quantum Computation, Complexity, and Many-Body Physics"
+#     `arXiv:quant-ph/0512209 <https://arxiv.org/abs/quant-ph/0512209>`__, 2005.
+#
+#
+
+##############################################################################
+# About the author
+# ----------------
+# .. include:: ../_static/authors/korbinian_kottmann.txt