From 093668d2abc7b3096baed31781b2f4c536812c1b Mon Sep 17 00:00:00 2001 From: Michael Vu Date: Tue, 16 Jul 2024 08:50:42 -0400 Subject: [PATCH] sync master to dev (#1161) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit merges changes from `master` into `dev`. # motivation #1155 merged `dev` to `master` with modifications, but these modifications did not make their way into `dev`. This PR does exactly that. --------- Co-authored-by: Astral Cai Co-authored-by: GitHub Nightly Merge Action Co-authored-by: Mudit Pandey Co-authored-by: Christina Lee Co-authored-by: Romain Moyard Co-authored-by: Matthew Silverman Co-authored-by: lillian542 <38584660+lillian542@users.noreply.github.com> Co-authored-by: Tom Bromley <49409390+trbromley@users.noreply.github.com> Co-authored-by: Josh Izaac Co-authored-by: Rashid N H M <95639609+rashidnhm@users.noreply.github.com> Co-authored-by: Guillermo Alonso-Linaje <65235481+KetpuntoG@users.noreply.github.com> Co-authored-by: soranjh <40344468+soranjh@users.noreply.github.com> Co-authored-by: CatalinaAlbornoz Co-authored-by: Jay Soni Co-authored-by: soranjh Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> Co-authored-by: Diego <67476785+DSGuala@users.noreply.github.com> Co-authored-by: Utkarsh Co-authored-by: Stepan Fomichev Co-authored-by: soranjh Co-authored-by: Alvaro Ballon <91897656+alvaro-at-xanadu@users.noreply.github.com> Co-authored-by: Diego Co-authored-by: Lee J. O'Riordan Co-authored-by: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com> Co-authored-by: DanielNino27 <92994693+DanielNino27@users.noreply.github.com> Co-authored-by: Paul Finlay <50180049+doctorperceptron@users.noreply.github.com> Co-authored-by: ashishks0522 Co-authored-by: Mikhail Andrenkov Co-authored-by: David Wierichs Co-authored-by: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com> Co-authored-by: Ivana Kurečić Co-authored-by: Gopal Ramesh Dahale <49199003+Gopal-Dahale@users.noreply.github.com> Co-authored-by: Sankalp Sanand Co-authored-by: Ivana Kurečić Co-authored-by: Austin Huang <65315367+austingmhuang@users.noreply.github.com> Co-authored-by: Isaac De Vlugt <34751083+isaacdevlugt@users.noreply.github.com> Co-authored-by: WrathfulSpatula Co-authored-by: Olivia Di Matteo <2068515+glassnotes@users.noreply.github.com> Co-authored-by: Pietropaolo Frisoni Co-authored-by: Ahmed Darwish --- .github/workflows/upload-text.yml | 7 +- README.md | 2 +- _static/authors/ara_ghukasyan.jpeg | Bin 0 -> 63812 bytes _static/authors/ara_ghukasyan.txt | 6 + _static/authors/dan_strano.txt | 4 +- _static/authors/gopal_ramesh_dahale.jpeg | Bin 0 -> 40138 bytes _static/authors/gopal_ramesh_dahale.txt | 4 + _static/authors/isaac_de_vlugt.jpeg | Bin 0 -> 194632 bytes _static/authors/isaac_de_vlugt.txt | 4 + .../covalent_cloud_gpu_19_1.png | Bin 0 -> 36050 bytes .../thumbnail_covalent_cloud_gpu.png | Bin 0 -> 20147 bytes .../pl_real_world_example.png | Bin 0 -> 15705 bytes .../qiskit_parameterized_circuit.png | Bin 0 -> 6634 bytes _static/demonstration_assets/liesim/Ue.png | Bin 0 -> 7553 bytes _static/demonstration_assets/liesim/e.png | Bin 0 -> 6854 bytes .../liesim/thumbnail_gsim.png | Bin 0 -> 6959 bytes _static/demonstration_assets/liesim/wUe.png | Bin 0 -> 10039 bytes .../liesim_extension/2P_first_second.png | Bin 0 -> 51792 bytes .../liesim_extension/2P_fourth.png | Bin 0 -> 47335 bytes .../liesim_extension/2P_thirds.png | Bin 0 -> 77911 bytes .../liesim_extension/first_order_diagram.png | Bin 0 -> 34695 bytes .../liesim_extension/first_split.png | Bin 0 -> 24079 bytes .../liesim_extension/thumbnail_liesim3.png | Bin 0 -> 51792 bytes .../thumbnail_liesim_extension.png | Bin 0 -> 10903 bytes .../mapping/long_image.png | Bin 0 -> 789216 bytes .../mapping/thumbnail_mapping_2024-06-20.png | Bin 0 -> 38610 bytes ..._QuantumCircuitBornMachines_2024-05-13.png | Bin 0 -> 49215 bytes ..._QuantumCircuitBornMachines_2024-05-13.png | Bin 0 -> 12340 bytes _static/demonstration_assets/qrack/fig1.png | Bin 0 -> 53787 bytes _static/demonstration_assets/qrack/fig2.png | Bin 0 -> 44789 bytes _static/demonstration_assets/qrack/fig3.png | Bin 0 -> 39881 bytes _static/demonstration_assets/qrack/fig4.png | Bin 0 -> 34699 bytes _static/demonstration_assets/qrack/fig5.png | Bin 0 -> 57003 bytes _static/demonstration_assets/qrack/fig6.png | Bin 0 -> 58082 bytes .../qrack_catalyst_integration_shelf.png | Bin 0 -> 361000 bytes .../thumbnail_HowToUseQiskit1WithPL.png | Bin 0 -> 33314 bytes .../thumbnail_qrack_catalyst_integration.png | Bin 0 -> 25770 bytes _static/hardware_logos/covalent.png | Bin 0 -> 5322 bytes .../thumbnail_large_HowToUseQiskit1WithPL.png | Bin 0 -> 138669 bytes ..._QuantumCircuitBornMachines_2024-05-13.png | Bin 0 -> 52618 bytes .../thumbnail_large_covalent_cloud_gpu.png | Bin 0 -> 82619 bytes .../thumbnail_large_gsim.png | Bin 0 -> 29608 bytes .../thumbnail_large_liesim_extension.png | Bin 0 -> 42624 bytes .../thumbnail_large_mapping_2024-06-20.png | Bin 0 -> 153880 bytes ...bnail_large_qrack_catalyst_integration.png | Bin 0 -> 111702 bytes demonstrations/ahs_aquila.metadata.json | 2 +- .../braket-parallel-gradients.metadata.json | 2 +- .../covalent_cloud_gpu.metadata.json | 57 ++ demonstrations/covalent_cloud_gpu.py | 372 +++++++++++ ...o_use_qiskit1_with_pennylane.metadata.json | 52 ++ .../how_to_use_qiskit1_with_pennylane.py | 434 +++++++++++++ demonstrations/qrack.metadata.json | 70 +++ demonstrations/qrack.py | 460 ++++++++++++++ demonstrations/quantum_volume.metadata.json | 2 +- ...ircuits_with_tensor_networks.metadata.json | 4 +- .../tutorial_adaptive_circuits.metadata.json | 2 +- demonstrations/tutorial_block_encoding.py | 1 - .../tutorial_chemical_reactions.metadata.json | 2 +- ...rial_classically_boosted_vqe.metadata.json | 2 +- .../tutorial_diffable_shadows.metadata.json | 2 +- .../tutorial_differentiable_HF.metadata.json | 2 +- .../tutorial_error_mitigation.metadata.json | 2 +- .../tutorial_general_parshift.metadata.json | 2 +- demonstrations/tutorial_general_parshift.py | 4 +- .../tutorial_grovers_algorithm.metadata.json | 2 +- demonstrations/tutorial_grovers_algorithm.py | 20 +- ...al_initial_state_preparation.metadata.json | 2 +- .../tutorial_lcu_blockencoding.metadata.json | 2 +- demonstrations/tutorial_lcu_blockencoding.py | 2 +- demonstrations/tutorial_liealgebra.py | 1 - demonstrations/tutorial_liesim.metadata.json | 164 +++++ demonstrations/tutorial_liesim.py | 486 +++++++++++++++ .../tutorial_liesim_extension.metadata.json | 99 +++ demonstrations/tutorial_liesim_extension.py | 539 ++++++++++++++++ demonstrations/tutorial_mapping.metadata.json | 6 +- demonstrations/tutorial_mapping.py | 28 +- .../tutorial_mcm_introduction.metadata.json | 2 +- demonstrations/tutorial_mcm_introduction.py | 18 +- .../tutorial_mol_geo_opt.metadata.json | 2 +- .../tutorial_phase_kickback.metadata.json | 2 +- demonstrations/tutorial_phase_kickback.py | 2 +- demonstrations/tutorial_qcbm.metadata.json | 96 +++ demonstrations/tutorial_qcbm.py | 576 ++++++++++++++++++ .../tutorial_qft_arithmetics.metadata.json | 2 +- demonstrations/tutorial_qft_arithmetics.py | 2 +- .../tutorial_quantum_chemistry.metadata.json | 2 +- .../tutorial_qubit_tapering.metadata.json | 2 +- ...tutorial_resource_estimation.metadata.json | 2 +- demonstrations/tutorial_spsa.metadata.json | 2 +- .../tutorial_univariate_qvr.metadata.json | 11 +- demonstrations/tutorial_univariate_qvr.py | 2 - demonstrations/tutorial_vqe.metadata.json | 2 +- notebook_converter/notebook_to_demo.py | 4 +- 93 files changed, 3514 insertions(+), 67 deletions(-) create mode 100644 _static/authors/ara_ghukasyan.jpeg create mode 100644 _static/authors/ara_ghukasyan.txt create mode 100644 _static/authors/gopal_ramesh_dahale.jpeg create mode 100644 _static/authors/gopal_ramesh_dahale.txt create mode 100644 _static/authors/isaac_de_vlugt.jpeg create mode 100644 _static/authors/isaac_de_vlugt.txt create mode 100644 _static/demonstration_assets/covalent_cloud_gpu/covalent_cloud_gpu_19_1.png create mode 100644 _static/demonstration_assets/covalent_cloud_gpu/thumbnail_covalent_cloud_gpu.png create mode 100644 _static/demonstration_assets/how_to_use_qiskit_1_with_pennylane/pl_real_world_example.png create mode 100644 _static/demonstration_assets/how_to_use_qiskit_1_with_pennylane/qiskit_parameterized_circuit.png create mode 100644 _static/demonstration_assets/liesim/Ue.png create mode 100644 _static/demonstration_assets/liesim/e.png create mode 100644 _static/demonstration_assets/liesim/thumbnail_gsim.png create mode 100644 _static/demonstration_assets/liesim/wUe.png create mode 100644 _static/demonstration_assets/liesim_extension/2P_first_second.png create mode 100644 _static/demonstration_assets/liesim_extension/2P_fourth.png create mode 100644 _static/demonstration_assets/liesim_extension/2P_thirds.png create mode 100644 _static/demonstration_assets/liesim_extension/first_order_diagram.png create mode 100644 _static/demonstration_assets/liesim_extension/first_split.png create mode 100644 _static/demonstration_assets/liesim_extension/thumbnail_liesim3.png create mode 100644 _static/demonstration_assets/liesim_extension/thumbnail_liesim_extension.png create mode 100644 _static/demonstration_assets/mapping/long_image.png create mode 100644 _static/demonstration_assets/mapping/thumbnail_mapping_2024-06-20.png create mode 100644 _static/demonstration_assets/qcbm/OGthumbnail_large_QuantumCircuitBornMachines_2024-05-13.png create mode 100644 _static/demonstration_assets/qcbm/thumbnail_QuantumCircuitBornMachines_2024-05-13.png create mode 100644 _static/demonstration_assets/qrack/fig1.png create mode 100644 _static/demonstration_assets/qrack/fig2.png create mode 100644 _static/demonstration_assets/qrack/fig3.png create mode 100644 _static/demonstration_assets/qrack/fig4.png create mode 100644 _static/demonstration_assets/qrack/fig5.png create mode 100644 _static/demonstration_assets/qrack/fig6.png create mode 100644 _static/demonstration_assets/qrack/qrack_catalyst_integration_shelf.png create mode 100644 _static/demonstration_assets/regular_demo_thumbnails/thumbnail_HowToUseQiskit1WithPL.png create mode 100644 _static/demonstration_assets/regular_demo_thumbnails/thumbnail_qrack_catalyst_integration.png create mode 100644 _static/hardware_logos/covalent.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_HowToUseQiskit1WithPL.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_QuantumCircuitBornMachines_2024-05-13.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_covalent_cloud_gpu.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_gsim.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_liesim_extension.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_mapping_2024-06-20.png create mode 100644 _static/large_demo_thumbnails/thumbnail_large_qrack_catalyst_integration.png create mode 100644 demonstrations/covalent_cloud_gpu.metadata.json create mode 100644 demonstrations/covalent_cloud_gpu.py create mode 100644 demonstrations/how_to_use_qiskit1_with_pennylane.metadata.json create mode 100644 demonstrations/how_to_use_qiskit1_with_pennylane.py create mode 100644 demonstrations/qrack.metadata.json create mode 100644 demonstrations/qrack.py create mode 100644 demonstrations/tutorial_liesim.metadata.json create mode 100644 demonstrations/tutorial_liesim.py create mode 100644 demonstrations/tutorial_liesim_extension.metadata.json create mode 100644 demonstrations/tutorial_liesim_extension.py create mode 100644 demonstrations/tutorial_qcbm.metadata.json create mode 100644 demonstrations/tutorial_qcbm.py diff --git a/.github/workflows/upload-text.yml b/.github/workflows/upload-text.yml index 0a554835aa..e93bdf7a90 100644 --- a/.github/workflows/upload-text.yml +++ b/.github/workflows/upload-text.yml @@ -51,8 +51,11 @@ jobs: path: qml_text - name: Copy Concatenated Metadata into Build - run: | - jq -s . $(find demonstrations -name "*.metadata.json" -type f) > ${{ steps.qml_text.outputs.download-path }}/demos/metadata.json + run: > + jq -s . + $(find demonstrations -name "*.metadata.json" -type f + ! -name "demonstrations_categories.metadata.json") + > ${{ steps.qml_text.outputs.download-path }}/demos/metadata.json - name: Upload uses: XanaduAI/cloud-actions/push-to-s3-and-invalidate-cloudfront@main diff --git a/README.md b/README.md index 99c99e205d..13a0903747 100644 --- a/README.md +++ b/README.md @@ -59,7 +59,7 @@ quantum computing paper/result. ```python ############################################################################## - #.. figure:: ../_static/demonstrations_assets//image.png + #.. figure:: ../_static/demonstration_assets//image.png # :align: center # :width: 90% ``` diff --git a/_static/authors/ara_ghukasyan.jpeg b/_static/authors/ara_ghukasyan.jpeg new file mode 100644 index 0000000000000000000000000000000000000000..da3f8aae14c71dbf3583328b1f4000ce153de1bd GIT binary patch literal 63812 zcmb5VWmF|S)Gl~{#@!tncX!v*xHfulcelpf-5nZt_k%U=?$Wq4?$$svyx*O>?#z$* zF*}vyscorbWo1?EN0>;I!hFg0^A`INnVW>ynNXIB6Kg7Fh8d$>COhkZUV zmhoXGpBmq_c7l0$c7GMPM1bhW3133Oa^f~`WUjpFpsqG1H{ZNxq~|9LR`#4-STfC+#Z!1#&T0j!^y{l9VkwEd*VrT=^U82=A1cpCr^>izim z==?uC*FU==eW8T3!GE9T5N+?Qk@5Hu@iTP@g5Fxj6uETLu6iYXbn7v!6CP 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Agnostiq Inc. He has a B.Sc. in Math & Physics and a Ph.D. in Engineering Physics from McMaster University in Hamilton, Ontario. Ara’s interests include machine learning, physics, and quantum computing. + + diff --git a/_static/authors/dan_strano.txt b/_static/authors/dan_strano.txt index a310129b6a..b401e918a3 100644 --- a/_static/authors/dan_strano.txt +++ b/_static/authors/dan_strano.txt @@ -1,4 +1,4 @@ .. bio:: Dan Strano - :photo: ../_static/authors/dan_strano.jpg + :photo: ../_static/authors/dan_strano.jpeg - Dan Strano is a technical staff member at `Unitary Fund `__. Additionally, he has been the lead author of the Qrack simulator framework since 2017. + Dan Strano is a technical staff member at Unitary Fund. 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"dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": ["Quantum Hardware", "Devices and Performance", "Quantum Computing"], "tags": [], "previewImages": [ diff --git a/demonstrations/braket-parallel-gradients.metadata.json b/demonstrations/braket-parallel-gradients.metadata.json index 9e8d35856e..e27d083de7 100644 --- a/demonstrations/braket-parallel-gradients.metadata.json +++ b/demonstrations/braket-parallel-gradients.metadata.json @@ -12,7 +12,7 @@ } ], "dateOfPublication": "2020-12-08T00:00:00+00:00", - "dateOfLastModification": "2024-03-04T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Devices and Performance" ], diff --git a/demonstrations/covalent_cloud_gpu.metadata.json b/demonstrations/covalent_cloud_gpu.metadata.json new file mode 100644 index 0000000000..53d65d671e --- /dev/null +++ b/demonstrations/covalent_cloud_gpu.metadata.json @@ -0,0 +1,57 @@ +{ + "title": "Running GPU-accelerated quantum circuit simulations on Covalent Cloud using PennyLane", + "authors": [ + { + "id": "santosh_kumar_radha" + }, + { + "id": "ara_ghukasyan" + } + ], + "dateOfPublication": "2024-05-24T00:00:00+00:00", + "dateOfLastModification": "2024-05-24T00:00:00+00:00", + "categories": [ + "Quantum Machine Learning" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/covalent_cloud_gpu/thumbnail_covalent_cloud_gpu.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_covalent_cloud_gpu.png" + } + ], + "seoDescription": "Explore the process of running GPU-accelerated quantum circuit simulations on Covalent Cloud using PennyLane.", + "doi": "", + "canonicalURL": "/qml/demos/covalent_cloud_gpu", + "references": [], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_kernels_module", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_kernel_based_training", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_univariate_qvr", + "weight": 1.0 + } + ], + "hardware": [ + { + "id": "covalent", + "link": "https://docs.covalent.xyz/docs/cloud/tutorials-cloud/pennylane_tutorial/", + "logo": "/_static/hardware_logos/covalent.png" + } + ] +} diff --git a/demonstrations/covalent_cloud_gpu.py b/demonstrations/covalent_cloud_gpu.py new file mode 100644 index 0000000000..2dbcf02894 --- /dev/null +++ b/demonstrations/covalent_cloud_gpu.py @@ -0,0 +1,372 @@ +r"""Running GPU-accelerated quantum circuit simulations on Covalent Cloud using PennyLane +=================================================================== +""" + +############################################################################## +# +# In this tutorial, we’ll demonstrate how to run GPU-accelerated quantum circuit simulations +# on `Covalent Cloud `__ using PennyLane. We will focus on a specific example around +# quantum support vector machines (QSVMs) to demonstrate how easy it is to run GPU-accelerated quantum circuit simulations on Covalent Cloud. +# +# QSVMs are essentially `traditional +# SVMs `__ that rely on `embedding +# kernels `__ evaluated on +# a quantum computer—a.k.a. `quantum embedding +# kernel `__. +# These kernels provide a unique (and perhaps classically intractable) means of measuring pairwise +# similarity. +# +# Using GPUs to simulate quantum computers is worthwhile when qubit capacity and/or fidelity +# requirements are not met by the available quantum hardware. While QSVMs are relatively tolerant to +# noise (an important reason for their current popularity), evaluating kernels on *real* quantum +# hardware is not always practical nor necessary. +# + +############################################################################## +# Implementation +# -------------- +# +# Let’s start by importing the required packages. +# + +import covalent as ct +import covalent_cloud as cc +import matplotlib.pyplot as plt +import pennylane as qml +from matplotlib.colors import ListedColormap +from pennylane import numpy as np +from sklearn.datasets import make_blobs +from sklearn.inspection import DecisionBoundaryDisplay +from sklearn.model_selection import train_test_split +from sklearn.svm import SVC + +# cc.save_api_key("YOUR_API_KEY") + +############################################################################## +# Covalent Cloud allows us to create `reusable execution +# environments `__, as shown +# below. This environment represents a typical setup for running Pennylane on NVIDIA GPUs. +# + +cc.create_env( + name="pennylane-gpu", # identifier for referring to this environment + conda={ + "channels": ["conda-forge"], + "dependencies": ["cudatoolkit>=11.8"], + }, + pip=[ + "cuquantum==23.10.0", + "matplotlib==3.8.2", + "Pennylane==0.34.0", + "PennyLane-Lightning[GPU]==0.34.0", + "scikit-learn==1.3.1", + "torch==2.1.2", + ], + wait=True, +) + +############################################################################## +# .. rst-class :: sphx-glr-script-out +# +# .. code-block: none +# +# Waiting for environment pennylane-gpu to be ready.................. +# Name: pennylane-gpu +# Status: READY +# Estimated Time: 1002 seconds +# Notes: +# pip was added to the dependencies. +# Python version 3.10 was added to the dependencies. +# Environment file contains: +# ========================== +# channels: +# - conda-forge +# dependencies: +# - python=3.10 +# - pip +# - cudatoolkit>=11.8 +# - pip: +# - cuquantum==23.10.0 +# - matplotlib==3.8.2 +# - Pennylane==0.34.0 +# - PennyLane-Lightning[GPU]==0.34.0 +# - scikit-learn==1.3.1 +# - torch==2.1.2 +# - covalent-cloud +# name: pennylane-gpu +# + +############################################################################## +# Next, we’ll define our resource specifications by creating some +# `executors `__ +# for this workflow. Both executors will run tasks in our new environment, named ``”pennylane-gpu”``. +# + +cpu_executor = cc.CloudExecutor( # for lightweight non-quantum tasks + env="pennylane-gpu", + num_cpus=2, + memory="2GB", +) +gpu_executor = cc.CloudExecutor( # for GPU-powered circuit simulations + env="pennylane-gpu", num_cpus=4, memory="12GB", num_gpus=1, gpu_type="v100" +) + +############################################################################## +# On