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Repository: QISKit/qiskit-tutorial
Branch: master
Commit: 2fc7ed53fcc7
Files: 45
Total size: 6.6 MB
Directory structure:
gitextract_bmptrtaj/
├── .github/
│ ├── CODE_OF_CONDUCT.md
│ ├── CONTRIBUTING.md
│ ├── ISSUE_TEMPLATE/
│ │ ├── bug-report.yml
│ │ ├── documentation.yml
│ │ └── feature-request.yml
│ └── PULL_REQUEST_TEMPLATE.md
├── .gitignore
├── .mergify.yml
├── CODE_OF_CONDUCT.md
├── CONTRIBUTING.md
├── INSTALL.md
├── LICENSE
├── README.md
├── azure-pipelines.yml
├── conf.py
├── constraints.txt
├── index.rst
├── requirements-dev.txt
├── start_here.ipynb
├── tox.ini
└── tutorials/
├── algorithms/
│ ├── 01_algorithms_introduction.ipynb
│ ├── 02_vqe_advanced_options.ipynb
│ ├── 03_vqe_simulation_with_noise.ipynb
│ ├── 04_vqd.ipynb
│ ├── 05_qaoa.ipynb
│ ├── 06_grover.ipynb
│ ├── 07_grover_examples.ipynb
│ ├── 09_IQPE.ipynb
│ ├── 10_pvqd.ipynb
│ ├── 11_VarQTE.ipynb
│ └── 12_gradients_framework.ipynb
├── circuits/
│ ├── 01_circuit_basics.ipynb
│ ├── 1_getting_started_with_qiskit.ipynb
│ ├── 2_plotting_data_in_qiskit.ipynb
│ └── 3_summary_of_quantum_operations.ipynb
├── circuits_advanced/
│ ├── 01_advanced_circuits.ipynb
│ ├── 02_operators_overview.ipynb
│ ├── 03_advanced_circuit_visualization.ipynb
│ ├── 04_transpiler_passes_and_passmanager.ipynb
│ ├── 05_pulse_gates.ipynb
│ ├── 06_building_pulse_schedules.ipynb
│ ├── 07_pulse_scheduler.ipynb
│ └── 08_gathering_system_information.ipynb
└── operators/
├── 01_operator_flow.ipynb
└── 02_gradients_framework.ipynb
================================================
FILE CONTENTS
================================================
================================================
FILE: .github/CODE_OF_CONDUCT.md
================================================
# Contributor Covenant Code of Conduct
## Our Pledge
In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation.
## Our Standards
Examples of behavior that contributes to creating a positive environment include:
* Using welcoming and inclusive language
* Being respectful of differing viewpoints and experiences
* Gracefully accepting constructive criticism
* Focusing on what is best for the community
* Showing empathy towards other community members
Examples of unacceptable behavior by participants include:
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* Trolling, insulting/derogatory comments, and personal or political attacks
* Public or private harassment
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## Our Responsibilities
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## Enforcement
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Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project's leadership.
## Attribution
This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4, available at [http://contributor-covenant.org/version/1/4][version]
[homepage]: http://contributor-covenant.org
[version]: http://contributor-covenant.org/version/1/4/
================================================
FILE: .github/CONTRIBUTING.md
================================================
# Contributing
If you would like to contribute to the Qiskit IQX tutorials, there are a number of ways to
get involved:
* **Issues**: Issues can be reported with GitHub [issue
reporting](https://github.com/Qiskit/qiskit-tutorial/issues) for this repository.
Select `New issue`, fill in a descriptive title, and provide as much detail
as is needed for the issue to be reproduced.
* **Notebooks**: If you would like to contribute a notebook, please
create a [fork](https://help.github.com/articles/fork-a-repo/) of the repository
from the `master` branch and create a
[pull request](https://help.github.com/articles/about-pull-requests) for your change.
## Contributor License Agreement
We'd love to accept your code! Before we can, we have to get a few legal
requirements sorted out. By having you sign a Contributor License Agreement (CLA), we
ensure that the community is free to use your contributions.
When you contribute to the Qiskit project with a new pull request, a bot will
evaluate whether you have signed the CLA. If required, the bot will comment on
the pull request, including a link to accept the agreement. The
[individual CLA](https://qiskit.org/license/qiskit-cla.pdf) document is
available for review as a PDF.
