From 3f6ed17c11674af98def29bf77c174ce597cb90c Mon Sep 17 00:00:00 2001 From: qottmann Date: Mon, 11 Nov 2024 20:45:31 +0100 Subject: [PATCH] Fixed Depth Hamiltonian Simulation via Cartan Decomposition demo --- demonstrations/tutorial_fdhs.metadata.json | 114 +++++++++++++++++++++ demonstrations/tutorial_fdhs.py | 104 +++++++++++++++++++ 2 files changed, 218 insertions(+) create mode 100644 demonstrations/tutorial_fdhs.metadata.json create mode 100644 demonstrations/tutorial_fdhs.py diff --git a/demonstrations/tutorial_fdhs.metadata.json b/demonstrations/tutorial_fdhs.metadata.json new file mode 100644 index 0000000000..817ae86bf4 --- /dev/null +++ b/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 + } + ] +} diff --git a/demonstrations/tutorial_fdhs.py b/demonstrations/tutorial_fdhs.py new file mode 100644 index 0000000000..91b84aa04a --- /dev/null +++ b/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 `_, +# 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 `). +# 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 `__, 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 `__, 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 `__, 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 `__, 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 `__, 2023. +# +# .. [#Goh] +# +# Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Frédéric Sauvage +# "Lie-algebraic classical simulations for variational quantum computing" +# `arXiv:2308.01432 `__, 2023. +# +# .. [#Somma] +# +# Rolando D. Somma +# "Quantum Computation, Complexity, and Many-Body Physics" +# `arXiv:quant-ph/0512209 `__, 2005. +# +# + +############################################################################## +# About the author +# ---------------- +# .. include:: ../_static/authors/korbinian_kottmann.txt