to the algorithm! +# +# Here’s a function returns a simple quantum kernel based on Pennylane’s `IQP +# Embedding `__ template. +# We’ll use it as-is inside our workflow. +# + +QML_DEVICE = "lightning.qubit" + + +def get_kernel_circuit(n_wires): + + @qml.qnode(qml.device(QML_DEVICE, wires=n_wires, shots=None)) + def circuit(x1, x2): + qml.IQPEmbedding(x1, wires=range(n_wires), n_repeats=4) + qml.adjoint(qml.IQPEmbedding)(x2, wires=range(n_wires), n_repeats=4) + return qml.probs(wires=range(n_wires)) + + return lambda x1, x2: circuit(x1, x2)[0] # |0..0> state probability + + +############################################################################## +# Next, each function destined for remote execution is decorated with ``@ct.electron``, with an +# `executor `__ +# specified therein. Only tasks that evaluate the simulated quantum kernel should require +# ``gpu_executor``. For example, we don’t need GPUs to generate our input data: +# + + +@ct.electron(executor=cpu_executor) # lightweight non-quantum task +def get_split_data(n_samples=18, test_size=0.2): + centers = [(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)] + X, y = make_blobs(n_samples, centers=centers, cluster_std=0.25, shuffle=False) + # rescale labels to be -1, 1 + mapping = {0: -1, 1: 1, 2: -1, 3: 1, 4: -1, 5: 1, 6: -1, 7: 1, 8: -1} + y = np.array([mapping[i] for i in y]) + X = X.astype(np.float32) + y = y.astype(int) + + # X_train, X_test, y_train, y_test + return train_test_split(X, y, test_size=test_size, random_state=3) + + +############################################################################## +# Classifying with the SVM, on the other hand, requires :math:`O(n^2)` kernel evaluations, where +# :math:`n` is the dataset size. Accordingly, we’ll use GPUs (i.e. ``gpu_executor``) to speed up this +# process. +# + +DISP_SETTINGS = { + "grid_resolution": 50, + "response_method": "predict", + "alpha": 0.5, + "cmap": plt.cm.RdBu, +} + + +@ct.electron(executor=gpu_executor) +def classify_with_qsvm(Xtr, Xte, ytr, yte): + kernel = get_kernel_circuit(n_wires=Xtr.shape[1]) + + kernel_matrix_fn = lambda X, Z: qml.kernels.kernel_matrix(X, Z, kernel) + svc = SVC(kernel=kernel_matrix_fn).fit(Xtr, ytr) + + # train/test accuracy + accuracy_tr = svc.score(Xtr, ytr) + accuracy_te = svc.score(Xte, yte) + + # decision boundary + cm_bright = ListedColormap(["#FF0000", "#0000FF"]) + disp = DecisionBoundaryDisplay.from_estimator(svc, Xte, **DISP_SETTINGS) + disp.ax_.scatter(Xtr[:, 0], Xtr[:, 1], c=ytr, cmap=cm_bright) + disp.ax_.scatter(Xte[:, 0], Xte[:, 1], c=yte, cmap=cm_bright, marker="$\u25EF$") + + return accuracy_tr, accuracy_te, disp + + +############################################################################## +# Putting it all together, we can define a QSVM training and testing workflow. This special function +# gets decorated with ``@ct.lattice``. +# + + +@ct.lattice(workflow_executor=cpu_executor, executor=cpu_executor) +def run_qsvm(n_samples, test_size): + Xtr, Xte, ytr, yte = get_split_data(n_samples, test_size) + return classify_with_qsvm(Xtr, Xte, ytr, yte) + + +############################################################################## +# Now, to dispatch ``run_qsvm`` to Covalent Cloud, we call it after wrapping with ``ct.dispatch``, as +# usual. +# + +dispatch_id = cc.dispatch(run_qsvm)(n_samples=64, test_size=0.2) +print("Dispatch ID:", dispatch_id) + +############################################################################## +# .. rst-class :: sphx-glr-script-out +# +# .. code-block: none +# +# Dispatch ID: 0b5d3a08-fe9c-4dc2-910b-0be6eb925663 + +############################################################################## +# Here’s what we get when we query and display the results. +# + +result = cc.get_result(dispatch_id, wait=True) +result.result.load() + +train_acc, test_acc, decision_boundary_figure = result.result.value +print(f"Train accuracy: {train_acc * 100:.1f}%") +print(f"Test accuracy: {test_acc * 100:.1f}%") + +decision_boundary_figure + +############################################################################## +# .. rst-class :: sphx-glr-script-out +# +# .. code-block: none +# +# Train accuracy: 64.7% +# Test accuracy: 76.9% +# +# .. figure:: ../_static/demonstration_assets/covalent_cloud_gpu/covalent_cloud_gpu_19_1.png +# :align: center +# :width: 90% + +############################################################################## +# Conclusion +# ---------- +# +# In this tutorial, we demonstrated how to run quantum circuit simulations on GPUs via Covalent Cloud. +# We used PennyLane to define a simple quantum kernel, and then trained and tested a QSVM on a +# 2-dimensional dataset. To make the most of this tutorial, try experimenting with different +# datasets/kernels or increasing the dataset dimension, to gain a greater advantage from GPU +# acceleration. +# +# The cost of running this workflow is approximately \$0.27. The full code is available below, and you can try it yourself with the *Run on Covalent Cloud* button in the side menu on the right. +# + +############################################################################## +# Full Code +# --------- +# + +############################################################################## +# .. code:: python +# +# import covalent as ct +# import covalent_cloud as cc +# import matplotlib.pyplot as plt +# import pennylane as qml +# from matplotlib.colors import ListedColormap +# from pennylane import numpy as np +# from sklearn.datasets import make_blobs +# from sklearn.inspection import DecisionBoundaryDisplay +# from sklearn.model_selection import train_test_split +# from sklearn.svm import SVC +# +# cc.save_api_key("API_KEY") +# +# cc.create_env( +# name="pennylane-gpu", # identifier for referring to this environment +# conda={ +# "channels": ["conda-forge"], +# "dependencies": ["cudatoolkit>=11.8"], +# }, pip=[ +# "cuquantum==23.10.0", +# "matplotlib==3.8.2", +# "Pennylane==0.34.0", +# "PennyLane-Lightning[GPU]==0.34.0", +# "scikit-learn==1.3.1", +# "torch==2.1.2", +# ], +# wait=True +# ) +# +# cpu_executor = cc.CloudExecutor( # for lightweight non-quantum tasks +# env="pennylane-gpu", +# num_cpus=2, +# memory="2GB", +# ) +# gpu_executor = cc.CloudExecutor( # for GPU-powered circuit simulations +# env="pennylane-gpu", +# num_cpus=4, +# memory="12GB", +# num_gpus=1, +# gpu_type="v100" +# ) +# +# QML_DEVICE = "lightning.gpu" +# +# def get_kernel_circuit(n_wires): +# +# @qml.qnode(qml.device(QML_DEVICE, wires=n_wires, shots=None)) +# def circuit(x1, x2): +# qml.IQPEmbedding(x1, wires=range(n_wires), n_repeats=4) +# qml.adjoint(qml.IQPEmbedding)(x2, wires=range(n_wires), n_repeats=4) +# return qml.probs(wires=range(n_wires)) +# +# return lambda x1, x2: circuit(x1, x2)[0] # |0..0> state probability +# +# @ct.electron(executor=cpu_executor) # lightweight non-quantum task +# def get_split_data(n_samples=18, test_size=0.2): +# centers = [(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)] +# X, y = make_blobs(n_samples, centers=centers, cluster_std=0.25, shuffle=False) +# # rescale labels to be -1, 1 +# mapping = {0: -1, 1: 1, 2: -1, 3: 1, 4: -1, 5: 1, 6: -1, 7: 1, 8: -1} +# y = np.array([mapping[i] for i in y]) +# X = X.astype(np.float32) +# y = y.astype(int) +# +# # X_train, X_test, y_train, y_test +# return train_test_split(X, y, test_size=test_size, random_state=3) +# +# DISP_SETTINGS = {"grid_resolution": 50, "response_method": "predict", "alpha": 0.5, "cmap": plt.cm.RdBu} +# +# @ct.electron(executor=gpu_executor) +# def classify_with_qsvm(Xtr, Xte, ytr, yte): +# kernel = get_kernel_circuit(n_wires=Xtr.shape[1]) +# +# kernel_matrix_fn = lambda X, Z: qml.kernels.kernel_matrix(X, Z, kernel) +# svc = SVC(kernel=kernel_matrix_fn).fit(Xtr, ytr) +# +# # train/test accuracy +# accuracy_tr = svc.score(Xtr, ytr) +# accuracy_te = svc.score(Xte, yte) +# +# # decision boundary +# cm_bright = ListedColormap(["#FF0000", "#0000FF"]) +# disp = DecisionBoundaryDisplay.from_estimator(svc, Xte, **DISP_SETTINGS) +# disp.ax_.scatter(Xtr[:, 0], Xtr[:, 1], c=ytr, cmap=cm_bright) +# disp.ax_.scatter(Xte[:, 0], Xte[:, 1], c=yte, cmap=cm_bright, marker="$\u25EF$") +# +# return accuracy_tr, accuracy_te, disp +# +# @ct.lattice(workflow_executor=cpu_executor, executor=cpu_executor) +# def run_qsvm(n_samples, test_size): +# Xtr, Xte, ytr, yte = get_split_data(n_samples, test_size) +# return classify_with_qsvm(Xtr, Xte, ytr, yte) +# +# dispatch_id = cc.dispatch(run_qsvm)(n_samples=64, test_size=0.2) +# print("Dispatch ID:", dispatch_id) +# +# result = cc.get_result(dispatch_id, wait=True) +# result.result.load() +# +# train_acc, test_acc, decision_boundary_figure = result.result.value +# print(f"Train accuracy: {train_acc * 100:.1f}%") +# print(f"Test accuracy: {test_acc * 100:.1f}%") +# + +############################################################################## +# About the author +# ---------------- +# diff --git a/demonstrations/how_to_use_qiskit1_with_pennylane.metadata.json b/demonstrations/how_to_use_qiskit1_with_pennylane.metadata.json new file mode 100644 index 0000000000..6cb9a65853 --- /dev/null +++ b/demonstrations/how_to_use_qiskit1_with_pennylane.metadata.json @@ -0,0 +1,52 @@ +{ + "title": "How to use Qiskit 1.0 with PennyLane", + "authors": [ + { + "id": "isaac_de_vlugt" + } + ], + "dateOfPublication": "2024-07-02T00:00:00+00:00", + "dateOfLastModification": "2024-07-03T00:00:00+00:00", + "categories": [ + "Quantum Computing" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/regular_demo_thumbnails/thumbnail_HowToUseQiskit1WithPL.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_HowToUseQiskit1WithPL.png" + } + ], + "seoDescription": "Learn how to get started using Qiskit 1.0 with PennyLane", + "doi": "", + "canonicalURL": "/qml/demos/how_to_use_qiskit1_with_pennylane", + "references": [], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_qubit_rotation", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_diffable-mitigation", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_jax_transformations", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_qnn_module_torch", + "weight": 1.0 + } + ] +} diff --git a/demonstrations/how_to_use_qiskit1_with_pennylane.py b/demonstrations/how_to_use_qiskit1_with_pennylane.py new file mode 100644 index 0000000000..1a6e0ca61a --- /dev/null +++ b/demonstrations/how_to_use_qiskit1_with_pennylane.py @@ -0,0 +1,434 @@ +r"""How to use Qiskit 1.0 with PennyLane +==================================== + +The PennyLane-Qiskit plugin enables you to integrate your existing Qiskit code and run circuits on IBM +devices with PennyLane, encompassing two real-world scenarios: (1) working in PennyLane from the start +and executing your work on an IBM device and (2) converting your existing Qiskit code to PennyLane and +executing that on *any* device, including IBM devices, :doc:`Amazon Braket ` +— you name it! + +With the `first stable release of Qiskit `__ in February 2024, we subsequently shipped some +excellent features and upgrades with the PennyLane-Qiskit plugin, allowing +anyone familiar with +Qiskit to jump into the PennyLane ecosystem and land on both feet. +In this demo, we want to show you how easy these features are to use, letting you make that +aforementioned jump like it’s nothing 😌. +""" + +###################################################################### +# .. note :: +# +# To follow along, we recommend installing the PennyLane-Qiskit plugin in a separate virtual environment. +# +# .. code-block:: none +# +# pip install -U pennylane-qiskit +# +# This will install PennyLane, the plugin, and the latest Qiskit 1.0 version that the plugin supports. +# If you use an environment that contains a pre-1.0 version of Qiskit, upgrading to Qiskit 1.0 could +# cause issues. In that case, we recommend following `Qiskit's upgrade instructions `__. +# + +###################################################################### +# Coding in PennyLane, executing on IBM Quantum devices +# ----------------------------------------------------- +# +# If you want to distill how a PennyLane plugin works down to one thing, it’s all in the provided devices! In +# PennyLane, you just :doc:`create your circuit (a quantum function) ` and decorate it with +# the QNode decorator :func:`@qml.qnode(dev) `, where ``dev`` is (one of) the plugin’s device(s). +# +# In PennyLane and its plugins, +# `devices `__ are called upon by their short name, and can be loaded via the :func:`~pennylane.device` function: +# +# .. code-block:: +# +# qml.device("shortname", *device_options) +# +# If you’ve +# seen PennyLane code before, you’ve probably seen ``"default.qubit"`` or ``"lightning.qubit"`` as +# short names for our Python and C++ statevector simulators, respectively. +# +# In the PennyLane-Qiskit plugin, there are `many IBM +# devices `__ you can use, but there are +# two heavy hitters for Qiskit 1.0: +# +# - ``"qiskit.basicsim"``: uses the Qiskit ``BasicSimulator`` backend from the ``basic_provider`` +# module in Qiskit 1.0. +# +# - ``"qiskit.remote"``: lets you run PennyLane code on any Qiskit device, where you can choose between +# different backends — either simulators tailor-made to emulate the real hardware, or the real +# hardware itself. +# +# +# If you want to use any of these devices in PennyLane, simply put those short names into +# ``qml.device`` and any quantum function decorated with ``@qml.qnode(dev)`` will execute on the +# corresponding device. +# + +###################################################################### +# To show how easy this is, let’s say we have this simple circuit in Qiskit 1.0. +# + +import qiskit +from qiskit import QuantumCircuit +from qiskit.providers.basic_provider import BasicSimulator + +qc = QuantumCircuit(2, 1) + +qc.h(0) +qc.cx(0, 1) +qc.measure(1, 0) + +backend = BasicSimulator() +counts = backend.run(qc).result().get_counts() + +print(counts) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# {'0': 523, '1': 501} +# + +###################################################################### +# In PennyLane, we can execute the exact same circuit on the exact same device and backend like so: +# + +import pennylane as qml + +dev = qml.device("qiskit.basicsim", wires=2, shots=1024) + +@qml.qnode(dev) +def circuit(): + qml.Hadamard(0) + qml.CNOT([0, 1]) + return qml.counts(wires=1) + +print(circuit()) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# {'0': tensor(474, requires_grad=True), '1': tensor(550, requires_grad=True)} +# + +###################################################################### +# Magic! With one line of code, you can work inside PennyLane and ship the execution off to your +# favourite IBM device. It’s exactly like using Qiskit 1.0, but you interact with PennyLane instead. +# + +###################################################################### +# Converting Qiskit 1.0 code to PennyLane +# --------------------------------------- +# +# This is probably what a lot of the audience is wondering: “Can I combine my existing work in Qiskit +# with PennyLane?” *YES.* And don’t worry, you don’t need to import a ton of things or use a bunch of +# functions — you only need to know *two* functions: +# +# - :func:`~pennylane.from_qiskit`: converts an entire Qiskit ``QuantumCircuit`` — the whole thing — into a +# PennyLane quantum function. It will faithfully convert Qiskit-side measurements (even mid-circuit +# measurements), or you can append Pennylane-side measurements directly to it. +# +# - :func:`~pennylane.from_qiskit_op`: converts a ``SparsePauliOp`` in Qiskit 1.0 to the equivalent operator +# in PennyLane. +# +# +# Both of these functions give you all the functionality you need to access PennyLane’s features and +# user interface starting from the side of Qiskit 1.0. Let’s look at an example where both of these +# functions are used. +# + +###################################################################### +# Let’s say you’ve created the following Qiskit code that prepares a modified GHZ state for an +# arbitrary amount of qubits and measures several expectation values of ``SparsePauliOp`` operators. +# + +from qiskit.quantum_info import SparsePauliOp + +n = 5 + +def qiskit_GHZ_circuit(n): + qc = QuantumCircuit(n) + qc.h(0) + for i in range(n - 1): + qc.cx(i, i + 1) + qc.rx(0.1967, i) + return qc + +qc = qiskit_GHZ_circuit(n) + +operator_strings = ["I" * i + "ZZ" + "I" * (n - 2 - i) for i in range(n - 1)] +operators = [SparsePauliOp(operator_string) for operator_string in operator_strings] +print(operators) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [SparsePauliOp(['ZZIII'], +# coeffs=[1.+0.j]), SparsePauliOp(['IZZII'], +# coeffs=[1.+0.j]), SparsePauliOp(['IIZZI'], +# coeffs=[1.+0.j]), SparsePauliOp(['IIIZZ'], +# coeffs=[1.+0.j])] +# + +###################################################################### +# With the circuit and operators defined, we can create a +# `StatevectorEstimator `__ +# primitive in Qiskit to execute the circuit and calculate expectation values. +# + +from qiskit.primitives import StatevectorEstimator + +estimator = StatevectorEstimator() +job_estimator = estimator.run([(qc, operators)]) +result_estimator = job_estimator.result()[0].data.evs + +print(result_estimator) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [0.98071685 0.96180554 0.96180554 0.96180554] +# + +###################################################################### +# To convert this work into PennyLane, let’s start with the Qiskit-side ``SparsePauliOp`` operators +# and converting them to PennyLane objects with ``qml.from_qiskit_op``. +# + +pl_operators = [qml.from_qiskit_op(qiskit_op) for qiskit_op in operators] +print(pl_operators) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [Z(3) @ Z(4), Z(2) @ Z(3), Z(1) @ Z(2), Z(0) @ Z(1)] +# + +###################################################################### +# .. note :: +# +# PennyLane wires are enumerated from left to right, while the Qiskit convention is to +# enumerate from right to left. This means a ``SparsePauliOp`` term defined by the string “XYZ” in Qiskit +# applies ``Z`` on wire ``0``, ``Y`` on wire ``1``, and ``X`` on wire ``2``. For more details, see +# the `String `__ representation +# section of the Qiskit documentation for the ``Pauli`` class. +# + +###################################################################### +# Next, we show how to convert the Qiskit ``QuantumCircuit``, ``qc``, to PennyLane with ``qml.from_qiskit``. We +# can append the measurements — expectation values (:func:`~pennylane.expval`) of ``pl_operators`` — with the +# ``measurements`` keyword argument, which accepts a list of PennyLane measurements. +# + +measurements = [qml.expval(op) for op in pl_operators] # expectation values + +qc = qiskit_GHZ_circuit(n) +pl_qfunc = qml.from_qiskit(qc, measurements=measurements) + +###################################################################### +# The last thing to do is make ``pl_func`` a QNode. We can’t decorate ``pl_qfunc`` with +# ``@qml.qnode``, but we can equivalently wrap it with ``qml.QNode`` and supply the device. +# + +pl_circuit = qml.QNode(pl_qfunc, device=qml.device("lightning.qubit", wires=n)) +pl_circuit() + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [0.9807168489852623, 0.961805537883582, 0.961805537883582, 0.961805537883582] +# + +###################################################################### +# What’s really useful about being able to append measurements to the end of a circuit with +# :func:`~pennylane.from_qiskit` is being able to measure something that isn’t available in Qiskit 1.0 but is +# available in PennyLane, like the :doc:`classical shadow ` measurement protocol, for example. In PennyLane, +# you can measure this with :func:`~pennylane.classical_shadow`. +# + +measurements = [qml.classical_shadow(wires=range(n))] +pl_qfunc = qml.from_qiskit(qc, measurements=measurements) + +pl_circuit = qml.QNode(pl_qfunc, device=qml.device("default.qubit", wires=n)) +pl_circuit(shots=5) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [array([[[0, 