If you work for a company that wants to allow you to contribute your work,
then you'll need to sign a [corporate CLA](https://qiskit.org/license/qiskit-corporate-cla.pdf)
and email it to us at qiskit@qiskit.org.
================================================
FILE: .github/ISSUE_TEMPLATE/bug-report.yml
================================================
name: 🐛Bug Report
description: Create a report to help us improve 🤔.
labels: ["bug"]
body:
- type: markdown
attributes:
value: |
⚠️ If you do not respect this template, your issue will be closed
⚠️ Make sure to browse the opened and closed issues before submitting your issue
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id: what-happened
attributes:
label: What is the current behavior?
description: Please describe the current behavior.
validations:
required: true
- type: textarea
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label: Information
description: |
examples:
- **Qiskit version**: 0.36.2
- **Python version**: 3.10.10
- **Operating system**: Ubuntu 20.04
value: |
- Qiskit version:
- Python version:
- Operating System:
render: Markdown
validations:
required: true
- type: textarea
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FILE: .github/ISSUE_TEMPLATE/documentation.yml
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name: 📚 Documentation
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- type: checkboxes
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label: Code of Conduct
description: By submitting this issue, you agree to follow our [Code of Conduct](https://github.com/Qiskit/qiskit-tutorials/blob/master/.github/CODE_OF_CONDUCT.md)
options:
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================================================
FILE: .github/ISSUE_TEMPLATE/feature-request.yml
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name: 🚀Feature request
description: Suggest an idea for this project🌟.
labels: ["enhancement"]
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⚠️ If you do not respect this template, your issue will be closed
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FILE: .github/PULL_REQUEST_TEMPLATE.md
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### Summary
### Details and comments
================================================
FILE: .gitignore
================================================
__pycache__/
.cache/
# ignores any checkpoints folder anywhere
.ipynb_checkpoints/
# editor files
.vscode/
.idea/
# Distribution / packaging
*.egg-info/
# Spyder project settings
.spyderproject
.spyproject
.DS_Store
.stestr/
_build/
.tox/
================================================
FILE: .mergify.yml
================================================
queue_rules:
- name: automerge
conditions:
- check-success=Qiskit.qiskit-tutorials
pull_request_rules:
- name: automatic merge on CI success and review
conditions:
- base=master
- "#approved-reviews-by>=1"
- label=automerge
- label!=on hold
- check-success=Qiskit.qiskit-tutorials
actions:
queue:
name: automerge
method: squash
================================================
FILE: CODE_OF_CONDUCT.md
================================================
<!-- Copyright Contributors to the Qiskit project. -->
# Code of Conduct
All members of this project agree to adhere to the Qiskit Code of Conduct listed at [https://github.com/Qiskit/qiskit/blob/master/CODE_OF_CONDUCT.md](https://github.com/Qiskit/qiskit/blob/master/CODE_OF_CONDUCT.md)
----
License: [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/),
Copyright Contributors to Qiskit.
================================================
FILE: CONTRIBUTING.md
================================================
<img src="images/gallery_shot.png" >
# Contributing
## What makes a good tutorial?
## Adding a tutorial
## Setting gallery thumbnails
To set the gallery thumbnail for a given tutorial (as seen in the image above) one needs to set a cell tag in the notebook for a cell that generates an image as its output. To make the tabs visible do:
<img src="images/menu_tags.png" width="50%" >
The cell's whos output you would like to use, you must add the tag: `nbsphinx-thumbnail`.
<img src="images/set_tag.png" >
If a tag is not set, then the Qiskit logo is used as a placeholder.
================================================
FILE: INSTALL.md
================================================
# Qiskit Tutorials
## Installation and setup
### Get the tutorials
For the full experience, you can start by downloading the latest release of the
tutorials from [here](https://github.com/Qiskit/qiskit-iqx-tutorials/releases).
Unzip the archive in the directory of your choice (this is the recommended
way).
To properly view and run the tutorials, you will need to install [Jupyter
Notebook](https://jupyter.readthedocs.io/en/latest/install.html).
### Install Qiskit
At least [Python 3.7 or later](https://www.python.org/downloads/) is required
to install and use Qiskit. If you have multiple Python versions installed (and
particularly if the command `python --version` returns an incompatible
version), you will need to ensure that your versions are [managed
correctly](https://conda.io/projects/conda/en/latest/user-guide/getting-started.html#managing-python).
This can be done using the `environment.yml` file, as detailed below.