0, 0, 0, 1], +# [1, 1, 1, 0, 1], +# [0, 1, 0, 0, 0], +# [1, 1, 0, 0, 0], +# [0, 0, 0, 0, 0]], +# +# [[0, 0, 2, 2, 1], +# [2, 0, 2, 0, 1], +# [1, 0, 2, 0, 2], +# [1, 0, 1, 1, 1], +# [1, 0, 2, 0, 2]]], dtype=int8)] +# + +###################################################################### +# And that’s it! Now you have a copy of your work in PennyLane, where you can access +# fully-differentiable and hardware-agnostic quantum programming — the entire quantum programming +# ecosystem is at your disposal 💪. +# + +###################################################################### +# A real-world example +# -------------------- +# +# One of the things you’ll almost certainly encounter in the wild is a cost function to optimize with +# tunable parameters belonging to a circuit — it’s common 😉! PennyLane is a great option for these +# problems because of its end-to-end differentiability and long list of `optimization methods `_ you can +# leverage. So, maybe you have a home-cooked :doc:`variational circuit ` written in Qiskit and you want to +# access PennyLane’s seamless differentiability — yep, the PennyLane-Qiskit plugin has you covered +# here, too 🙌. +# +# To keep things simple, let’s use the following Qiskit circuit as our variational circuit. +# + +from qiskit.circuit import ParameterVector, Parameter + +n = 3 + +angles1 = ParameterVector("phis", n - 1) +angle2 = Parameter("theta") + +qc = QuantumCircuit(3) +qc.rx(angles1[0], [0]) +qc.ry(angles1[1], [1]) +qc.ry(angle2, [2]) + +qc.draw("mpl") + +###################################################################### +# .. rst-class:: image-no-text-wrap +# +# .. figure:: ../_static/demonstration_assets/how_to_use_qiskit_1_with_pennylane/qiskit_parameterized_circuit.png +# :align: center +# :width: 30% +# + +###################################################################### +# This circuit contains two sets of differentiable parameters: ``phis`` (length 2) and ``theta`` +# (scalar). +# +# If we give this Qiskit circuit to ``qml.from_qiskit``, we get a quantum function that can +# subsequently be called within a circuit — it’s as if the gates and operations contained within it +# get transferred over to our new QNode. +# + +import pennylane.numpy as np + +pl_qfunc = qml.from_qiskit(qc) + +dev = qml.device("lightning.qubit", wires=n) + +@qml.qnode(dev) +def differentiable_circuit(phis, theta): + pl_qfunc(phis, theta) + return [qml.expval(qml.Z(i)) for i in range(n)] + +phis = np.array([0.6, 0.7]) +theta = np.array([0.19]) + +print(differentiable_circuit(phis, theta)) +print(qml.draw_mpl(differentiable_circuit)(phis, theta)) + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# [0.8253356149096783, 0.7648421872844883, 0.9820042351172701] +# + +###################################################################### +# .. rst-class:: image-no-text-wrap +# +# .. figure:: ../_static/demonstration_assets/how_to_use_qiskit_1_with_pennylane/pl_real_world_example.png +# :align: center +# :width: 45% +# + +###################################################################### +# You’ll notice, too, that ``pl_func`` has the call signature that you would expect: +# ``pl_qfunc(phis, theta)``, just like the name we gave them when we defined them in Qiskit +# (``ParameterVector("phis", n-1)`` and ``Parameter("theta")``). +# +# With the circuit being immediately differentiable to PennyLane, let’s define a dummy cost function +# that will sum the output of ``differentiable_circuit``. +# + +def cost(phis, theta): + return np.sum(differentiable_circuit(phis, theta)) + +###################################################################### +# Now we’re in business and can optimize! You can use any suitable optimizer in PennyLane that you +# like, and by calling its ``step_and_cost`` method you can access the updated parameters and cost +# function value after each optimization step. +# + +opt = qml.AdamOptimizer(0.1) + +for i in range(100): + (phis, theta), new_loss = opt.step_and_cost(cost, phis, theta) + +print(f"Optimized parameters: phis = {phis}, theta = {theta}") +print(f"Optimized cost function value: {new_loss}") + +###################################################################### +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# Optimized parameters: phis = [3.12829384 3.12823583], theta = [3.1310224] +# Optimized cost function val: -2.999796472821245 +# + +###################################################################### +# As we expect, the minimum value that our cost function can take is :math:`-3` when all angles of +# rotation are :math:`\pi` (all qubits are rotated into the :math:`\vert 1 \rangle` state). Of course, +# this is just a toy example of an easy optimization problem. But, you can apply this process to a +# larger, more complicated circuit ansatze without worries. +# + +###################################################################### +# Further resources +# ----------------- +# +# There’s so much more to learn about what’s possible in PennyLane, and if you’re coming from Qiskit +# you’re in good hands! The `PennyLany-Qiskit plugin `__ is your personal chaperone to the PennyLane +# ecosystem. You can dive deeper into what’s possible with the PennyLane-Qiskit plugin by visiting the +# plugin homepage and, in the +# mean time, if you have any questions about the plugin, PennyLane, or even Qiskit, drop a question on +# our `Discussion Forum `__ and we’ll promptly respond. +# +# Now that you’ve used PennyLane, every road in the wonderful world of quantum programming SDKs is +# open with no set speed limits 🏎️. Explore our website to see +# the latest and greatest `PennyLane features `__, `Demos `__ and our `blog posts `__, and follow us on +# `LinkedIn `__ or `X (formerly +# Twitter) `__ to stay updated! +# + +###################################################################### +# About the author +# ---------------- +# .. include:: ../_static/authors/isaac_de_vlugt.txt +# diff --git a/demonstrations/qrack.metadata.json b/demonstrations/qrack.metadata.json new file mode 100644 index 0000000000..c14c3070b0 --- /dev/null +++ b/demonstrations/qrack.metadata.json @@ -0,0 +1,70 @@ +{ + "title": "QJIT compilation with Qrack and Catalyst", + "authors": [ + { + "id": "dan_strano" + } + ], + "dateOfPublication": "2024-07-10T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", + "categories": [ + "Devices and Performance" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/regular_demo_thumbnails/thumbnail_qrack_catalyst_integration.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_qrack_catalyst_integration.png" + } + ], + "seoDescription": "Quantum JIT compilation (QJIT) using the Qrack device for PennyLane and Catalyst, with GPU-acceleration and novel optimization.", + "doi": "", + "canonicalURL": "/qml/demos/qrack", + "references": [ + { + "id": "QECReport", + "type": "preprint", + "title": "Exact and approximate simulation of large quantum circuits on a single GPU", + "authors": "Daniel Strano, Benn Bollay, Aryan Blaauw, Nathan Shammah, William J. Zeng, Andrea Mari", + "year": "2023", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.2304.14969", + "url": "https://arxiv.org/abs/2304.14969" + }, + { + "id": "Wille", + "type": "preprint", + "title": "Decision Diagrams for Quantum Computing", + "authors": "Robert Wille, Stefan Hillmich, Lukas Burgholzer", + "year": "2023", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.2302.04687", + "url": "https://arxiv.org/abs/2302.04687" + } + ], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_qft", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_clifford_circuit_simulations", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_mcm_introduction", + "weight": 1.0 + } + ] +} diff --git a/demonstrations/qrack.py b/demonstrations/qrack.py new file mode 100644 index 0000000000..29ca523cb0 --- /dev/null +++ b/demonstrations/qrack.py @@ -0,0 +1,460 @@ +r""" +QJIT compilation with Qrack and Catalyst +======================================== + +`Qrack `__ is a GPU-accelerated quantum +computer simulator with many novel optimizations, and `PyQrack +`__ is its Python wrapper, written in +pure (``ctypes``) Python language standard. Founded in 2017 by Dan Strano and +Benn Bollay, Qrack's vision was always to provide the best possible (classical) +quantum computer emulator, targeting the use case of running +industrially-relevant quantum workloads without recourse to genuine quantum +computer hardware. + +In this tutorial you will learn how to use Qrack with +PennyLane and quantum just-in-time (QJIT) compilation via +`Catalyst +`__ --- enabling +your hybrid quantum-classical Python program to be compiled and executed +with Qrack with significant performance boosts. + +You'll learn certain suggested cases of use where Qrack might particularly excel +at delivering lightning-fast performance or minimizing required memory resources +— for example, special cases of the quantum or discrete :doc:`Fourier transform +`, circuits with predominantly :doc:`Clifford +` or classical preambles, +circuits with :doc:`mid-circuit measurement +`, and high-width circuits with +low-complexity representations in terms of a QBDD (quantum binary decision +diagram). However, Qrack is a general-purpose simulator, so you might +employ it for all their applications and still see parity with or improvement +over available device back ends. + +.. figure:: ../_static/demonstration_assets/qrack/qrack_catalyst_integration_shelf.png + :align: center + :width: 90% + :target: javascript:void(0); + +How Qrack works +--------------- + +When developing `Qrack `__, we wanted to +provide the emulator as open source, free of charge, agnostic to any specific +GPU or hardware accelerator provider, backwards compatible to serve those with +very limited classical computer hardware resources, but (nonetheless) capable of +scaling to supercomputer systems, as secure and free of external dependencies as +possible, and under the reasonably permissive LGPL license, with bindings and +wrappers for third-party libraries provided under even more permissive licenses +like MIT and Apache 2.0. Our hope was that the global floor of minimal access to +cost-competitive quantum workload throughput would never be lower than the +capabilities of Qrack. + +When simulating quantum subroutines of varying qubit widths, Qrack will +transparently, automatically, and dynamically transition between GPU-based and +CPU-based simulation techniques for maximal execution speed, to respond to +situations when qubit registers might be too narrow to benefit from the large +parallel processing element count of a GPU (up to maybe roughly 20 qubits, +depending upon the classical hardware platform). Qrack also offers so-called +hybrid stabilizer simulation (with fallback to universal simulation) and +near-Clifford simulation with a greatly reduced memory footprint on Clifford +gate sets with the inclusion of the `RZ` variational Pauli Z-axis rotation gate. +(For more information, see the `QCE'23 report `__ [#QCEReport]_ by the Qrack and `Unitary Fund `__ teams.) + +Particularly for systems that don't rely on GPU acceleration, Qrack offers a +quantum binary decision diagram (QBDD) simulation algorithm option that might +significantly reduce the memory footprint or execution complexity for circuits +with low entanglement, as judged by the complexity of a QBDD to represent the +state. (Qrack's implementation of QBDD is entirely original source code, but it +is based on reports like `this one `__ +[#Wille]_.) Qrack also offers approximation options aimed at trading off minimal +fidelity reduction for maximum reduction in simulation complexity (as opposed to +models of physical noise), including methods based on the Schmidt decomposition +rounding parameter (SDRP) [#QCEReport]_ and the near-Clifford rounding parameter +(NCRP). + +The Qrack simulator doesn't fit neatly into a single canonical category of +quantum computer simulation algorithm: it optionally and by default leverages +elements of state vector simulation, tensor network simulation, stabilizer and +near-Clifford simulation, and QBDD simulation, often all at once, while it +introduces some novel algorithmic tricks for the Schmidt decomposition of +state vectors in a manner similar to matrix product state (MPS) simulation. + +Demonstrating Qrack with the quantum Fourier transform +------------------------------------------------------ + +The :doc:`quantum Fourier transform (QFT) ` is a building-block +subroutine of many other quantum algorithms. Qrack exhibits unique capability +for many cases of the QFT algorithm, and its worst-case performance is +competitive with other popular quantum computer simulators [#QCEReport]_. In this +section, you'll be presented with examples of Qrack's uniquely optimal +performance on the QFT. + +In the case of a *trivial* computational basis eigenstate input, Qrack can +simulate basically any QFT width. Below, we pick a random eigenstate +initialization and perform the QFT across a width of 60 qubits, with Catalyst's `qjit `__. +""" + +import pennylane as qml +from pennylane import numpy as np +from catalyst import qjit + +import matplotlib.pyplot as plt + +import random + +qubits = 60 +dev = qml.device("qrack.simulator", qubits, shots=8) + +@qjit +@qml.qnode(dev) +def circuit(): + for i in range(qubits): + if random.uniform(0, 1) < 0.5: + qml.X(wires=[i]) + qml.QFT(wires=range(qubits)) + return qml.sample(wires=range(qubits)) + +def counts_from_samples(samples): + counts = {} + for sample in samples: + s = 0 + + for bit in sample: + s = (s << 1) | bit + + s = str(s) + + if s in counts: + counts[s] = counts[s] + 1 + else: + counts[s] = 1 + + return counts + +counts = counts_from_samples(circuit()) + +plt.bar(counts.keys(), counts.values()) +plt.title(f"QFT on {qubits} Qubits with Random Eigenstate Init. (8 samples)") +plt.xlabel("|x⟩") +plt.ylabel("counts") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig1.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# In this image we have represented only 8 measurement samples so we can visualize the result more easily. +# +# This becomes harder if we request a non-trivial initialization. In general, Qrack will use +# Schmidt decomposition techniques to try to break up circuits into separable subsystems of +# qubits to simulate semi-independently, combining them just-in-time (JIT) with Kronecker +# products when they need to interact, according the used circuit definition. +# +# The circuit becomes much harder for Qrack if we randomly initialize the input qubits +# with Haar-random `U3 gates `__, which you can see below, +# but the performance is still significantly better than the worst case (of +# `GHZ state `__ initialization). + +qubits = 12 +dev = qml.device("qrack.simulator", qubits, shots=8) + +@qjit +@qml.qnode(dev) +def circuit(): + for i in range(qubits): + th = random.uniform(0, np.pi) + ph = random.uniform(0, np.pi) + dl = random.uniform(0, np.pi) + qml.U3(th, ph, dl, wires=[i]) + qml.QFT(wires=range(qubits)) + return qml.sample(wires=range(qubits)) + +counts = counts_from_samples(circuit()) + +plt.bar(counts.keys(), counts.values()) +plt.title(f"QFT on {qubits} Qubits with Random U3 Init. (8 samples)") +plt.xlabel("|x⟩") +plt.ylabel("counts") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig2.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# Alternate simulation algorithms (QBDD and near-Clifford) +# -------------------------------------------------------- +# By default, Qrack relies on a combination of state vector simulation, "hybrid" stabilizer and +# near-Clifford simulation, and Schmidt decomposition optimization techniques. Alternatively, we could use +# pure stabilizer simulation or QBDD simulation if the circuit is at all amenable to optimization in this way. +# +# To demonstrate this, we prepare a 60-qubit GHZ state, which would commonly be intractable in the case of state vector simulation. + +qubits = 60 +dev = qml.device( + "qrack.simulator", + qubits, + shots=8, + isBinaryDecisionTree=False, + isStabilizerHybrid=True, + isSchmidtDecompose=False, +) + +@qjit +@qml.qnode(dev) +def circuit(): + qml.Hadamard(0) + for i in range(1, qubits): + qml.CNOT(wires=[i - 1, i]) + return qml.sample(wires=range(qubits)) + +counts = counts_from_samples(circuit()) + +plt.bar(counts.keys(), counts.values()) +plt.title(f"{qubits}-Qubit GHZ preparation (8 samples)") +plt.xlabel("|x⟩") +plt.ylabel("counts") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig3.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# As you can see, Qrack was able to construct the 60-qubit GHZ state (without +# exceeding memory limitations), and the probability is peaked at bit strings of all 0 and all 1. +# +# It's trivial for Qrack to perform large GHZ state preparations with "hybrid" stabilizer +# or near-Clifford simulation if Schmidt decomposition is deactivated. +# QBDD cannot be accelerated by GPU, so its application might be limited, but it is parallel +# over CPU processing elements, hence it might be particularly well-suited for systems with no GPU at all. +# Qrack's default simulation methods will likely still outperform QBDD on BQP-complete problems +# like random circuit sampling or quantum volume certification. +# + +qubits = 24 +dev = qml.device( + "qrack.simulator", qubits, shots=8, isBinaryDecisionTree=True, isStabilizerHybrid=False +) + +@qjit +@qml.qnode(dev) +def circuit(): + qml.Hadamard(0) + for i in range(1, qubits): + qml.CNOT(wires=[i - 1, i]) + return qml.sample(wires=range(qubits)) + +counts = counts_from_samples(circuit()) + +plt.bar(counts.keys(), counts.values()) +plt.title(f"{qubits}-Qubit GHZ preparation (8 samples)") +plt.xlabel("|x⟩") +plt.ylabel("counts") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig4.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# If your gate set is restricted to Clifford with general :class:`~pennylane.RZ` gates +# (being mindful of the fact that compilers like Catalyst might optimize such a gate set basis into different gates), +# the time complexity for measurement samples becomes doubly exponential with near-Clifford simulation, +# but the space complexity is almost exactly that of stabilizer simulation for the logical qubits plus +# an ancillary qubit per (non-optimized) :class:`~.pennylane.RZ` gate, scaling like the square of the +# sum of the count of the logical and ancillary qubits put together. +# +# Comparing performance +# --------------------- +# We've already seen that the Qrack device back end can do some tasks that most other simulators, or +# basically any other simulator, simply can't do, like 60-qubit-wide special cases of the QFT or GHZ state +# preparation with a Clifford or universal (QBDD) simulation algorithm, for example. However, +# in the worst case for circuit complexity, Qrack will tend perform similarly to state vector simulation. +# +# How does the performance of Qrack compare with other simulators' on a non-trivial problem, +# like the U3 initialization we used above for the `QFT algorithm <#demonstrating-qrack-with-the-quantum-fourier-transform>`_? + +import time + +def bench(n, results): + for device in ["qrack.simulator", "lightning.qubit"]: + dev = qml.device(device, n, shots=1) + + @qjit + @qml.qnode(dev) + def circuit(): + for i in range(n): + th = random.uniform(0, np.pi) + ph = random.uniform(0, np.pi) + dl = random.uniform(0, np.pi) + qml.U3(th, ph, dl, wires=[i]) + qml.QFT(wires=range(n)) + return qml.sample(wires=range(n)) + + start_ns = time.perf_counter_ns() + circuit() + results[ + f"Qrack ({n} qb)" if device == "qrack.simulator" else f"Lightning ({n} qb)" + ] = time.perf_counter_ns() - start_ns + + return results + +results = {} +results = bench(6, results) +results = bench(12, results) +results = bench(18, results) + +bar_colors = ["purple", "yellow", "purple", "yellow"] +plt.bar(results.keys(), results.values(), color=bar_colors) +plt.title("Performance comparison, QFT with U3 initialization (1 sample apiece)") +plt.xlabel("|x⟩") +plt.ylabel("Nanoseconds") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig5.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# Benchmarks will differ somewhat when running this code on your local machine, for example, +# but we tend to see that Qrack manages to demonstrate good performance compared to the +# `Lightning simulators `__ on this task case. +# (Note that this initialization case isn't specifically the hardest case of the QFT for Qrack; +# that's probably rather a GHZ state input.) +# +# Similarly, we can use quantum just-in-time (QJIT) compilation from PennyLane's +# `Catalyst `__, for both Qrack and +# `Lightning `__. How does Qrack with QJIT compare to Qrack without it? + +def bench(n, results): + dev = qml.device("qrack.simulator", n, shots=1) + + @qjit + @qml.qnode(dev) + def circuit(): + for i in range(n): + th = random.uniform(0, np.pi) + ph = random.uniform(0, np.pi) + dl = random.uniform(0, np.pi) + qml.U3(th, ph, dl, wires=[i]) + qml.QFT(wires=range(n)) + return qml.sample(wires=range(n)) + + start_ns = time.perf_counter_ns() + circuit() + results[f"QJIT Qrack ({n} qb)"] = time.perf_counter_ns() - start_ns + + @qml.qnode(dev) + def circuit(): + for i in range(n): + th = random.uniform(0, np.pi) + ph = random.uniform(0, np.pi) + dl = random.uniform(0, np.pi) + qml.U3(th, ph, dl, wires=[i]) + qml.QFT(wires=range(n)) + return qml.sample(wires=range(n)) + + start_ns = time.perf_counter_ns() + circuit() + results[f"PyQrack ({n} qb)"] = time.perf_counter_ns() - start_ns + + return results + +# Make sure OpenCL has been initalized in PyQrack: +bench(6, results) + +results = {} +results = bench(6, results) +results = bench(12, results) +results = bench(18, results) + +bar_colors = ["purple", "yellow", "purple", "yellow"] +plt.bar(results.keys(), results.values(), color=bar_colors) +plt.title("Performance comparison, QFT with U3 initialization (1 sample apiece)") +plt.xlabel("|x⟩") +plt.ylabel("Nanoseconds") +plt.show() + +############################################################################## +# .. figure:: ../_static/demonstration_assets/qrack/fig6.png +# :align: center +# :width: 90% +# :target: javascript:void(0); + +############################################################################## +# Again, your mileage may vary somewhat, depending on your local system, but Qrack tends +# to be significantly faster with Catalyst's QJIT than without! +# +# As a basic test of validity, if we compare the inner product between both simulator +# state vector outputs on some QFT case, do they agree? + +def validate(n): + results = [] + for device in ["qrack.simulator", "lightning.qubit"]: + dev = qml.device(device, n, shots=1) + + @qjit + @qml.qnode(dev) + def circuit(): + qml.Hadamard(0) + for i in range(1, n): + qml.CNOT(wires=[i - 1, i]) + qml.QFT(wires=range(n)) + return qml.state() + + start_ns = time.perf_counter_ns() + results.append(circuit()) + + return np.abs(sum([np.conj(x) * y for x, y in zip(results[0], results[1])])) + +print("Qrack cross entropy with Lightning:", validate(12), "out of 1.0") + +############################################################################## +# .. rst-class:: sphx-glr-script-out +# +# .. code-block:: none +# +# Qrack cross entropy with Lightning: 0.9999997797266185 out of 1.0 + +############################################################################## +# Conclusion +# ---------- +# In this tutorial, we've demonstrated the basics of using the `Qrack `__ +# simulator back end and showed examples of special cases on which Qrack's novel optimizations can lead +# to huge increases in performance or maximum achievable qubit widths. Remember the Qrack device back +# end for PennyLane if you'd like to leverage GPU acceleration but don't want to complicate your +# choice of devices or device initialization, to handle a mixture of wide and narrow qubit registers in your subroutines. + +############################################################################## +# +# References +# ---------- +# +# .. [#QCEReport] +# +# Daniel Strano, Benn Bollay, Aryan Blaauw, Nathan Shammah, William J. Zeng, Andrea Mari +# "Exact and approximate simulation of large quantum circuits on a single GPU" +# `arXiv:2304.14969 `__, 2023. +# +# .. [#Wille] +# +# Robert Wille, Stefan Hillmich, Lukas Burgholzer +# "Decision Diagrams for Quantum Computing" +# `arXiv:2302.04687 `__, 2023. + +############################################################################## +# About the author +# ---------------- +# .. include:: ../_static/authors/dan_strano.txt diff --git a/demonstrations/quantum_volume.metadata.json b/demonstrations/quantum_volume.metadata.json index b5c6853ce0..38b4d3e69f 100644 --- a/demonstrations/quantum_volume.metadata.json +++ b/demonstrations/quantum_volume.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2020-12-15T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Hardware", "Quantum Computing" diff --git a/demonstrations/tutorial_How_to_simulate_quantum_circuits_with_tensor_networks.metadata.json b/demonstrations/tutorial_How_to_simulate_quantum_circuits_with_tensor_networks.metadata.json index b20484153c..7ae6b71e75 100644 --- a/demonstrations/tutorial_How_to_simulate_quantum_circuits_with_tensor_networks.metadata.json +++ b/demonstrations/tutorial_How_to_simulate_quantum_circuits_with_tensor_networks.metadata.json @@ -27,7 +27,7 @@ ], "seoDescription": "Learn how to simulate quantum circuits with tensor networks using the default.tensor PennyLane device.", "doi": "", - "canonicalURL": "/qml/demos/tutorial_how_simulate_quantum_circuits_with_tensor_networks_using_DefaultTensor", + "canonicalURL": "/qml/demos/tutorial_How_to_simulate_quantum_circuits_with_tensor_networks", "references": [ { "id": "orus", @@ -48,4 +48,4 @@ "weight": 1.0 } ] -} \ No newline at end of file +} diff --git a/demonstrations/tutorial_adaptive_circuits.metadata.json b/demonstrations/tutorial_adaptive_circuits.metadata.json index e67d68f452..2a995b5d0b 100644 --- a/demonstrations/tutorial_adaptive_circuits.metadata.json +++ b/demonstrations/tutorial_adaptive_circuits.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2021-09-13T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_block_encoding.py b/demonstrations/tutorial_block_encoding.py index 6bb0854b44..8aa36801c5 100644 --- a/demonstrations/tutorial_block_encoding.py +++ b/demonstrations/tutorial_block_encoding.py @@ -82,7 +82,6 @@ The :class:`~.pennylane.FABLE` circuit is implemented in PennyLane and can be easily used to block encode matrices of any given shape. Here, we manually construct the circuit for a structured :math:`4 \times 4` matrix. - """ import pennylane as qml diff --git a/demonstrations/tutorial_chemical_reactions.metadata.json b/demonstrations/tutorial_chemical_reactions.metadata.json index c5f6771c4d..5d42c23e44 100644 --- a/demonstrations/tutorial_chemical_reactions.metadata.json +++ b/demonstrations/tutorial_chemical_reactions.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2021-07-23T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_classically_boosted_vqe.metadata.json b/demonstrations/tutorial_classically_boosted_vqe.metadata.json index 3dba26f11d..8592187187 100644 --- a/demonstrations/tutorial_classically_boosted_vqe.metadata.json +++ b/demonstrations/tutorial_classically_boosted_vqe.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2022-10-31T00:00:00+00:00", - "dateOfLastModification": "2024-03-04T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_diffable_shadows.metadata.json b/demonstrations/tutorial_diffable_shadows.metadata.json index caa7dc5ba2..4a6d90475d 100644 --- a/demonstrations/tutorial_diffable_shadows.metadata.json +++ b/demonstrations/tutorial_diffable_shadows.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2022-10-07T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Algorithms", "Quantum Computing" diff --git a/demonstrations/tutorial_differentiable_HF.metadata.json b/demonstrations/tutorial_differentiable_HF.metadata.json index 859759d162..68c58c88f6 100644 --- a/demonstrations/tutorial_differentiable_HF.metadata.json +++ b/demonstrations/tutorial_differentiable_HF.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2022-05-09T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_error_mitigation.metadata.json b/demonstrations/tutorial_error_mitigation.metadata.json index 26c7828233..edff4395db 100644 --- a/demonstrations/tutorial_error_mitigation.metadata.json +++ b/demonstrations/tutorial_error_mitigation.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2021-11-29T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Algorithms", "Quantum Computing" diff --git a/demonstrations/tutorial_general_parshift.metadata.json b/demonstrations/tutorial_general_parshift.metadata.json index 4f8fc062d2..ba0e971d16 100644 --- a/demonstrations/tutorial_general_parshift.metadata.json +++ b/demonstrations/tutorial_general_parshift.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2021-08-23T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-05T00:00:00+00:00", "categories": [ "Optimization" ], diff --git a/demonstrations/tutorial_general_parshift.py b/demonstrations/tutorial_general_parshift.py index a397447aa0..56d1651150 100644 --- a/demonstrations/tutorial_general_parshift.py +++ b/demonstrations/tutorial_general_parshift.py @@ -601,8 +601,8 @@ def reconstruction(x): # E_\text{even}(x) &= \sum_{\mu=0}^R E_\text{even}(x_\mu) \hat{D}_\mu(x)\\ # \hat{D}_\mu(x) &= # \begin{cases} -# \frac{\sin(Rx)}{2R \tan(x/2)} &\text{if } \mu = 0 \\[12pt] -# \frac{\sin(R (x-x_\mu))}{2R \tan\left(\frac{1}{2} (x-x_\mu)\right)} + \frac{\sin(R (x+x_\mu))}{2R \tan\left(\frac{1}{2} (x+x_\mu)\right)} & \text{if } \mu \in [R-1] \\[12pt] +# \frac{\sin(Rx)}{2R \tan(x/2)} &\text{if } \mu = 0 \\ +# \frac{\sin(R (x-x_\mu))}{2R \tan\left(\frac{1}{2} (x-x_\mu)\right)} + \frac{\sin(R (x+x_\mu))}{2R \tan\left(\frac{1}{2} (x+x_\mu)\right)} & \text{if } \mu \in [R-1] \\ # \frac{\sin(R (x-\pi))}{2R \tan\left(\frac{1}{2} (x-\pi)\right)} & \text{if } \mu = R. # \end{cases} # diff --git a/demonstrations/tutorial_grovers_algorithm.metadata.json b/demonstrations/tutorial_grovers_algorithm.metadata.json index e8e5a3e9b9..79b6d7e56d 100644 --- a/demonstrations/tutorial_grovers_algorithm.metadata.json +++ b/demonstrations/tutorial_grovers_algorithm.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2023-07-03T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-06-24T00:00:00+00:00", "categories": [ "Getting Started", "Algorithms", diff --git a/demonstrations/tutorial_grovers_algorithm.py b/demonstrations/tutorial_grovers_algorithm.py index 82ac8d3330..934a0ae97d 100644 --- a/demonstrations/tutorial_grovers_algorithm.py +++ b/demonstrations/tutorial_grovers_algorithm.py @@ -5,7 +5,7 @@ ================== .. meta:: - :property="og:description": Learn how to find an entry in a list using Grover's Algorithm + :property="og:description": Learn how to find an entry in a list using Grover's algorithm :property="og:image": https://pennylane.ai/qml/_static/demonstration_assets//thumbnail_tutorial_grovers_algorithm.png .. related:: @@ -15,7 +15,7 @@ *Author: Ludmila Botelho. — Posted: 3 July 2023.* -Grover's Algorithm is an `oracle `__-based quantum +`Grover's algorithm `__ is an `oracle `__-based quantum algorithm, proposed by Lov Grover [#Grover1996]_. In the original description, the author approaches the following problem: suppose that we are searching for a specific phone number in a randomly-ordered catalogue containing :math:`N` entries. To find such a number with a probability of @@ -31,12 +31,12 @@ answer, whereas any classical algorithm would require :math:`O(N)` queries. In this tutorial, we are going to implement a search for an n-bit string item using a quantum -circuit based on Grover's Algorithm. +circuit based on Grover's algorithm. The algorithm can be broken down into the following steps: 1. Prepare the initial state -2. Implement the Oracle +2. Implement the oracle 3. Apply the Grover diffusion operator 4. Repeat steps 2 and 3 approximately :math:`\frac{\pi}{4}\sqrt{N}` times 5. Measure @@ -240,8 +240,8 @@ def circuit(): # Finally, the combination of :math:`U_{\omega}` with :math:`U_D` rotates the state # :math:`\vert s \rangle` by an angle of # :math:`\theta =2 \arcsin{\tfrac {1}{\sqrt {N}}}`. For more geometric insights -# about the Oracle and the diffusion operator, please refer to this `codebook -# section `__. +# about the oracle and the diffusion operator, please refer to this `PennyLane Codebook +# section `__. # # # .. figure:: ../_static/demonstration_assets/grovers_algorithm/rotation.gif @@ -307,7 +307,7 @@ def circuit(): # # which is easily implemented using :class:`~.pennylane.GroverOperator`. # -# Finally, we have all the tools to build the circuit for Grover's Algorithm, as we can see in the +# Finally, we have all the tools to build the circuit for Grover's algorithm, as we can see in the # code below. For simplicity, we are going to search for the states # :math:`\vert 0\rangle ^{\otimes n}` and :math:`\vert 1\rangle ^{\otimes n}`, where # :math:`n = \log_2 N` is the number of qubits. @@ -366,10 +366,10 @@ def circuit(): # # Grover's algorithm in principle can be used to speed up more sophisticated computation, for # instance, when used as a subroutine for problems that require extensive search -# and is the basis of a whole family of algorithms, such as the `Amplitude -# amplification `__ technique. +# and is the basis of a whole family of algorithms, such as the amplitude +# amplification technique. # -# If you would like to learn more about Grover's Algorithm, check out `this video `__! +# If you would like to learn more about Grover's algorithm, check out `this video `__! # # diff --git a/demonstrations/tutorial_initial_state_preparation.metadata.json b/demonstrations/tutorial_initial_state_preparation.metadata.json index 1a37af2747..ad9dc665e2 100644 --- a/demonstrations/tutorial_initial_state_preparation.metadata.json +++ b/demonstrations/tutorial_initial_state_preparation.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2023-10-20T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_lcu_blockencoding.metadata.json b/demonstrations/tutorial_lcu_blockencoding.metadata.json index 11002512f7..f7951b4d37 100644 --- a/demonstrations/tutorial_lcu_blockencoding.metadata.json +++ b/demonstrations/tutorial_lcu_blockencoding.metadata.json @@ -12,7 +12,7 @@ } ], "dateOfPublication": "2023-10-25T00:00:00+00:00", - "dateOfLastModification": "2024-05-13T00:00:00+00:00", + "dateOfLastModification": "2024-05-31T00:00:00+00:00", "categories": [ "Algorithms", "Quantum Computing" diff --git a/demonstrations/tutorial_lcu_blockencoding.py b/demonstrations/tutorial_lcu_blockencoding.py index ab956720e9..dc77bc785e 100644 --- a/demonstrations/tutorial_lcu_blockencoding.py +++ b/demonstrations/tutorial_lcu_blockencoding.py @@ -259,7 +259,7 @@ def lcu_circuit(): # block_encode return qml.state() -output_matrix = qml.matrix(lcu_circuit, wire_order=[0, "ancilla"])() +output_matrix = qml.matrix(lcu_circuit, wire_order=["ancilla", 0])() print("Block-encoded projector:\n") print(np.real(np.round(output_matrix,2))) diff --git a/demonstrations/tutorial_liealgebra.py b/demonstrations/tutorial_liealgebra.py index f5e7837caf..3491e039e2 100644 --- a/demonstrations/tutorial_liealgebra.py +++ b/demonstrations/tutorial_liealgebra.py @@ -6,7 +6,6 @@ online search attempts and found yourself overwhelmed by high energy physics literature? Then this demo might be for you, as we are going to introduce the basic concepts of Lie theory from a perspective that is amenable to quantum scientists, engineers, and practitioners. -Let's see what the fuzz is all about, shall we? Introduction ------------ diff --git a/demonstrations/tutorial_liesim.metadata.json b/demonstrations/tutorial_liesim.metadata.json new file mode 100644 index 0000000000..4a2704bf70 --- /dev/null +++ b/demonstrations/tutorial_liesim.metadata.json @@ -0,0 +1,164 @@ +{ + "title": "g-sim: Lie-algebraic classical simulations for variational quantum computing", + "authors": [ + { + "id": "korbinian_kottmann" + } + ], + "dateOfPublication": "2024-06-07T00:00:00+00:00", + "dateOfLastModification": "2024-06-18T00:00:00+00:00", + "categories": [ + "Quantum Computing", + "Getting Started" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/liesim/thumbnail_gsim.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_gsim.png" + } + ], + "seoDescription": "A differentiable implementation of g-sim in PennyLane", + "doi": "", + "canonicalURL": "/qml/demos/tutorial_liesim", + "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": "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" + }, + { + "id": "Somma2", + "type": "preprint", + "title": "Efficient solvability of Hamiltonians and limits on the power of some quantum computational models", + "authors": "Rolando Somma, Howard Barnum, Gerardo Ortiz, Emanuel Knill", + "year": "2006", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.quant-ph/0601030", + "url": "https://arxiv.org/abs/quant-ph/0601030" + }, + { + "id": "Galitski", + "type": "preprint", + "title": "Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach", + "authors": "Victor Galitski", + "year": "2010", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.1012.2873", + "url": "https://arxiv.org/abs/1012.2873" + }, + { + "id": "Cerezo", + "type": "preprint", + "title": "Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing", + "authors": "M. Cerezo, Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz, Zoë Holmes", + "year": "2023", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.2312.09121", + "url": "https://arxiv.org/abs/2312.09121" + }, + { + "id": "Mazzola", + "type": "preprint", + "title": "Quantum computing for chemistry and physics applications from a Monte Carlo perspective", + "authors": "Guglielmo Mazzola", + "year": "2023", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.2308.07964", + "url": "https://arxiv.org/abs/2308.07964" + }, + { + "id": "Park", + "type": "preprint", + "title": "Hardware-efficient ansatz without barren plateaus in any depth", + "authors": "Chae-Yeun Park, Minhyeok Kang, Joonsuk Huh", + "year": "2024", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.2403.04844", + "url": "https://arxiv.org/abs/2403.04844" + } + ], + "basedOnPapers": ["10.48550/arXiv.2308.01432"], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_liealgebra", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_barren_plateaus", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_How_to_optimize_QML_model_using_JAX_and_Optax", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_liesim_extension", + "weight": 1.0 + } + ] +} diff --git a/demonstrations/tutorial_liesim.py b/demonstrations/tutorial_liesim.py new file mode 100644 index 0000000000..0cb3ffabb2 --- /dev/null +++ b/demonstrations/tutorial_liesim.py @@ -0,0 +1,486 @@ +r"""g-sim: Lie-algebraic classical simulations for variational quantum computing +================================================================================ + +For the most part, we now know the phenomenon of :doc:`barren plateaus ` +can be reduced to the dimension of the circuit's :doc:`dynamical Lie algebra (DLA) `. +In particular, exponentially sized DLAs lead to exponentially vanishing gradients (barren plateaus). +Conversely, it has been realized that circuits with polynomially sized DLAs can be efficiently simulated using a technique called :math:`\mathfrak{g}`-sim, +leading to discussions on whether all trainable parametrized circuits are also efficiently classically simulable. + +So what is all the fuss about? How does :math:`\mathfrak{g}`-sim work? What are its restrictions? How can I run it in PennyLane? +We are going to try to answer all these questions in the demo below. + +Introduction +------------ + +Lie algebras are tightly connected to quantum physics [#Kottmann]_. +While Lie algebra theory is an integral part of high energy and condensed matter physics, +recent