When there are no issues with dependencies, Qiskit can be installed using
```
pip install qiskit
```
Or, a pre-installed Qiskit can be updated using
```
pip install -U qiskit
```
However, in case of issues with dependencies, we recommend the following
installation procedure:
1. **Install [conda](https://conda.io/docs/index.html)**
2. **Create conda environment for Qiskit and install packages** (with the
accompanying `environment.yml` file)
```
cd qiskit-tutorials
conda env create -f environment.yml
```
If you have already created `environment`, you can upgrade it by running
```
conda env update -f environment.yml
```
## 3. Configure your IBM Q Provider
- Create an [IBM Q](https://quantumexperience.ng.bluemix.net) account if
you haven't already done so
- Get an API token from the IBM Q website under “My Account" > "Qiskit in
local environment"
- We are now going to add the necessary credentials to Qiskit. Take your
token, here called `MY_API_TOKEN`, and pass it to the `IBMQ.save_account()`
function:
```python
from qiskit import IBMQ
IBMQ.save_account('MY_API_TOKEN')
```
- Your credentials will be stored on disk. Once they are stored, at any point
in the future you can load and use them via:
```python
from qiskit import IBMQ
provider = IBMQ.load_account()
```
- For those who do not want to save their credentials to disk, please use
```python
from qiskit import IBMQ
provider = IBMQ.enable_account('MY_API_TOKEN')
```
and the token will only be active for the session.
## 4. Explore the Tutorials
**Activate the environment**<BR>
For MacOS and Linux, run:
```
source activate Qiskitenv
```
For Windows, run:
```
activate Qiskitenv
```
**Note for conda users**<BR>
Verify that you have installed the right Jupyter Kernel, because in the last
conda version it's not installed by default.
```
python -m ipykernel install --user --name Qiskitenv --display-name "Python (Qiskitenv)"
```
**Start Jupyter with the index notebook**<BR>
```
jupyter notebook index.ipynb
```
## 5. [Optional] Visualizing Circuits with LaTeX
You can visualize your quantum circuits directly from Qiskit. Qiskit circuit
drawers support text, LaTeX and matplotlib. The text and matplotlib version is
entirely native to Python, and thus easy to use. The LaTeX version produces
publication-quality circuit images, but relies on some pre-requisite software.
These include the `pdflatex` compiler for rendering LaTeX documents, and the
Poppler library for converting PDF to image. To get these:
On Linux:
- Install [MiKTeX](https://miktex.org/download#unx)
- Install Poppler:
- Run: `apt-get install -y poppler-utils`
On MacOS:
- Install [MiKTeX](https://miktex.org/download).
- Install Poppler:
- Run: `brew install poppler`
On Windows:
- Install [MiKTeX](https://miktex.org/download).
- Install Poppler:
- Download the [latest binary](http://blog.alivate.com.au/wp-content/uploads/2017/01/poppler-0.51_x86.7z).
- Extract the downloaded `.7z` file into user directory: `c:\Users\<user_name>\`.
Note: You will need to have the [7zip software](https://www.7-zip.org/download.html) for this.
- Add to PATH:
- Right click on "This PC" -> Properties -> Advanced System Settings -> Environment Variables
- Add `C:\Users\<user_name>\poppler-0.51\bin` to the user's path.
================================================
FILE: LICENSE
================================================
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================================================
FILE: README.md
================================================
# Qiskit Tutorials
[](https://opensource.org/licenses/Apache-2.0)
> :warning: **This repository is archived**: The content in this repository [was moved to other locations](https://github.com/Qiskit/qiskit-tutorials/issues/1473). If you have issues or PR, please submit them to their new location.
* `algorithms` folder -> [`qiskit-algorithms`](https://qiskit.org/ecosystem/algorithms/tutorials/index.html) ([GitHub](https://github.com/qiskit-community/qiskit-algorithms/tree/main/docs/tutorials))
* `circuits` folder -> [Qiskit](https://qiskit.org/documentation/tutorials.html) ([GitHub](https://github.com/Qiskit/qiskit/tree/main/docs/tutorials/circuits))
* `circuits_advanced` folder -> [Qiskit](https://qiskit.org/documentation/tutorials.html) ([GitHub](https://github.com/Qiskit/qiskit/tree/main/docs/tutorials/circuits_advanced))
* `opflow` folder -> [Qiskit](https://qiskit.org/documentation/tutorials.html) ([GitHub](https://github.com/Qiskit/qiskit/tree/main/docs/tutorials/opflow))
* `simulators` folder -> [`qiskit-aer`](https://qiskit.org/ecosystem/aer/tutorials/index.html) ([GitHub](https://github.com/qiskit/qiskit-aer/tree/main/docs/tutorials))
* `textbook` folder -> removed in favor of https://www.qiskit.org/learn
## Contents
Welcome to the [Qiskit](https://www.qiskit.org/) Tutorials!