developments have shown connections to quantum simulation and quantum computing. +In particular, the infamous :doc:`barren plateau problem ` has been fully characterized by the underlying +:doc:`dynamical Lie algebra (DLA) ` [#Fontana]_ [#Ragone]_. +The main result of these works is that the dimension of the circuit's DLA is inversely proportional to the variance of the mean of the gradient +(over a uniform parameter distribution), leading to exponentially vanishing gradients in the uniform average case whenever the +DLA scales exponentially in system size. + +At the same time, there exist Lie algebraic techniques with which one can classically simulate expectation values of circuits with a complexity polynomial +in the dimension of the circuit's DLA [#Somma]_ [#Somma2]_ [#Galitski]_ [#Goh]_. +Hence, circuits with guaranteed non-exponentially vanishing gradients in the uniform average case are classically simulable, +leading to some debate on whether the field of variational quantum computing is doomed or not [#Cerezo]_. +The majority of DLAs are in fact exponentially sized [#Wiersema]_, shifting this debate towards the question of whether or not uniform average case results +are relevant in practice for variational methods [#Mazzola]_, with some arguing for better initialization methods [#Park]_. + +In this demo, we want to focus on those cases where efficient classical simulation is possible due to polynomially sized DLAs. +These instances are rather limited as it mainly concerns DLAs of non-interacting systems as well as the transverse-field Ising model and variations thereof (see [#Wiersema]_ for details). + +Lie algebra basics +------------------ + +Before going into the specifics of Lie algebra simulation (:math:`\mathfrak{g}`-sim), +we want to briefly recap the most important concepts of Lie algebra theory that are relevant for us. +More info can be found in our +:doc:`Intro to (Dynamical) Lie Algebras for quantum practitioners `. + +Given Hermitian operators :math:`G = \{h_i\}` (think Hermitian observables like terms of a Hamiltonian), +the dynamical Lie algebra :math:`\mathfrak{g}` +can be computed via the Lie closure :math:`\langle \cdot \rangle_\text{Lie}` (see :func:`~pennylane.lie_closure`), + +.. math:: \mathfrak{g} = \langle \{h_i\} \rangle_\text{Lie} \subseteq \mathfrak{su}(2^n). + +That is, by computing all possible nested commutators until no new operators emerge. This leads to a set of operators that is closed under commutation, +hence the name. +In particular, the result of the commutator between any two elements in :math:`\mathfrak{g}` +can be decomposed as a linear combination of other elements in :math:`\mathfrak{g}`, + +.. math:: [h_\alpha, h_\beta] = \sum_\gamma f^\gamma_{\alpha \beta} h_\gamma. + +The coefficients :math:`f^\gamma_{\alpha \beta}` are called the structure constants of the DLA and can be computed via the standard +projection in vector spaces (as is :math:`\mathfrak{g}`), + +.. math:: f^\gamma_{\alpha \beta} = \frac{\langle h_\gamma, [h_\alpha, h_\beta]\rangle}{\langle h_\gamma, h_\gamma\rangle}. + +The main difference from the usual vector spaces like :math:`\mathbb{R}^N` or :math:`\mathbb{C}^N` is that here we +use the trace inner product between operators :math:`\langle h_\alpha, h_\beta \rangle = \text{tr}\left[h_\alpha^\dagger h_\beta \right]` + +.. note:: + + Technically, the (dynamical) Lie algebra is formed by skew-Hermitian operators :math:`\{i h_i\}`. + We avoid this distinction here since for all practical purposes one can also look at Hermitian + operators and explicitly add imaginary units in the exponents where appropriate. + For more details, see the note in the "Lie algebras" section of our :doc:`Intro to (Dynamical) Lie Algebras for quantum practitioners `. + +:math:`\mathfrak{g}`-sim theory +------------------------------- + +In Lie algebra simulation, :math:`\mathfrak{g}`-sim, we are interested in how expectation values of Lie algebra elements are transformed under unitary evolution. +We start from an initial expectation value vector of the input state :math:`\rho^0` with respect to each DLA element, + +.. math:: (\vec{e}^0)_\alpha = \text{tr}\left[h_\alpha \rho^0 \right]. + +Graphically, we can represent this as a tensor with one leg. + +.. figure:: ../_static/demonstration_assets/liesim/e.png + :align: center + :width: 33% + +When we transform the state :math:`\rho^0` with a unitary evolution :math:`U`, we can use the cyclic property of the trace to shift the +evolution onto the DLA element, + +.. math:: (\vec{e}^1)_\alpha = \text{tr}\left[ h_\alpha U \rho^0 U^\dagger \right] = \text{tr}\left[ U^\dagger h_\alpha U \rho^0 \right]. + +In the context of :math:`\mathfrak{g}`-sim, we assume the unitary operator to be generated by DLA elements :math:`h_\mu \in \mathfrak{g}`; in particular, we have + +.. math:: U = e^{-i \theta h_\mu} + +with some real parameter :math:`\theta \in \mathbb{R}`. + +As a consequence of the `Baker–Campbell–Hausdorff formula `__, +we know that any :math:`h_\alpha \in \mathfrak{g}` transformed under such a :math:`U` is again in :math:`\mathfrak{g}` +(because it leads to a sum of nested commutators between DLA elements, and the DLA is closed under commutation). +In fact, it is a well-known result that the resulting operator is given by the exponential of the structure constants + +.. math:: e^{i \theta h_\mu} h_\alpha e^{-i \theta h_\mu} = \sum_\beta e^{-i \theta f^\mu_{\alpha \beta}} h_\beta. + +This is the identity connecting the adjoint representations of a Lie group, :math:`\text{Ad}_{e^{-ih_\mu}}(x) = e^{ih_\mu} x e^{-ih_\mu}`, +and the adjoint representation of the associated Lie algebra, :math:`\left(\text{ad}_{h_\mu}\right)_{\alpha \beta} = f^\mu_{\alpha \beta}`. +It can be summarized as + +.. math:: \text{Ad}_{e^{-ih_\mu}} = e^{-i \text{ad}_{h_\mu}}. + +To the best of our knowledge there is no universally accepted name for this identity +(see, e.g. `Adjoint representation (Wikipedia) `__ +or `Lemma 3.14 in Introduction to Lie Groups and Lie Algebras `__), +so we shall refer to it as the "adjoint identity" from here on. + +With this, we can see how the initial expectation value vector is transformed under unitary evolution, + +.. math:: (\vec{e}^1)_\alpha = \sum_\beta e^{-i \theta f^\mu_{\alpha \beta}} \text{tr}\left[h_\beta \rho^0 \right]. + +This is simply the matrix-vector product between the adjoint representation of the unitary gate and the initial expectation value vector. +For a unitary circuit composed of multiple gates, + +.. math:: \mathcal{U} = \prod_j e^{-i \theta_j h_j}, + +this becomes the product of multiple adjoint representations of said gates, + +.. math:: \tilde{U} = \prod_j e^{-i \theta_j \text{ad}_{h_j}}. + +So overall, the evolution can be summarized graphically as the following. + +.. figure:: ../_static/demonstration_assets/liesim/Ue.png + :align: center + :width: 33% + +We are typically interested in expectation values of observables composed of DLA elements, +:math:`\langle \hat{O} \rangle = \sum_\alpha w_\alpha h_\alpha`. +Overall, the computation in :math:`\mathfrak{g}`-sim is a vector-matrix-vector product, + +.. math:: \langle \hat{O} \rangle = \text{tr}\left[\hat{O} \mathcal{U} \rho^0 \mathcal{U}^\dagger \right] = \sum_{\alpha \beta} w_\alpha \tilde{U}_{\alpha \beta} e_\beta = \vec{w} \cdot \tilde{U} \cdot \vec{e}. + +Or, graphically: + +.. figure:: ../_static/demonstration_assets/liesim/wUe.png + :align: center + :width: 33% + +The dimension of :math:`\left(\text{ad}_{h_j}\right)_{\alpha \beta} = f^j_{\alpha \beta}` is +:math:`\text{dim}(\mathfrak{g}) \times \text{dim}(\mathfrak{g})`. So while we evolve a :math:`2^n`-dimensional +complex vector in state vector simulators, we evolve a :math:`\text{dim}(\mathfrak{g})`-dimensional expectation +vector in :math:`\mathfrak{g}`-sim, which is more efficient whenever :math:`\text{dim}(\mathfrak{g}) < 2^n`. In general, it is efficient +whenever :math:`\text{dim}(\mathfrak{g}) = O\left(\text{poly}(n)\right)`. + +:math:`\mathfrak{g}`-sim in PennyLane +------------------------------------- + +Let us put this into practice and write a differentiable :math:`\mathfrak{g}`-simulator in PennyLane. +We start with some boilerplate PennyLane imports. + +""" + +import pennylane as qml +from pennylane import X, Z, I +import numpy as np + +import jax +import jax.numpy as jnp +from jax.scipy.linalg import expm + +jax.config.update("jax_enable_x64", True) +jax.config.update("jax_platform_name", "cpu") + +############################################################################## +# +# System DLA +# ~~~~~~~~~~ +# +# As mentioned before, polynomially sized DLAs are rare, with the transverse-field Ising model (TFIM) with nearest neighbors being one of them. +# We take, for simplicity, the one-dimensional variant with open boundary conditions, +# +# .. math:: H_\text{TFIM} = \sum_{j=1}^{n-1} J X_j X_{j+1} + \sum_{i=1}^{n} h Z_j. +# +# We define its generators and compute the :func:`~pennylane.lie_closure`. + +n = 10 # number of qubits. +generators = [X(i) @ X(i+1) for i in range(n-1)] +generators += [Z(i) for i in range(n)] + +# work with PauliSentence instances for efficiency +generators = [op.pauli_rep for op in generators] + +dla = qml.pauli.lie_closure(generators, pauli=True) +dim_g = len(dla) + +############################################################################## +# We are using the :class:`~pennylane.pauli.PauliSentence` representation of the operators via the ``op.pauli_rep`` attribute for more efficient arithmetic and processing. +# +# Initial expectation value vector +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# With that, we can compute the initial expectation value vector for the :math:`\rho_0 = |0 \rangle \langle 0 |` initial state for every DLA element. +# We are doing a trick of representing the initial state as a Pauli operator, :math:`|0 \rangle \langle 0 |^{\otimes n} = \prod_{i=1}^n (I_i + Z_i)/2`. +# We take advantage of the locality of the DLA elements +# and use the analytic, normalized trace method :meth:`~.pennylane.pauli.PauliSentence.trace`, all to avoid having to go to the full Hilbert space. + +# compute initial expectation value vector +e_in = np.zeros(dim_g, dtype=float) + +for i, h_i in enumerate(dla): + # initial state |0x0| = (I + Z)/2, note that trace function + # below already normalizes by the dimension, + # so we can ommit the explicit factor /2 + rho_in = qml.prod(*(I(i) + Z(i) for i in h_i.wires)) + rho_in = rho_in.pauli_rep + + e_in[i] = (h_i @ rho_in).trace() + +e_in = jnp.array(e_in) +e_in + + +############################################################################## +# Observable +# ~~~~~~~~~~ +# +# We can compute the expectation value of any linear combination of DLA elements. We choose the TFIM Hamiltonian itself, +# +# .. math:: \hat{O} = H_\text{TFIM} = \sum_j J X_j X_{j+1} + h Z_j. +# +# So just the generators with some coefficients. Here we choose :math:`J=h=0.5` for simplicity. +# We generate the :math:`\vec{w}` vector by setting the appropriate coefficients to ``0.5``. + +w = np.zeros(dim_g, dtype=float) +w[:len(generators)] = 0.5 +w = jnp.array(w) + +############################################################################## +# Forward and backward pass +# ~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# Together with the structure constants computed via :func:`~pennylane.structure_constants` we now have all ingredients to define +# the forward pass of the expectation value computation. For demonstration purposes, +# we choose a random subset of ``depth=10`` generators for gates from the DLA. + +adjoint_repr = qml.pauli.structure_constants(dla) + +depth = 10 +gate_choice = np.random.choice(dim_g, size=depth) +gates = adjoint_repr[gate_choice] + +def forward(theta): + # simulation + e_t = e_in + for i in range(depth): + e_t = expm(theta[i] * gates[i]) @ e_t + + # final expectation value + result_g_sim = w @ e_t + + return result_g_sim.real + +theta = jax.random.normal(jax.random.PRNGKey(0), shape=(10,)) + +gsim_forward, gsim_backward = forward(theta), jax.grad(forward)(theta) +gsim_forward, gsim_backward + +############################################################################## +# As a sanity check, we compare the computation with the full state vector equivalent circuit. + +H = 0.5 * qml.sum(*[op.operation() for op in generators]) + +@qml.qnode(qml.device("default.qubit"), interface="jax") +def qnode(theta): + for i, mu in enumerate(gate_choice): + qml.exp(-1j * theta[i] * dla[mu].operation()) + return qml.expval(H) + +statevec_forward, statevec_backward = qnode(theta), jax.grad(qnode)(theta) +statevec_forward, statevec_backward + + +############################################################################## +# We see that both simulations yield the same results, while full state vector simulation is done with a +# :math:`2^n = 1024` dimensional state vector, and :math:`\mathfrak{g}`-sim with a :math:`\text{dim}(g) = 2n (2n-1)/2 = 190` dimensional +# expectation value vector. + +print( + qml.math.allclose(statevec_forward, gsim_forward), + qml.math.allclose(statevec_backward, gsim_backward), +) + +############################################################################## +# Beyond 6 qubits, :math:`\mathfrak{g}`-sim is more efficient in simulating circuits generated by the TFIM Hamiltonian. +# + +import matplotlib.pyplot as plt +ns = np.arange(2, 17) + +plt.plot(ns, 2*ns*(2*ns-1)/2, "x-", label="dim(g)") +plt.plot(ns, 2**ns, ".-", label="2^n") +plt.yscale("log") +plt.legend() +plt.xlabel("n qubits") +plt.show() + +############################################################################## +# +# VQE +# ~~~ +# +# Let us do a quick run of the :doc:`variational quantum eigensolver (VQE) ` on the system at hand. +# +# First, we define our optimization loop in jax. Consider this boilerplate code and see our demo +# on :doc:`how to optimize a QML model using JAX and Optax ` +# for details. + +import optax +from datetime import datetime + +def run_opt(value_and_grad, theta, n_epochs=100, lr=0.1, b1=0.9, b2=0.999, E_exact=0., verbose=True): + + optimizer = optax.adam(learning_rate=lr, b1=b1, b2=b2) + opt_state = optimizer.init(theta) + + energy = np.zeros(n_epochs) + gradients = [] + thetas = [] + + @jax.jit + def step(opt_state, theta): + val, grad_circuit = value_and_grad(theta) + updates, opt_state = optimizer.update(grad_circuit, opt_state) + theta = optax.apply_updates(theta, updates) + + return opt_state, theta, val + + + t0 = datetime.now() + + ## Optimization loop + for n in range(n_epochs): + opt_state, theta, val = step(opt_state, theta) + + energy[n] = val + thetas.append(theta) + t1 = datetime.now() + if verbose: + print(f"final loss: {val - E_exact}; min loss: {np.min(energy) - E_exact}; after {t1 - t0}") + + return thetas, energy, gradients + +############################################################################## +# We can use the Hamiltonian variational ansatz as a natural parametrization of an ansatz circuit to obtain +# the ground-state energy. +# +# In particular, we use the full Hamiltonian generator with a trainable parameter for each term, +# +# .. math:: \prod_{\ell=1}^{10} e^{-i \sum_j \theta^X_j X_j X_{j+1} + \theta^Z_j Z_j}, +# +# and repeat that over ``depth=10`` layers. + +# Pick the adjoint repr of only the Hamiltonian generators +ham_terms = adjoint_repr[:len(generators)] + +def forward(theta): + # simulation + e_t = jnp.array(e_in) + + for i in range(depth): + e_t = expm(jnp.einsum("j,jkl->kl", theta[i], ham_terms)) @ e_t + + # final expectation values + result_g_sim = w @ e_t + + return result_g_sim.real + +############################################################################## +# Now we can run the optimization to find the ground-state energy. + +theta = jax.random.normal(jax.random.PRNGKey(0), shape=(depth, len(generators),)) + +value_and_grad = jax.jit(jax.value_and_grad(forward)) + +value_and_grad(theta) # jit-compile first + +E_exact = H.eigvals().min() + +_, energies, _ = run_opt(value_and_grad, theta, E_exact=E_exact, verbose=True) + +import matplotlib.pyplot as plt +plt.plot(energies-E_exact) +plt.yscale("log") +plt.ylabel("$E - E_{exact}$") +plt.xlabel("epochs") +plt.show() + +############################################################################## +# We see good convergence to the true ground-state energy after ``100`` epochs. + +############################################################################## +# +# Conclusion +# ---------- +# +# We learned about the conceptually intriguing connection between unitary evolution and the adjoint representation of the system DLA via the adjoint identity, +# and saw how this connection can be used for classical simulation. In particular, for specific systems like the TFIM we can efficiently simulate circuit +# expectation values. +# +# In case you are more curious about Lie algebraic simulation techniques, check out the follow-up demo on :doc:`(g+P)-sim ` +# an extension of :math:`\mathfrak{g}`-sim. + + + +############################################################################## +# +# References +# ---------- +# +# .. [#Kottmann] +# +# Korbinian Kottmann +# "Introducing (Dynamical) Lie Algebras for quantum practitioners" +# `PennyLane Demos `__, 2024. +# +# .. [#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. +# +# .. [#Somma] +# +# Rolando D. Somma +# "Quantum Computation, Complexity, and Many-Body Physics" +# `arXiv:quant-ph/0512209 `__, 2005. +# +# .. [#Somma2] +# +# Rolando Somma, Howard Barnum, Gerardo Ortiz, Emanuel Knill +# "Efficient solvability of Hamiltonians and limits on the power of some quantum computational models" +# `arXiv:quant-ph/0601030 `__, 2006. +# +# .. [#Galitski] +# +# Victor Galitski +# "Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach" +# `arXiv:1012.2873 `__, 2010. +# +# .. [#Goh] +# +# Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Frédéric Sauvage +# "Lie-algebraic classical simulations for variational quantum computing" +# `arXiv:2308.01432 `__, 2023. +# +# .. [#Cerezo] +# +# M. Cerezo, Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz, Zoë Holmes +# "Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing" +# `arXiv:2312.09121 `__, 2023. +# +# .. [#Wiersema] +# +# 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. +# +# .. [#Mazzola] +# +# Guglielmo Mazzola +# "Quantum computing for chemistry and physics applications from a Monte Carlo perspective" +# `arXiv:2308.07964 `__, 2023. +# +# .. [#Park] +# +# Chae-Yeun Park, Minhyeok Kang, Joonsuk Huh +# "Hardware-efficient ansatz without barren plateaus in any depth" +# `arXiv:2403.04844 `__, 2024. +# + +############################################################################## +# About the author +# ---------------- +# diff --git a/demonstrations/tutorial_liesim_extension.metadata.json b/demonstrations/tutorial_liesim_extension.metadata.json new file mode 100644 index 0000000000..654f8394d8 --- /dev/null +++ b/demonstrations/tutorial_liesim_extension.metadata.json @@ -0,0 +1,99 @@ +{ + "title": "(g + P)-sim: Extending g-sim by non-DLA observables and gates", + "authors": [ + { + "id": "korbinian_kottmann" + } + ], + "dateOfPublication": "2024-06-18T00:00:00+00:00", + "dateOfLastModification": "2024-06-18T00:00:00+00:00", + "categories": [ + "Quantum Computing", + "Quantum Machine Learning" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/liesim_extension/thumbnail_liesim_extension.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_liesim_extension.png" + } + ], + "seoDescription": "(g + P)-sim: Extending g-sim by non-DLA observables and gates", + "doi": "", + "canonicalURL": "/qml/demos/tutorial_liesim_extension", + "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": "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" + }, + { + "id": "Somma2", + "type": "preprint", + "title": "Efficient solvability of Hamiltonians and limits on the power of some quantum computational models", + "authors": "Rolando Somma, Howard Barnum, Gerardo Ortiz, Emanuel Knill", + "year": "2006", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.quant-ph/0601030", + "url": "https://arxiv.org/abs/quant-ph/0601030" + }, + { + "id": "Galitski", + "type": "preprint", + "title": "Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach", + "authors": "Victor Galitski", + "year": "2010", + "publisher": "", + "journal": "", + "doi": "10.48550/arXiv.1012.2873", + "url": "https://arxiv.org/abs/1012.2873" + } + ], + "basedOnPapers": ["10.48550/arXiv.2308.01432"], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_liealgebra", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_liesim", + "weight": 1.0 + } + ] +} diff --git a/demonstrations/tutorial_liesim_extension.py b/demonstrations/tutorial_liesim_extension.py new file mode 100644 index 0000000000..689ea8a0d1 --- /dev/null +++ b/demonstrations/tutorial_liesim_extension.py @@ -0,0 +1,539 @@ +r"""(g + P)-sim: Extending g-sim by non-DLA observables and gates +================================================================= + +In a :doc:`previous demo `, we introduced the core concepts of +Lie-algebraic simulation techniques [#Somma]_ [#Somma2]_ [#Galitski]_, such as :math:`\mathfrak{g}`-sim [#Goh]_. +With that, we can compute quantum circuit expectation values using the so-called :doc:`dynamical Lie algebra (DLA) ` of the circuit. +The complexity of :math:`\mathfrak{g}`-sim is determined by the dimension of the corresponding Lie algebra, :math:`\mathfrak{g}`. +Adding operators to :math:`\mathfrak{g}` can transform a polynomially sized DLA to an exponentially sized, but we show here that +when one is using only a few of a specific kind of non-DLA gates, the increase in size is polynomial. + +.. note:: + + The contents of this demo are self-contained. However, familiarity with + :doc:`dynamical Lie algebras ` and :doc:`g-sim in PennyLane ` is advised. + +Introduction +------------ + +Lie-algebraic simulation techniques such as :math:`\mathfrak{g}`-sim can be handy in the niche cases where the +:doc:`dynamical Lie algebra (DLA) ` scales polynomially with +the number of qubits. Because those cases essentially boil down to the transverse field Ising model (TFIM) and variants thereof in 1D [#Wiersema]_, +we will do a case study on its DLA specifically. + +We are interested in the case where we want to extend the DLA :math:`\mathfrak{g}` by a few additional gates +that are outside the DLA. For :math:`n` qubits we get a DLA dimension of +:math:`\text{dim}(\mathfrak{g}) = 2n(2n-1)/2` for the TFIM (see :doc:`here `). +Suppose we want to expand the DLA by a single operator :math:`p` in order to use it as a gate, +and let us assume that :math:`p` is the product of two DLA operators that, itself, is not part of the DLA. +Adding product operators to the TFIM DLA and computing their new Lie closure can lead to an exponential increase with a new dimension up to :math:`2(2^{2n-2}-1)`. +In that worst case, we get the so-called `associative algebra` of :math:`\mathfrak{g}`; that is, the algebra from the closure over multiplication, +i.e. which looks at all possible products of operators. This is also a Lie algebra. + +Here, we show how to extend the DLA by such a :math:`p` gate without going to the exponentially large associative algebra, but instead make use of the fact that :math:`p` is +a product of DLA elements. We do so by looking at `moments` of :math:`\mathfrak{g}` instead. The :math:`m`-th order moments are products of :math:`(m+1)` DLA elements. +E.g. :math:`p = h_{\alpha_1} h_{\alpha_2} \notin \mathfrak{g}` is a first order moment. Depending on their order, every non-DLA moment gate increases +the highest moment order considered in the computation, :math:`m_\text{comp}`. The overall cost scales with the maximum order :math:`\text{dim}(\mathfrak{g})^{m_\text{comp}}`. + +In the worst case, each moment expands the space of operators by a factor :math:`\text{dim}(\mathfrak{g})`, such that for :math:`m` moments, +we are dealing with a :math:`\text{dim}(\mathfrak{g})^{m+2}` dimensional space. In that sense, this is similar to +:doc:`Clifford+T simulators ` where +expensive :math:`T` gates come with an exponential cost. +A key difference is that for a finite dimensional DLA, there is a maximum moment :math:`m_\text{max}`. This corresponds to simply constructing the full associative algebra again. +In the case that the required :math:`m_\text{comp} = m_\text{max}`, we can just perform regular :math:`\mathfrak{g}`-sim with the associative algebra. Here we will consider +the case :math:`m_\text{comp} < m_\text{max}`. + +In [#Goh]_, the authors already hint at the possibility of extending :math:`\mathfrak{g}`-sim by expectation values +of products of DLA elements. In this demo, we extend this notion to `gates` generated by moments of the DLA. + +:math:`\mathfrak{g}`-sim +------------------------ + +Let us briefly recap the core principles of :math:`\mathfrak{g}`-sim. We consider a Lie algebra :math:`\mathfrak{g} = \{h_1, .., h_d\}`, which is closed +under commutation (see :func:`~pennylane.lie_closure`). We know that gates :math:`e^{-i \theta h_\alpha}` transform Lie algebra elements into Lie +algebra elements, + +.. math:: e^{i \theta h_\mu} h_\alpha e^{-i \theta h_\mu} = \sum_\beta \left(e^{-i \theta \text{ad}_{h_\mu}}\right)_{\alpha \beta} h_\beta. + +This is the adjoint identity with the adjoint representation of the Lie algebra given by the :func:`~pennylane.structure_constants`, +:math:`f^\mu_{\alpha \beta} = -i \left(\text{ad}_{h_\mu}\right)_{\alpha \beta}`. + +This lets us evolve any expectation value of DLA elements using the adjoint representation of the DLA. +For that, we define the expectation value vector :math:`(\boldsymbol{e})_\alpha = \text{tr}[h_\alpha \rho]`. + +Also, let us write :math:`U = e^{-i \theta \text{ad}_{h_\mu}}` corresponding to a unitary :math:`\mathcal{U} = e^{-i \theta h_\mu}`. +Using the adjoint identity above and the cyclic property of the trace, we can write an evolved expectation value vector as + +.. math:: \text{tr}\left[h_\alpha \mathcal{U} \rho \mathcal{U}^\dagger\right] = \sum_\beta U_{\alpha \beta} \text{tr}\left[h_\beta \rho \right]. + +Hence, the expectation value vector is simply transformed by matrix multiplication with :math:`U` and we have + +.. math:: \boldsymbol{e}^\text{out} = U \boldsymbol{e}^\text{in} + +for some input expectation value vector :math:`\boldsymbol{e}^\text{in}`. + +A circuit comprised of multiple unitaries :math:`\mathcal{U}` then simply corresponds to evolving the expectation value vector +with :math:`U`. + +We are going to concretely use the DLA of the transverse field Ising model, + +.. math:: H_\text{Ising} = J \sum_{i=1}^{n-1} X_i X_{i+1} + h \sum_{i=1}^n Z_i. + +This is one of the few systems that yield a polynomially sized DLA. +Let us construct its DLA via :func:`~pennylane.lie_closure`. + +""" + +import pennylane as qml +import numpy as np + +from pennylane import X, Y, Z, I +from pennylane.pauli import PauliSentence, PauliWord +from scipy.linalg import expm + +import copy + +# TFIM generators +def TFIM(n): + generators = [X(i) @ X(i+1) for i in range(n-1)] + generators += [Z(i) for i in range(n)] + generators = [op.pauli_rep for op in generators] + + dla = qml.pauli.lie_closure(generators, pauli=True) + dim_dla = len(dla) + return generators, dla, dim_dla + +generators, dla, dim_g = TFIM(n=4) + +############################################################################## +# In regular :math:`\mathfrak{g}`-sim, the unitary evolution :math:`\mathcal{U}` of the expectation vector +# is simply generated by the adjoint representation :math:`U`. + +adjoint_repr = qml.structure_constants(dla) +gate = adjoint_repr[-1] +theta = 0.5 + +U = expm(theta * gate) + +############################################################################## +# +# :math:`(\mathfrak{g}+P)`-sim +# ---------------------------- +# +# We now want to extend :math:`\mathfrak{g}`-sim by operators that are not in the DLA, but a product +# of DLA operators. Note that while the DLA is closed under commutation, it is not closed under multiplication, +# such that products of DLA elements are in general not in :math:`\mathfrak{g}`. +# +# Let us look at the adjoint action of a gate generated by :math:`p = h_{\mu_1} h_{\mu_2} .. \notin \mathfrak{g}`, +# +# .. math:: e^{i \theta h_{\mu_1} h_{\mu_2} ..} h_\alpha e^{-i \theta h_{\mu_1} h_{\mu_2} ..} = \sum_\beta \boldsymbol{P}^0_{\alpha \beta} h_\beta + \sum_{\beta_1 \beta_2} \boldsymbol{P}^1_{\alpha \beta_1 \beta_2} h_{\beta_1} h_{\beta_2} + ... +# +# Here, :math:`\boldsymbol{P}^m` correspond to the contributions of the :math:`m`-th moments in :math:`\mathfrak{g}`. +# Let us look at the case where we use a first order product, :math:`\mathcal{P} = e^{-i \theta h_{\mu_1} h_{\mu_2}}`, and only DLA operators and first order moments contribute to the adjoint action. +# +# For that, let us construct a concrete example. First we pick two elements from :math:`\mathfrak{g}` such that their product is not in :math:`\mathfrak{g}`. + +p = dla[-5] @ dla[-2] +p = next(iter(p)) # strip any scalar coefficients +dla_vspace = qml.pauli.PauliVSpace(dla, dtype=complex) +dla_vspace.is_independent(p.pauli_rep) + + +############################################################################## +# +# .. note:: +# +# For DLAs consisting of Pauli words — as is the case for the TFIM — we can simply remove any scalar factors to avoid having additional imaginary factors in the exponent of gates. +# +# Now, we compute :math:`e^{i \theta h_{\mu_2} h_{\mu_1}} h_\alpha e^{-i \theta h_{\mu_1} h_{\mu_2}}` and decompose it in the DLA and first moments. +# +# Note that since the product basis is overcomplete, we only keep track of the linearly independent elements and ignore the rest. + +def exppw(theta, ps): + # assert that it is indeed a pure Pauli word, not a sentence + assert (len(ps) == 1 and isinstance(ps, PauliSentence)) or isinstance(ps, PauliWord) + return np.cos(theta) * PauliWord({}) + 1j * np.sin(theta) * ps + +theta = 0.5 + +P = exppw(theta, p) +P_dagger = exppw(-theta, p) # complex conjugate with p just being a hermitian pauli word + +P0 = np.zeros((dim_g, dim_g), dtype=float) + +for i, h1 in enumerate(dla): + res = P @ h1 @ P_dagger + for j, h2 in enumerate(dla): + # decompose the result in terms of DLA elements + # res = ∑ (res · h_j / ||h_j||^2) * h_j + value = (res @ h2).trace().real + value = value / (h2 @ h2).trace() + P0[i, j] = value + +P1 = np.zeros((dim_g, dim_g, dim_g), dtype=float) + +for i, h1 in enumerate(dla): + res = P @ h1 @ P_dagger + dla_and_M1_vspace = copy.deepcopy(dla_vspace) + for j, h2 in enumerate(dla): + for l, h3 in enumerate(dla): + prod = h2 @ h3 + + if not dla_and_M1_vspace.is_independent(prod): + continue + + # decompose the result in terms of products of DLA elements + # res = ∑ (res · p_j / ||p_j||^2) * p_j + value = (res @ prod).trace().real + value = value / (prod @ prod).trace().real + P1[i, j, l] = value + dla_and_M1_vspace.add(prod) + +############################################################################## +# We want to confirm that the adjoint action of :math:`\mathcal{P}` is indeed fully described by the zeroth and first moments. +# +# For that, we reconstruct the transformed DLA elements and compare them with the decomposition. + +for i, h1 in enumerate(dla): + res = P @ h1 @ P_dagger + res.simplify() + + reconstruct = sum([P0[i, j] * dla[j] for j in range(dim_g)]) + reconstruct += sum([P1[i, j, l] * dla[j] @ dla[l] for j in range(dim_g) for l in range(dim_g)]) + reconstruct.simplify() + + assert res == reconstruct + + +############################################################################## +# Now that we have successfully constructed a :math:`\mathcal{P}` gate, +# let us look how entering it in a circuit transforms DLA elements (and therefore expectation value vector elements). +# +# .. math:: +# +# \begin{align*} +# (\boldsymbol{e})_\alpha & = \text{tr}\left[h_\alpha \mathcal{P} \rho \mathcal{P}^\dagger \right] = \text{tr}\left[\mathcal{P}^\dagger h_\alpha \mathcal{P} \rho \right] \\ +# \ & = \sum_\beta \boldsymbol{P}^0_{\alpha \beta} \text{tr}\left[ h_\beta \rho \right] + \sum_{\beta_1 \beta_2} \boldsymbol{P}^1_{\alpha \beta_1 \beta_2} \text{tr}\left[ h_{\beta_1} h_{\beta_2} \rho \right] \\ +# \ & = \sum_\beta \boldsymbol{P}^0_{\alpha \beta} \boldsymbol{E}^0_\beta + \sum_{\beta_1 \beta_2} \boldsymbol{P}^1_{\alpha \beta_1 \beta_2} \boldsymbol{E}^1_{\beta_1 \beta_2} +# \end{align*} +# +# Here we have defined the expectation tensor +# :math:`(\boldsymbol{E}^m)_{\beta_1 , .. , \beta_{m+1}} = \text{tr}\left[ h_{\beta_1} .. h_{\beta_{m+1}} \rho \right]` for the :math:`m`-th moment. +# Note that :math:`\boldsymbol{e} = \boldsymbol{E}^0` is the expectation value vector for regular :math:`\mathfrak{g}`-sim. +# +# +# Such a computation corresponds to the branching off from the original diagram, with an extra contribution coming from the higher moments. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/first_split.png +# :width: 45% +# :align: center +# +# When inserting an arbitrary DLA gate :math:`U` before and :math:`V` after the :math:`\mathcal{P}` gate, +# we obtain the following diagram. Note that :math:`U` and :math:`V` can be compositions of multiple DLA gates again. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/first_order_diagram.png +# :width: 45% +# :align: center +# +# Note that in one vertical column the :math:`U` correspond to the same matrix. +# +# +# Example +# ~~~~~~~ +# +# Let us compute an example. For that we start by computing the initial expectation vector and tensor. + +E0_in = np.zeros((dim_g), dtype=float) +E1_in = np.zeros((dim_g, dim_g), dtype=float) +E_in = [E0_in, E1_in] + +for i, hi in enumerate(dla): + rho_in = qml.prod(*(I(i) + Z(i) for i in hi.wires)) + rho_in = rho_in.pauli_rep + + E_in[0][i] = (hi @ rho_in).trace() + +for i, hi in enumerate(dla): + for j, hj in enumerate(dla): + prod = hi @ hj + if prod.wires != qml.wires.Wires([]): + rho_in = qml.prod(*(I(i) + Z(i) for i in prod.wires)) + else: + rho_in = PauliWord({}) # identity + rho_in = rho_in.pauli_rep + + E_in[1][i, j] = (prod @ rho_in).trace().real + +############################################################################## +# +# Now we need to compute the two branches from the diagram above. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/first_order_diagram.png +# :width: 45% +# :align: center +# + +# some other DLA gate V +V = expm(0.5 * adjoint_repr[-2]) + +# contract first branch +# V - P - U - E^0_in +res0 = U @ E_in[0] +res0 = P0 @ res0 +res0 = V @ res0 + +# contract second branch + +# --U-==-+--------+ -+------+ +# | E^1_in | = | res | +# --U-==-+--------+ -+------+ +res = np.einsum("ij,jl->il", U, E_in[1]) +res = np.einsum("kl,il->ik", U, res) + +# +-----+-==-+------+ +# -V-==-| P^1 | | res | +# +-----+-==-+------+ +res = np.einsum("ijl,jl->i", P1, res) +res = V @ res + +res = res + res0 + +############################################################################## +# As a sanity check, let us compare this to the same circuit but using our default state vector simulator in PennyLane. + +@qml.qnode(qml.device("default.qubit")) +def true(): + qml.exp(-1j * theta * dla[-1].operation()) + qml.exp(-1j * 0.5 * p.operation()) + qml.exp(-1j * 0.5 * dla[-2].operation()) + return [qml.expval(op.operation()) for op in dla] + +true_res = np.array(true()) + +np.allclose(true_res, res) + +############################################################################## +# We find that indeed both results coincide and expectation value vectors are correctly transformed in :math:`(\mathfrak{g}+P)`-sim. + +############################################################################## +# Higher moments +# ~~~~~~~~~~~~~~ +# +# We can extend the above approach by a second :math:`P` gate in the circuit. +# This leads to contributions from up to the third order. The diagram for a circuit :math:`P V P U` has the following five branches. +# +# First, the zeroth- and first-order contribution. This can be seen as the branching off from the first previous diagram. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/2P_first_second.png +# :width: 35% +# :align: center +# +# We also obtain the third-order diagram containing both :math:`\boldsymbol{P}^1` tensors. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/2P_fourth.png +# :width: 35% +# :align: center +# +# To get the correct results, we also obtain intermediate second-order diagrams. +# +# .. figure:: /_static/demonstration_assets/liesim_extension/2P_thirds.png +# :width: 90% +# :align: center +# + +############################################################################## +# Moment vector space +# ------------------- +# +# +# The above diagrams are handy to understand the maximum moment order required for adding :math:`P` gates of a certain order. +# There is, however, a lot of redundancy due to the overcompleteness of naively looking at moments as `all` possible products between DLA elements. +# +# Instead, we can also work in the vector space of unique moments +# +# .. math:: \mathcal{M}^m := \{p | p= h_{\alpha_1} .. h_{\alpha_m+1} \notin \mathcal{M}^{m-1} \} \cup \mathcal{M}^{m-1} +# +# that is iteratively built from :math:`\mathcal{M}^0 = \mathfrak{g}`. +# +# Even though these spaces in general do `not` form +# Lie algebras, we can still compute their (pseudo) adjoint representations and use them for :math:`\mathfrak{g}`-sim as long as +# we work in a large enough space with the correct maximum moment order. +# +# We now set up the moment vector spaces starting from the DLA and keep adding linearly independent product operators. + +def Moment_step(ops, dla): + MomentX = qml.pauli.PauliVSpace(ops.copy()) + for i, op1 in enumerate(dla): + for op2 in ops[i+1:]: + prod = op1 @ op2 + # ignore scalar coefficient + pw = next(iter(prod.keys())) + + MomentX.add(pw) + + return MomentX.basis + +Moment0 = dla.copy() +Moment = [Moment0] +dim = [len(Moment0)] +for i in range(1, 5): + Moment.append(Moment_step(Moment[-1], dla)) + dim.append(len(Moment[-1])) + +dim + +############################################################################## +# +# We see that for the considered example of :math:`n = 4` we reach the +# maximum moment already for the second order +# (the additional operator in the third moment space is just the identity). +# +# We can repeat our original computation for the first moments using the +# :math:`98`-dimensional first-order moment vector space :math:`\mathcal{M}^1`. +# +# The recipe follows the exact same steps as :math:`\mathfrak{g}`-sim but using :math:`\mathcal{M}^1` instead. +# First, we compute the input expectation value vector. + +comp_moment = 1 + +e_in = np.zeros((dim[comp_moment]), dtype=float) + +for i, hi in enumerate(Moment[comp_moment]): + rho_in = qml.prod(*(I(i) + Z(i) for i in hi.wires)) + rho_in = rho_in.pauli_rep + + e_in[i] = (hi @ rho_in).trace() + +############################################################################## +# +# Next, we compute the (pseudo-)adjoint representation of :math:`\mathcal{M}^1`. + +adjoint_repr = qml.structure_constants(Moment[comp_moment]) + +############################################################################## +# +# We can now choose arbitrary DLA gates and a maximum of `one` :math:`P` gate to evolve the expectation value vector. + +e_t = e_in +e_t = expm(0.5 * adjoint_repr[dim_g-1]) @ e_t # the same U gate +e_t = expm(0.5 * adjoint_repr[74]) @ e_t # the same P gate +e_t = expm(0.5 * adjoint_repr[dim_g-2]) @ e_t # the same V gate + +############################################################################## +# The final result matches the state vector result again + +np.allclose(e_t[:dim_g], true_res) + +############################################################################## +# Limitations +# ----------- +# +# We saw how we can make use of moment vector spaces to extend :math:`\frak{g}`-sim by non-DLA elements under certain conditions. +# The upside is that while the Lie closure or construction of the