In this repository, we've put together a collection of Jupyter notebooks aimed at teaching people who want to use Qiskit for writing quantum computing programs, and executing them on one of several backends (online quantum processors, online simulators, and local simulators). The online quantum processors are the [IBM Quantum](https://quantum-computing.ibm.com) systems.
For our community-contributed tutorials, please check out the [qiskit-community-tutorials](https://github.com/Qiskit/qiskit-community-tutorials) repository.
## Contribution Guidelines
If you'd like to contribute to Qiskit Tutorials, please take a look at our [contribution guidelines](.github/CONTRIBUTING.md). This project adheres to Qiskit's [code of conduct](.github/CODE_OF_CONDUCT.md). By participating you are expected to uphold this code.
### Tutorial limitations
Because the tutorials are executed as part of the build process, and eventually turned into RST documentation, there are several limitations to be aware of:
1. There is currently a three minute per cell execution time limit. Cells that go over this limit will raise an exception.
2. Tutorials cannot make calls to the IBM Quantum Experience, e.g. no `IBMQ.load_account()`.
3. It is important to maintain strict header compliance. All notebooks should start with, and contain only one, top level (h1) header:
```
# I am a top level header
```
Additionally, the nesting of headers should make sense:
```
# I am a top level header
## I am a secondary header
### I am a tertiary header
## I am another secondary header
## I am another secondary header
```
4. All math equations expressed using `$$ ... $$` need to be surrounded on top and bottom by white space.
5. In order for a tutorial to show up in the Qiskit documentation, after successful merging, an additional PR needs to be made in the [Qiskit meta-repo](https://github.com/Qiskit/qiskit) to trigger the rebuilding of the documentation.
### Adding a gallery image
To add a gallery image to a notebook, select a cell with an output image and add `nbsphinx-thumbnail` as a cell tag. To see the cell tags go to: `View -> Cell Toolbar -> Tags` in the notebook menu. Adding gallery images from images not generated inside of the notebooks themselves should be avoided if possible as this gets messy in the present build system.
## Building documentation
In addition to serving up standalone notebooks, this repository also includes the infrastructure needed to build the tutorials into HTML documentation using [Sphinx](https://www.sphinx-doc.org/).
We use [Tox](https://tox.wiki/en/latest/), which you will need to install globally (e.g. using [`pipx`](https://pypa.github.io/pipx/)).
1. Fork and clone the forked repository.
2. `tox -e docs`
Sometimes Sphinx's caching can get in a bad state. First, try running `tox -e docs-clean`, which will remove Sphinx's cache. If you are still having issues, try running `tox -e docs -r`. `-r` tells Tox to reinstall the dependencies.
## Authors and Citation
Qiskit Tutorials is the work of [many people](https://github.com/Qiskit/qiskit-tutorials/graphs/contributors) who contribute to the project at different levels. If you use Qiskit, please cite as per the included [BibTeX
file](https://github.com/Qiskit/qiskit-terra/blob/main/CITATION.bib).
## License
[Apache License 2.0](LICENSE)
================================================
FILE: azure-pipelines.yml
================================================
trigger:
branches:
include:
- master
- stable/*
pr:
autoCancel: true
branches:
include:
- '*'
pool:
vmImage: 'ubuntu-latest'
strategy:
matrix:
Python39:
python.version: '3.9'
variables:
PIP_CACHE_DIR: $(Pipeline.Workspace)/.pip
steps:
- task: UsePythonVersion@0
inputs:
versionSpec: '$(python.version)'
displayName: 'Use Python $(python.version)'
- task: Cache@2
inputs:
key: 'pip | "$(Agent.OS)" | "$(python.version)" | "$(Build.BuildNumber)"'
restoreKeys: |
pip | "$(Agent.OS)" | "$(python.version)"
pip | "$(Agent.OS)"
pip
path: $(PIP_CACHE_DIR)
displayName: Cache pip
- bash: |
set -e
sudo apt-get install -y pandoc graphviz
python -m pip install -U tox
displayName: 'Install system dependencies and tox'
- bash: tox -e docs
displayName: 'Build Docs'
- task: ArchiveFiles@2
inputs:
rootFolderOrFile: '_build/html'
archiveType: tar
archiveFile: '$(Build.ArtifactStagingDirectory)/html_docs.tar.gz'
verbose: true
- task: PublishBuildArtifacts@1
displayName: 'Publish docs'
inputs:
pathtoPublish: '$(Build.ArtifactStagingDirectory)'
artifactName: 'html_docs'
Parallel: true
ParallelCount: 8
================================================
FILE: conf.py
================================================
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2023.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