associative algebra leads to an exponential DLA in :math:`n`, we +# get away with a polynomial cost in :math:`n`, as we have :math:`O(\text{dim}(\mathfrak{g})^{m_{\text{comp}}})`-sized objects +# for some fixed maximum moment order :math:`m_{\text{comp}}` in the computation, with some additional reductions due to the redundancies in the moment spaces. +# +# However, we argue that while this is interesting in theory, there is little practical utility. +# To show that, we plot the dimensions of the first and second moments against the associative algebra dimension. + +dims_dla = [] +dims_moment = [] +dims_tempdla = [] + +ns = np.arange(2, 6) + +for n in ns: + _, dla, dim_g = TFIM(n) + + Moment0 = dla.copy() + Moment = [Moment0] + dim = [len(Moment0)] + for i in range(1, 5): + Moment.append(Moment_step(Moment[-1], dla)) + dim.append(len(Moment[-1])) + + tempdla = qml.lie_closure(dla + [Moment[1][-1]], pauli=True) + + dims_dla.append(dim_g) + dims_moment.append(dim) + dims_tempdla.append(len(tempdla)) + +import matplotlib.pyplot as plt + +plt.title("Dimensions of $\\langle g + P \\rangle_{{Lie}}$ vs $\mathcal{M}^m$") + +plt.plot(ns, dims_tempdla, "o--", label="${{dim}}(\\langle g + P \\rangle_{{Lie}})$", color="tab:blue") +plt.plot(ns, 2 * (2**(2*ns - 2) - 1), "-", label="$2(2^{{2n-2}}-1)$", color="tab:blue") + +color = ["tab:orange", "tab:green", "tab:cyan"] +dims_moment = np.array(dims_moment) +for i in range(3): + plt.plot(ns, dims_moment[:, i], "x--", label=f"$dim(\mathcal{{M}}^{i})$", color=color[i]) + fitcoeff = np.polyfit(ns, dims_moment[:, i], i+2) # polynomial fit of order m+1 + plt.plot(ns, np.poly1d(fitcoeff)(ns), "-", label=f"$O(n^{{{i}+2}})$", color=color[i]) + +plt.xticks(ns) +plt.yscale("log") + +plt.legend() +plt.xlabel("n") +plt.show() + +############################################################################## +# +# First, we note that the maximum moment is quickly reached for small system sizes. In that case we have :math:`m_\text{comp} = m_\text{max}` +# so we might as well look at the associative algebra and perform regular :math:`\mathfrak{g}`-sim. +# Secondly, we also note that the dimensions quickly explode and become hard to handle in reasonable times. +# +# For example, in all cases here there are no non-trivial third-order moments. We would have to go to :math:`n = 6`, +# for which there are :math:`1980` elements in :math:`\mathcal{M}^3`, which corresponds to iterating over +# :math:`1980^3 \approx 2^{32}` commutators to compute the (pseudo-)adjoint representation. This is +# already a stretch to accomplish with the available tools. +# +# Hence, this method is effectively restricted to very few non-DLA gates of Ising-type DLAs, +# rendering the method overall niche for practical applications. On the other hand, we gained some new theoretical insights +# into the relationship between the simulability of a quantum circuit and its DLA. In particular, we constructed a polynomial +# algorithm in the number of qubits :math:`n`, for simulating DLA circuits with up to :math:`m_\text{comp}` moments in :math:`\mathcal{O}(\text{dim}\left(\mathfrak{g}(n)\right)^{m_\text{comp} + 2}) = \mathcal{O}(\text{poly}(n))`. + + + +############################################################################## +# +# References +# ---------- +# +# .. [#Somma] +# +# Rolando D. Somma +# "Quantum Computation, Complexity, and Many-Body Physics" +# `arXiv:quant-ph/0512209 `__, 2005. +# +# .. [#Somma2] +# +# Rolando Somma, Howard Barnum, Gerardo Ortiz, Emanuel Knill +# "Efficient solvability of Hamiltonians and limits on the power of some quantum computational models" +# `arXiv:quant-ph/0601030 `__, 2006. +# +# .. [#Galitski] +# +# Victor Galitski +# "Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach" +# `arXiv:1012.2873 `__, 2010. +# +# .. [#Goh] +# +# Matthew L. Goh, Martin Larocca, Lukasz Cincio, M. Cerezo, Frédéric Sauvage +# "Lie-algebraic classical simulations for variational quantum computing" +# `arXiv:2308.01432 `__, 2023. +# +# .. [#Wiersema] +# +# 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. +# + +############################################################################## +# About the author +# ---------------- +# diff --git a/demonstrations/tutorial_mapping.metadata.json b/demonstrations/tutorial_mapping.metadata.json index 7f06573ef2..9b77001a2c 100644 --- a/demonstrations/tutorial_mapping.metadata.json +++ b/demonstrations/tutorial_mapping.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2024-05-06T00:00:00+00:00", - "dateOfLastModification": "2024-05-06T00:00:00+00:00", + "dateOfLastModification": "2024-06-19T00:00:00+00:00", "categories": [ "Algorithms", "Quantum Computing", @@ -16,11 +16,11 @@ "previewImages": [ { "type": "thumbnail", - "uri": "/_static/demonstration_assets/mapping/thumbnail_mapping_2024-05-01.png" + "uri": "/_static/demonstration_assets/mapping/thumbnail_mapping_2024-06-20.png" }, { "type": "large_thumbnail", - "uri": "/_static/large_demo_thumbnails/thumbnail_large_mapping_2024-05-01.png" + "uri": "/_static/large_demo_thumbnails/thumbnail_large_mapping_2024-06-20.png" } ], "seoDescription": "Learn how to map fermionic operators to qubit operators", diff --git a/demonstrations/tutorial_mapping.py b/demonstrations/tutorial_mapping.py index ec55d2090d..c2b93f5efb 100644 --- a/demonstrations/tutorial_mapping.py +++ b/demonstrations/tutorial_mapping.py @@ -12,9 +12,9 @@ will also learn how to use these mappings in the context of computing the ground state energy of a molecular system. -.. figure:: ../_static/demonstration_assets/mapping/OGthumbnail_large_mapping_2024-05-01.png +.. figure:: ../_static/demonstration_assets/mapping/long_image.png :align: center - :width: 50% + :width: 80% :target: javascript:void(0) Jordan-Wigner Mapping @@ -155,7 +155,7 @@ # `qubit tapering `__ demo. # Let's look at an example. -generators = [qml.prod(*[qml.Z(i) for i in range(qubits-1)]), qml.Z(qubits-1)] +generators = [qml.prod(*[qml.Z(i) for i in range(qubits - 1)]), qml.Z(qubits - 1)] paulixops = qml.paulix_ops(generators, qubits) paulix_sector = [1, 1] taper_op = qml.taper(pauli_pr, generators, paulixops, paulix_sector) @@ -204,9 +204,10 @@ from pennylane import qchem from pennylane import numpy as np -symbols = ['H', 'H'] -geometry = np.array([[0.0, 0.0, -0.69434785], - [0.0, 0.0, 0.69434785]], requires_grad = False) +symbols = ["H", "H"] +geometry = np.array( + [[0.0, 0.0, -0.69434785], [0.0, 0.0, 0.69434785]], requires_grad=False +) mol = qchem.Molecule(symbols, geometry) @@ -266,13 +267,16 @@ singles_fermi = [] for ex in singles: - singles_fermi.append(from_string(f"{ex[1]}+ {ex[0]}-") - - from_string(f"{ex[0]}+ {ex[1]}-")) + singles_fermi.append( + from_string(f"{ex[1]}+ {ex[0]}-") - from_string(f"{ex[0]}+ {ex[1]}-") + ) doubles_fermi = [] for ex in doubles: - doubles_fermi.append(from_string(f"{ex[3]}+ {ex[2]}+ {ex[1]}- {ex[0]}-") - - from_string(f"{ex[0]}+ {ex[1]}+ {ex[2]}- {ex[3]}-")) + doubles_fermi.append( + from_string(f"{ex[3]}+ {ex[2]}+ {ex[1]}- {ex[0]}-") + - from_string(f"{ex[0]}+ {ex[1]}+ {ex[2]}- {ex[3]}-") + ) ############################################################################## # The fermionic operators are now mapped to qubit operators. @@ -293,6 +297,7 @@ dev = qml.device("default.qubit", wires=qubits) + @qml.qnode(dev) def circuit(params): qml.BasisState(hf_state, wires=range(qubits)) @@ -305,7 +310,8 @@ def circuit(params): return qml.expval(h_pauli) -print('Energy =', circuit(params)) + +print("Energy =", circuit(params)) ############################################################################## # Using the above circuit, we produce the ground state energy of :math:`H_2` molecule. diff --git a/demonstrations/tutorial_mcm_introduction.metadata.json b/demonstrations/tutorial_mcm_introduction.metadata.json index f919427c9e..fe0471e3f5 100644 --- a/demonstrations/tutorial_mcm_introduction.metadata.json +++ b/demonstrations/tutorial_mcm_introduction.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2024-05-10T00:00:00+00:00", - "dateOfLastModification": "2024-05-10T00:00:00+00:00", + "dateOfLastModification": "2024-06-21T00:00:00+00:00", "categories": [ "Getting Started", "Quantum Computing" diff --git a/demonstrations/tutorial_mcm_introduction.py b/demonstrations/tutorial_mcm_introduction.py index 4a2f99d021..b5d4168210 100644 --- a/demonstrations/tutorial_mcm_introduction.py +++ b/demonstrations/tutorial_mcm_introduction.py @@ -35,7 +35,7 @@ # Given how fundamental those question are, there is a plethora of learning # resources on this topic, from textbooks [#mike_n_ike]_ and (video) lectures # [#feynman]_, [#zwiebach]_ to interactive studying material like -# `the Xanadu Quantum Codebook `__ +# `the PennyLane Codebook `__ # or Ref. [#van_der_Sar]_. # Furthermore, discussing measurements quickly # leads to questions about the interpretation of quantum mechanics and philosophical, @@ -126,11 +126,13 @@ dev = qml.device("default.qubit") + @qml.qnode(dev) def before(): qml.Hadamard(0) # Create |+> state return qml.expval(qml.X(0)), qml.expval(qml.Z(0)) + b = before() print(f"Expectation values before any measurement: {b[0]:.1f}, {b[1]:.1f}") @@ -164,12 +166,14 @@ def before(): # variable to its outcome. # + @qml.qnode(dev) def after(): qml.Hadamard(0) # Create |+> state qml.measure(0) # Measure without recording the outcome return qml.expval(qml.X(0)), qml.expval(qml.Z(0)) + a = after() print(f"Expectation value after the measurement: {a[0]:.1f}, {a[1]:.1f}") @@ -191,12 +195,14 @@ def after(): # ``qml.measure``: # + @qml.qnode(dev) def after(): qml.Hadamard(0) # Create |+> state qml.measure(0, postselect=0) # Measure and only accept 0 as outcome return qml.expval(qml.X(0)), qml.expval(qml.Z(0)) + a = after() print(f"Expectation value after the postselected measurement: {a[0]:.1f}, {a[1]:.1f}") @@ -228,11 +234,13 @@ def after(): # need to discuss what to return from it! # + def bell_pair_preparation(**kwargs): qml.Hadamard(0) qml.CNOT([0, 1]) # Create a Bell pair qml.measure(0, **kwargs) # Measure first qubit, using keyword arguments + ###################################################################### # Without recording the outcome, i.e., ``postselect=None``, we obtain the state # @@ -251,11 +259,13 @@ def bell_pair_preparation(**kwargs): # And those will be the return types to complete our quantum function: # + @qml.qnode(dev) def bell_pair(postselect): bell_pair_preparation(postselect=postselect) return qml.purity([0, 1]), qml.vn_entropy(0) + ###################################################################### # So let's compare the purities and von Neumann entropies of the Bell state # after measurement: @@ -297,11 +307,13 @@ def bell_pair(postselect): # can simply pass the keyword argument ``reset`` to activate the qubit reset: # + @qml.qnode(dev) def bell_pair_with_reset(reset): bell_pair_preparation(reset=reset) return qml.expval(qml.Z(0)), qml.expval(qml.Z(1)), qml.expval(qml.Z(0) @ qml.Z(1)) + no_reset = bell_pair_with_reset(reset=False) reset = bell_pair_with_reset(reset=True) @@ -359,12 +371,14 @@ def bell_pair_with_reset(reset): magic_state = np.array([1, np.exp(1j * np.pi / 4)]) / np.sqrt(2) + def t_gadget(wire, aux_wire): qml.QubitStateVector(magic_state, aux_wire) qml.CNOT([wire, aux_wire]) mcm = qml.measure(aux_wire, reset=True) # Resetting disentangles aux qubit qml.cond(mcm, qml.S)(wire) # Apply qml.S(wire) if mcm was 1 + ###################################################################### # We will not derive why this works (see, e.g., [#zhou]_ instead), but # illustrate that this gadget implements a ``T`` gate by combining it with an adjoint @@ -380,6 +394,7 @@ def t_gadget(wire, aux_wire): # - return the expectation value :math:`\langle X_0\rangle`. # + @qml.qnode(dev) def test_t_gadget(init_state): qml.Hadamard(0) # Create |+> state @@ -391,6 +406,7 @@ def test_t_gadget(init_state): return qml.expval(qml.X(0)) + print(f" with initial state |+>: {test_t_gadget('+'):4.1f}") print(f" with initial state |->: {test_t_gadget('-'):4.1f}") diff --git a/demonstrations/tutorial_mol_geo_opt.metadata.json b/demonstrations/tutorial_mol_geo_opt.metadata.json index 68d3ef79a8..33d2118d3d 100644 --- a/demonstrations/tutorial_mol_geo_opt.metadata.json +++ b/demonstrations/tutorial_mol_geo_opt.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2021-06-30T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_phase_kickback.metadata.json b/demonstrations/tutorial_phase_kickback.metadata.json index 1bd36a4a85..a167b494e1 100644 --- a/demonstrations/tutorial_phase_kickback.metadata.json +++ b/demonstrations/tutorial_phase_kickback.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2023-08-01T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-06-21T00:00:00+00:00", "categories": [ "Getting Started", "Algorithms", diff --git a/demonstrations/tutorial_phase_kickback.py b/demonstrations/tutorial_phase_kickback.py index db07460891..72895a2f21 100644 --- a/demonstrations/tutorial_phase_kickback.py +++ b/demonstrations/tutorial_phase_kickback.py @@ -35,7 +35,7 @@ # :align: center # :width: 50% # -# If you want to know more about the details, do not hesitate to consult the node `[P.1] `_ of the Xanadu Quantum Codebook. +# If you want to know more about the details, do not hesitate to consult the node `[P.1] `_ of the PennyLane Codebook. ###################################################################### # Setting up PennyLane diff --git a/demonstrations/tutorial_qcbm.metadata.json b/demonstrations/tutorial_qcbm.metadata.json new file mode 100644 index 0000000000..f8be1488d1 --- /dev/null +++ b/demonstrations/tutorial_qcbm.metadata.json @@ -0,0 +1,96 @@ +{ + "title": "Quantum Circuit Born Machines", + "authors": [ + { + "id": "gopal_ramesh_dahale", + "affiliation": "Indian Institute of Technology Bhilai" + } + ], + "dateOfPublication": "2024-05-22T00:00:00+00:00", + "dateOfLastModification": "2024-05-22T00:00:00+00:00", + "categories": ["Quantum Machine Learning"], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demonstration_assets/qcbm/thumbnail_QuantumCircuitBornMachines_2024-05-13.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/large_demo_thumbnails/thumbnail_large_QuantumCircuitBornMachines_2024-05-13.png" + } + ], + "seoDescription": "Learn how to use the Quantum Circuit Born Machines (QCBMs).", + "doi": "", + "canonicalURL": "/qml/demos/tutorial_qcbm", + "references": [ + { + "id": "Liu", + "type": "article", + "title": "Differentiable learning of quantum circuit Born machines", + "authors": "Liu, Jin-Guo and Wang, Lei", + "year": "2018", + "publisher": "American Physical Society", + "journal": "Phys. Rev. A", + "doi": "10.1103/PhysRevA.98.062324", + "url": "https://link.aps.org/doi/10.1103/PhysRevA.98.062324" + }, + { + "id": "Ben", + "type": "article", + "title": "A generative modeling approach for benchmarking and training shallow quantum circuits", + "authors": "Benedetti, Marcello and Garcia-Pintos, Delfina and Nam, Yunseong and Perdomo-Ortiz, Alejandro", + "year": "2018", + "journal": "npj Quantum Information", + "doi": "10.1038/s41534-019-0157-8" + }, + { + "id": "Du", + "type": "article", + "title": "Expressive power of parametrized quantum circuits", + "authors": "Du, Yuxuan and Hsieh, Min-Hsiu and Liu, Tongliang and Tao, Dacheng", + "year": "2020", + "publisher": "American Physical Society", + "journal": "Phys. Rev. Res.", + "doi": "10.1103/PhysRevResearch.2.033125", + "url": "https://link.aps.org/doi/10.1103/PhysRevResearch.2.033125" + }, + { + "id": "Ack", + "type": "article", + "title": "A learning algorithm for boltzmann machines", + "authors": "David H. Ackley and Geoffrey E. Hinton and Terrence J. Sejnowski", + "year": "1985", + "journal": "Cognitive Science", + "doi": "10.1016/S0364-0213(85)80012-4", + "url": "https://www.sciencedirect.com/science/article/pii/S0364021385800124" + }, + { + "id": "Gret", + "type": "article", + "title": "A Kernel Method for the Two-Sample-Problem", + "authors": "Gretton, Arthur and Borgwardt, Karsten and Rasch, Malte and Schölkopf, Bernhard and Smola, Alexander", + "year": "2006", + "journal": "Advances in neural information processing systems" + }, + { + "id": "Kull", + "type": "article", + "title": "On Information and Sufficiency", + "authors": "Solomon Kullback and R. A. Leibler", + "year": "1951", + "journal": "Annals of Mathematical Statistics", + "url": "https://api.semanticscholar.org/CorpusID:120349231" + } + ], + "basedOnPapers": ["10.1103/PhysRevA.98.062324"], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_kernels_module", + "weight": 1.0 + } + ], + "hardware": [] +} \ No newline at end of file diff --git a/demonstrations/tutorial_qcbm.py b/demonstrations/tutorial_qcbm.py new file mode 100644 index 0000000000..fc54816994 --- /dev/null +++ b/demonstrations/tutorial_qcbm.py @@ -0,0 +1,576 @@ +r"""Quantum Circuit Born Machines +============================= + +Unsupervised generative modelling emerges as a promising application for achieving practical quantum advantage +on classical data due to its high complexity relative to supervised machine learning tasks. This makes them +a suitable candidate for leveraging the potential of near-term quantum computers. A popular quantum generative +model known as Quantum Circuit Born Machines (QCBMs) has shown impressive results in modelling distributions +across various datasets, including both toy and real-world datasets, and you will learn about them in this demo. + +.. figure:: ../_static/demonstration_assets/qcbm/OGthumbnail_large_QuantumCircuitBornMachines_2024-05-13.png + :align: center + :width: 50% + :target: javascript:void(0) + + +Generative modelling with QCBMs +------------- + +Quantum Circuit Born machines (QCBMs) show promise in unsupervised generative modelling, aiming to learn and +represent classical dataset probability distributions through pure quantum states [#Liu]_ [#Ben]_. They are popular +due to their high expressive power [#Du]_. Born machines leverage the probabilistic interpretation of +quantum wavefunctions, representing probability distributions with pure quantum states instead of +thermal distributions like Boltzmann machines. This allows Born machines to directly generate +samples through projective measurements on qubits, offering a faster alternative to the Gibbs +sampling approach [#Ack]_. + +For a dataset :math:`\mathcal{D} = \{x\}` with independent and identically distributed samples from +an unknown target distribution :math:`\pi(x)`, QCBM is used to generate samples closely resembling +the target distribution. QCBM transforms the input product state :math:`|\textbf{0} \rangle` to a +parameterized quantum state :math:`|\psi_\boldsymbol{\theta}\rangle`. Measuring this output state in the +computational basis yields a sample of bits :math:`x \sim p_\theta(x)`. + +.. math:: + + p_\boldsymbol{\theta}(x) = |\langle x | \psi_\boldsymbol{\theta} \rangle|^2. + +The objective is to align the model probability distribution :math:`p_\boldsymbol{\theta}` with the target +distribution :math:`\pi`. + +In this tutorial, following [#Liu]_, we will implement a gradient-based algorithm for QCBM using +PennyLane. We describe the model and learning algorithm followed by its application to the +:math:`3 \times 3` Bars and Stripes dataset and double Gaussian peaks. + +To train the QCBM, we use the squared maximum mean discrepancy (MMD) as the loss function + +.. math:: + + \mathcal{L}(\boldsymbol{\theta}) = \left\|\sum_{x} p_\boldsymbol{\theta}(x) \phi(x)- \sum_{x} \pi(x) \phi(x) \right\|^2, + + +where :math:`\phi(x)` maps :math:`x` to a larger feature space. Using a kernel +:math:`K(x,y) = \phi(x)^T\phi(y)` allows us to work in a lower-dimensional space. We use the Radial +basis function (RBF) kernel for this purpose, which is defined as: + +.. math:: + + K(x,y) = \frac{1}{c}\sum_{i=1}^c \exp \left( \frac{|x-y|^2}{2\sigma_i^2} \right). + +Here, :math:`\sigma_i` is the bandwidth parameter controlling the Gaussian kernel's width. +:math:`\mathcal{L}` approaches to zero if and only if :math:`p_\boldsymbol{\theta}` approaches :math:`\pi` [#Gret]_. +To learn more about kernel methods, check out this :doc:`demo `. + +We can now write the loss function in terms of :math:`K(x,y)` as + +.. math:: + + \mathcal{L} = \underset{x, y \sim p_\boldsymbol{\theta}}{\mathbb{E}}[{K(x,y)}]-2\underset{x\sim p_\boldsymbol{\theta},y\sim \pi}{\mathbb{E}}[K(x,y)]+\underset{x, y \sim \pi}{\mathbb{E}}[K(x, y)] +""" + +###################################################################### +# Armed with these ingredients, we can write code for the QCBM and the loss function. +# We first define the ``MMD`` class for computing the squared MMD loss with radial basis +# function kernel. Upon initialization, it calculates the kernel function. +# + +import jax +import jax.numpy as jnp + +jax.config.update("jax_enable_x64", True) + + +class MMD: + + def __init__(self, scales, space): + gammas = 1 / (2 * (scales**2)) + sq_dists = jnp.abs(space[:, None] - space[None, :]) ** 2 + self.K = sum(jnp.exp(-gamma * sq_dists) for gamma in gammas) / len(scales) + self.scales = scales + + def k_expval(self, px, py): + # Kernel expectation value + return px @ self.K @ py + + def __call__(self, px, py): + pxy = px - py + return self.k_expval(pxy, pxy) + + +###################################################################### +# Defining classes helps in caching the kernel instead of calculating it everytime to find the +# expectation value. Next up, the ``QCBM`` holds the definition for the quantum circuit born machine +# and the objective function to minimize. +# + +from functools import partial + + +class QCBM: + + def __init__(self, circ, mmd, py): + self.circ = circ + self.mmd = mmd + self.py = py # target distribution π(x) + + @partial(jax.jit, static_argnums=0) + def mmd_loss(self, params): + px = self.circ(params) + return self.mmd(px, self.py), px + + +###################################################################### +# Learning the Bars and Stripes data distribution +# ----------------------------------------------- +# +# We train the QCBM on the Bars and stripes dataset. The dataset has binary black and white images of +# size :math:`n \times n` pixels. We consider :math:`n=3` for this tutorial, which will give 14 valid +# configurations. The dataset is represented by flattened bitstrings. The quantum circuit will use 9 +# qubits in total. +# + +###################################################################### +# Data generation +# ~~~~~~~~~~~~~~~ +# + +import numpy as np + + +def get_bars_and_stripes(n): + bitstrings = [list(np.binary_repr(i, n))[::-1] for i in range(2**n)] + bitstrings = np.array(bitstrings, dtype=int) + + stripes = bitstrings.copy() + stripes = np.repeat(stripes, n, 0) + stripes = stripes.reshape(2**n, n * n) + + bars = bitstrings.copy() + bars = bars.reshape(2**n * n, 1) + bars = np.repeat(bars, n, 1) + bars = bars.reshape(2**n, n * n) + return np.vstack((stripes[0 : stripes.shape[0] - 1], bars[1 : bars.shape[0]])) + + +n = 3 +size = n**2 +data = get_bars_and_stripes(n) +print(data.shape) + +###################################################################### +# The dataset has 9 features per data point. A visualization of one data point is shown below. Each +# data point represents a flattened bitstring. +# + +import matplotlib.pyplot as plt + +sample = data[1].reshape(n, n) + +plt.figure(figsize=(2, 2)) +plt.imshow(sample, cmap="gray", vmin=0, vmax=1) +plt.grid(color="gray", linewidth=2) +plt.xticks([]) +plt.yticks([]) + +for i in range(n): + for j in range(n): + text = plt.text( + i, j, sample[j][i], ha="center", va="center", color="gray", fontsize=12 + ) + +print(f"\nSample bitstring: {''.join(np.array(sample.flatten(), dtype='str'))}") + +###################################################################### +# We can plot the full dataset of :math:`3 \times 3` images. +# + +plt.figure(figsize=(4, 4)) +j = 1 +for i in data: + plt.subplot(4, 4, j) + j += 1 + plt.imshow(np.reshape(i, (n, n)), cmap="gray", vmin=0, vmax=1) + plt.xticks([]) + plt.yticks([]) + +###################################################################### +# Next we compute the integers represented by the valid configurations. We will use them later +# to evaluate the performance of the QCBM. +# + +bitstrings = [] +nums = [] +for d in data: + bitstrings += ["".join(str(int(i)) for i in d)] + nums += [int(bitstrings[-1], 2)] +print(nums) + +###################################################################### +# Using the dataset, we can compute the target probability distribution :math:`\pi(x)` which is visualized below. +# + +probs = np.zeros(2**size) +probs[nums] = 1 / len(data) + +plt.figure(figsize=(12, 5)) +plt.bar(np.arange(2**size), probs, width=2.0, label=r"$\pi(x)$") +plt.xticks(nums, bitstrings, rotation=80) + +plt.xlabel("Samples") +plt.ylabel("Prob. Distribution") +plt.legend(loc="upper right") +plt.subplots_adjust(bottom=0.3) +plt.show() + +###################################################################### +# One can observe that it is a uniform distribution and only the probabilities of the valid configurations are +# non-zero while rest are zero. Next we define a parameterized quantum circuit to train. This quantum circuit +# will act as a generative model, thus, realize a Born machine. +# + +import pennylane as qml + +np.random.seed(42) + + +n_qubits = size +dev = qml.device("default.qubit", wires=n_qubits) + +n_layers = 6 +wshape = qml.StronglyEntanglingLayers.shape(n_layers=n_layers, n_wires=n_qubits) +weights = np.random.random(size=wshape) + + +@qml.qnode(dev) +def circuit(weights): + qml.StronglyEntanglingLayers( + weights=weights, ranges=[1] * n_layers, wires=range(n_qubits) + ) + return qml.probs() + + +jit_circuit = jax.jit(circuit) + +###################################################################### +# Using the ``MMD`` and ``QCBM`` classes defined earlier, we create their respective objects. Using Optax, we +# define the Adam optimizer. +# + +import optax + +bandwidth = jnp.array([0.25, 0.5, 1]) +space = jnp.arange(2**n_qubits) + +mmd = MMD(bandwidth, space) +qcbm = QCBM(jit_circuit, mmd, probs) + +opt = optax.adam(learning_rate=0.1) +opt_state = opt.init(weights) + +###################################################################### +# We can also verify that the summation in the first line of :math:`\mathcal{L}` is equal to the +# expectation values in the second line. +# + +loss_1, px = qcbm.mmd_loss(weights) # squared MMD +loss_2 = mmd.k_expval(px, px) - 2 * mmd.k_expval(px, probs) + mmd.k_expval(probs, probs) +print(loss_1) +print(loss_2) + +###################################################################### +# Training +# ~~~~~~~~ +# +# We define the ``update_step`` method which +# +# - computes the squared MMD loss and gradients. +# +# - apply the update step of our optimizer. +# +# - updates the parameter values. +# +# - calculates the KL divergence. +# +# The KL divergence [#Kull]_ is a measure of how far the predicted distribution :math:`p_\boldsymbol{\theta}(x)` +# is from the target distribution :math:`\pi(x)`. +# + + +@jax.jit +def update_step(params, opt_state): + (loss_val, qcbm_probs), grads = jax.value_and_grad(qcbm.mmd_loss, has_aux=True)( + params + ) + updates, opt_state = opt.update(grads, opt_state) + params = optax.apply_updates(params, updates) + kl_div = -jnp.sum(qcbm.py * jnp.nan_to_num(jnp.log(qcbm_probs / qcbm.py))) + return params, opt_state, loss_val, kl_div + + +history = [] +divs = [] +n_iterations = 100 + +for i in range(n_iterations): + weights, opt_state, loss_val, kl_div = update_step(weights, opt_state) + + if i % 10 == 0: + print(f"Step: {i} Loss: {loss_val:.4f} KL-div: {kl_div:.4f}") + + history.append(loss_val) + divs.append(kl_div) + +###################################################################### +# Visualizing the training results, we get the following plot. +# + +fig, ax = plt.subplots(1, 2, figsize=(12, 5)) + +ax[0].plot(history) +ax[0].set_xlabel("Iteration") +ax[0].set_ylabel("MMD Loss") + +ax[1].plot(divs, color="green") +ax[1].set_xlabel("Iteration") +ax[1].set_ylabel("KL Divergence") +plt.show() + +###################################################################### +# Comparing the target probability distribution with the QCBM predictions, we can see that the +# predictions results in a good approximation. +# + +qcbm_probs = np.array(qcbm.circ(weights)) + +plt.figure(figsize=(12, 5)) + +plt.bar( + np.arange(2**size), probs, width=2.0, label=r"$\pi(x)$", alpha=0.4, color="tab:blue" +) +plt.bar( + np.arange(2**size), + qcbm_probs, + width=2.0, + label=r"$p_\theta(x)$", + alpha=0.9, + color="tab:green", +) + +plt.xlabel("Samples") +plt.ylabel("Prob. Distribution") + +plt.xticks(nums, bitstrings, rotation=80) +plt.legend(loc="upper right") +plt.subplots_adjust(bottom=0.3) +plt.show() + +###################################################################### +# Testing +# ~~~~~~~ +# +# To visualize the performance of the model, we generate samples and compute +# :math:`\chi \equiv` P(:math:`x` is a bar or stripe) which is a measure of +# generation quality. +# + + +def circuit(weights): + qml.StronglyEntanglingLayers( + weights=weights, ranges=[1] * n_layers, wires=range(n_qubits) + ) + return qml.sample() + + +for N in [2000, 20000]: + dev = qml.device("default.qubit", wires=n_qubits, shots=N) + circ = qml.QNode(circuit, device=dev) + preds = circ(weights) + mask = np.any( + np.all(preds[:, None] == data, axis=2), axis=1 + ) # Check for row-wise equality + chi = np.sum(mask) / N + print(f"χ for N = {N}: {chi:.4f}") + +print(f"χ for N = ∞: {np.sum(qcbm_probs[nums]):.4f}") + +###################################################################### +# Few of the samples are plotted below. The ones with a red border represents +# invalid images. +# + +plt.figure(figsize=(8, 8)) +j = 1 +for i, m in zip(preds[:64], mask[:64]): + ax = plt.subplot(8, 8, j) + j += 1 + plt.imshow(np.reshape(i, (n, n)), cmap="gray", vmin=0, vmax=1) + if ~m: + plt.setp(ax.spines.values(), color="red", linewidth=1.5) + plt.xticks([]) + plt.yticks([]) + +###################################################################### +# The model is able to learn the target distribution due to a circuit with larger layers. Also, +# [#Liu]_ has argued that training a QCBM with deeper circuits does not suffer from the +# vanishing gradients problem. +# + +###################################################################### +# Learning a mixture of Gaussians +# ------------------------------- +# +# Now we use a QCBM to model a mixture of Gaussians +# +# .. math:: +# +# \pi(x)\propto e^{-\frac{1}{2}\left(\frac{x-\mu_1}{\sigma}\right)^2}+e^{-\frac{1}{2}\left(\frac{x-\mu_2}{\sigma}\right)^2}, +# +# with :math:`x` ranging from :math:`0 \dots 2^{n}-1,` where :math:`n` is the +# number of qubits. +# + + +def mixture_gaussian_pdf(x, mus, sigmas): + mus, sigmas = np.array(mus), np.array(sigmas) + vars = sigmas**2 + values = [ + (1 / np.sqrt(2 * np.pi * v)) * np.exp(-((x - m) ** 2) / (2 * v)) + for m, v in zip(mus, vars) + ] + values = np.sum([val / sum(val) for val in values], axis=0) + return values / np.sum(values) + + +n_qubits = 6 +x_max = 2**n_qubits +x_input = np.arange(x_max) +mus = [(2 / 7) * x_max, (5 / 7) * x_max] +sigmas = [x_max / 8] * 2 +data = mixture_gaussian_pdf(x_input, mus, sigmas) + +plt.plot(data, label=r"$\pi(x)$") +plt.legend() +plt.show() + +###################################################################### +# In contrast to the Bars and Stripes dataset, the Gaussian mixture distribution exhibits +# a smooth and non-zero probability for every basis state. Similar to the previous experiment, +# we will create an ansatz and measure probabilities. +# + +dev = qml.device("default.qubit", wires=n_qubits) + +n_layers = 4 +wshape = qml.StronglyEntanglingLayers.shape(n_layers=n_layers, n_wires=n_qubits) +weights = np.random.random(size=wshape) + + +@qml.qnode(dev) +def circuit(weights): + qml.StronglyEntanglingLayers( + weights=weights, ranges=[1] * n_layers, wires=range(n_qubits) + ) + return qml.probs() + + +jit_circuit = jax.jit(circuit) + +qml.draw_mpl(circuit, expansion_strategy="device")(weights) +plt.show() + +###################################################################### +# With the quantum circuit defined, we are ready to optimize the squared MMD loss function +# which follows a code similar to the Bars and Stripes case. +# + +bandwidth = jnp.array([0.25, 60]) +space = jnp.arange(2**n_qubits) + +mmd = MMD(bandwidth, space) +qcbm = QCBM(jit_circuit, mmd, data) + +opt = optax.adam(learning_rate=0.1) +opt_state = opt.init(weights) + +history = [] +divs = [] +n_iterations = 100 + +for i in range(n_iterations): + weights, opt_state, loss_val, kl_div = update_step(weights, opt_state) + + if i % 10 == 0: + print(f"Step: {i} Loss: {loss_val:.4f} KL-div: {kl_div:.4f}") + + history.append(loss_val) + divs.append(kl_div) + +###################################################################### +# Finally, we plot the histogram with the probabilities obtained from QCBM and compare +# it with the actual probability distribution. +# + +qcbm_probs = qcbm.circ(weights) + +plt.plot(range(x_max), data, linestyle="-.", label=r"$\pi(x)$") +plt.bar(range(x_max), qcbm_probs, color="green", alpha=0.5, label="samples") + +plt.xlabel("Samples") +plt.ylabel("Prob. Distribution") + +plt.legend() +plt.show() + +###################################################################### +# The histogram (green bars) aligns remarkably well with the exact probability distribution (blue +# dashed curve). +# + +###################################################################### +# Conclusion +# ---------- +# +# In this tutorial, we introduced and implemented Quantum Circuit Born Machine (QCBM) using PennyLane. +# The algorithm is a gradient-based learning involving optimizing the squared MMD loss. We also +# evaluated QCBMs on the Bars and Stripes and two peaks datasets. One can also leverage the differentiable +# learning of the QCBM to solve combinatorial problems where the output is binary strings. +# + +###################################################################### +# References +# ---------- +# +# .. [#Liu] +# +# Liu, Jin-Guo, and Lei Wang. “Differentiable learning of quantum circuit born machines.” Physical +# Review A 98.6 (2018): 062324. +# +# .. [#Ben] +# +# Benedetti, Marcello, et al. “A generative modeling approach for benchmarking and training shallow +# quantum circuits.” npj Quantum Information 5.1 (2019): 45. +# +# .. [#Du] +# +# Du, Yuxuan, et al. "Expressive power of parametrized quantum circuits." Physical Review Research +# 2.3 (2020): 033125. +# +# .. [#Ack] +# +# Ackley, David H., Geoffrey E. Hinton, and Terrence J. Sejnowski. "A learning algorithm for +# Boltzmann machines." Cognitive science 9.1 (1985): 147-169. +# +# .. [#Gret] +# +# Gretton, Arthur, et al. "A kernel method for the two-sample-problem." Advances in neural +# information processing systems 19 (2006). +# +# .. [#Kull] +# +# Kullback, Solomon, and Richard A. Leibler. "On information and sufficiency." The annals +# of mathematical statistics 22.1 (1951): 79-86. +# +# + +###################################################################### +# About the author +# ---------------- diff --git a/demonstrations/tutorial_qft_arithmetics.metadata.json b/demonstrations/tutorial_qft_arithmetics.metadata.json index 117b813690..e962de2de1 100644 --- a/demonstrations/tutorial_qft_arithmetics.metadata.json +++ b/demonstrations/tutorial_qft_arithmetics.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2022-11-07T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-06-21T00:00:00+00:00", "categories": [ "Getting Started", "Algorithms", "Quantum Computing" ], diff --git a/demonstrations/tutorial_qft_arithmetics.py b/demonstrations/tutorial_qft_arithmetics.py index 9bddca9997..cfa4a47a4a 100644 --- a/demonstrations/tutorial_qft_arithmetics.py +++ b/demonstrations/tutorial_qft_arithmetics.py @@ -24,7 +24,7 @@ In this demo we will not focus on understanding how the QFT is built, as we can find a great explanation in the -`Xanadu Quantum Codebook `__. Instead, we will develop the +`PennyLane Codebook `__. Instead, we will develop the intuition for how it works and how we can best take advantage of it. Motivation diff --git a/demonstrations/tutorial_quantum_chemistry.metadata.json b/demonstrations/tutorial_quantum_chemistry.metadata.json index b686050945..23c33b991d 100644 --- a/demonstrations/tutorial_quantum_chemistry.metadata.json +++ b/demonstrations/tutorial_quantum_chemistry.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2020-08-02T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_qubit_tapering.metadata.json b/demonstrations/tutorial_qubit_tapering.metadata.json index 84931b8b49..872e4bff5b 100644 --- a/demonstrations/tutorial_qubit_tapering.metadata.json +++ b/demonstrations/tutorial_qubit_tapering.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2022-05-16T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_resource_estimation.metadata.json b/demonstrations/tutorial_resource_estimation.metadata.json index 9ec79662f1..7b2da77bde 100644 --- a/demonstrations/tutorial_resource_estimation.metadata.json +++ b/demonstrations/tutorial_resource_estimation.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2022-11-21T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry" ], diff --git a/demonstrations/tutorial_spsa.metadata.json b/demonstrations/tutorial_spsa.metadata.json index 2caadf692d..314a21f412 100644 --- a/demonstrations/tutorial_spsa.metadata.json +++ b/demonstrations/tutorial_spsa.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2023-03-19T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Optimization" ], diff --git a/demonstrations/tutorial_univariate_qvr.metadata.json b/demonstrations/tutorial_univariate_qvr.metadata.json index 6a6be8ed06..9f9520e2a2 100644 --- a/demonstrations/tutorial_univariate_qvr.metadata.json +++ b/demonstrations/tutorial_univariate_qvr.metadata.json @@ -9,7 +9,7 @@ } ], "dateOfPublication": "2023-02-07T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-05-20T00:00:00+00:00", "categories": [ "Quantum Machine Learning" ], @@ -76,5 +76,12 @@ "id": "tutorial_qaoa_intro", "weight": 1.0 } + ], + "hardware": [ + { + "id": "covalent", + "link": "https://github.com/AgnostiqHQ/QuantumVariationalRewinding", + "logo": "/_static/hardware_logos/covalent.png" + } ] -} \ No newline at end of file +} diff --git a/demonstrations/tutorial_univariate_qvr.py b/demonstrations/tutorial_univariate_qvr.py index 27298aaefb..a5e5830700 100644 --- a/demonstrations/tutorial_univariate_qvr.py +++ b/demonstrations/tutorial_univariate_qvr.py @@ -9,10 +9,8 @@ .. related:: tutorial_qaoa_intro Intro to QAOA - *Authors: Jack Stephen Baker, Santosh Kumar Radha — Posted: 7 February 2023.* - Systems producing observable characteristics which evolve with time are almost everywhere we look. The temperature changes as day turns to night, stock markets fluctuate and the bacteria colony living in the coffee cup to your diff --git a/demonstrations/tutorial_vqe.metadata.json b/demonstrations/tutorial_vqe.metadata.json index bae70f2f90..5c337b9a10 100644 --- a/demonstrations/tutorial_vqe.metadata.json +++ b/demonstrations/tutorial_vqe.metadata.json @@ -6,7 +6,7 @@ } ], "dateOfPublication": "2020-02-08T00:00:00+00:00", - "dateOfLastModification": "2024-01-01T00:00:00+00:00", + "dateOfLastModification": "2024-07-10T00:00:00+00:00", "categories": [ "Quantum Chemistry", "Getting Started" ], diff --git a/notebook_converter/notebook_to_demo.py b/notebook_converter/notebook_to_demo.py index 921e6fbbb1..8af8c5df66 100755 --- a/notebook_converter/notebook_to_demo.py +++ b/notebook_converter/notebook_to_demo.py @@ -182,9 +182,9 @@ def generate_code_output_block(output_source: List[str] = None, only_header: boo [ f"# {line}" for line in [ - ".. rst-class :: sphx-glr-script-out", + ".. rst-class:: sphx-glr-script-out", "", - ".. code-block: none", + ".. code-block:: none", "", ] ]

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