# Configuration file for the Sphinx documentation builder.
#
# This file does only contain a selection of the most common options. For a
# full list see the documentation:
# http://www.sphinx-doc.org/en/master/config
# -- Project information -----------------------------------------------------
project = 'Qiskit Tutorials'
copyright = '2020, Qiskit Development Team' # pylint: disable=redefined-builtin
author = 'Qiskit Development Team'
# The short X.Y version
version = ''
# The full version, including alpha/beta/rc tags
release = '0.18.0'
# -- General configuration ---------------------------------------------------
extensions = [
'sphinx.ext.mathjax',
'sphinx.ext.extlinks',
'nbsphinx',
"qiskit_sphinx_theme",
]
html_static_path = ['_static']
exclude_patterns = ['*.ipynb', '_build', 'legacy_tutorials',
'**.ipynb_checkpoints', '.tox']
nbsphinx_timeout = 300
nbsphinx_execute = 'always'
nbsphinx_widgets_path = ""
html_sourcelink_suffix = ""
nbsphinx_thumbnails = {"**": "_static/no_image.png"}
nbsphinx_prolog = """
{% set docname = env.doc2path(env.docname, base=None) %}
.. only:: html
.. role:: raw-html(raw)
:format: html
.. note::
This page was generated from `{{ docname }}`__.
Run interactively in the `IBM Quantum lab <https://quantum-computing.ibm.com/jupyter/tutorial/{{ env.doc2path(env.docname, base=None)|replace("tutorials/", "") }}>`_.
__ https://github.com/Qiskit/qiskit-tutorials/blob/master/{{ docname }}
"""
# If true, figures, tables and code-blocks are automatically numbered if they
# have a caption.
numfig = True
# A dictionary mapping 'figure', 'table', 'code-block' and 'section' to
# strings that are used for format of figure numbers. As a special character,
# %s will be replaced to figure number.
numfig_format = {
'table': 'Table %s'
}
language = "en"
# The name of the Pygments (syntax highlighting) style to use.
pygments_style = 'colorful'
# A boolean that decides whether module names are prepended to all object names
# (for object types where a “module” of some kind is defined), e.g. for
# py:function directives.
add_module_names = False
# -- Options for HTML output -------------------------------------------------
html_theme = 'qiskit_sphinx_theme'
html_logo = 'images/logo.png'
html_last_updated_fmt = '%Y/%m/%d'
html_theme_options = {
'logo_only': False,
'display_version': True,
'prev_next_buttons_location': 'bottom',
'style_external_links': True,
}
autoclass_content = 'both'
================================================
FILE: constraints.txt
================================================
docplex==2.15.194
decorator==4.4.2
================================================
FILE: index.rst
================================================
================
Qiskit Tutorials
================
Quantum circuits
================
.. nbgallery::
:glob:
tutorials/circuits/*
Advanced circuits
=================
.. nbgallery::
:glob:
tutorials/circuits_advanced/*
Algorithms
==========
.. nbgallery::
:glob:
tutorials/algorithms/*
Operators
=========
.. nbgallery::
:glob:
tutorials/operators/*
.. Hiding - Indices and tables
:ref:`genindex`
:ref:`modindex`
:ref:`search`
================================================
FILE: requirements-dev.txt
================================================
qiskit>=0.38.0
jupyter
sphinx
nbsphinx
qiskit_sphinx_theme
networkx
scikit-learn
matplotlib
qiskit[visualization]
qiskit_aer
cvxpy
pyscf
================================================
FILE: start_here.ipynb
================================================
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Qiskit Tutorials\n",
"\n",
"Welcome Qiskitters.\n",
"\n",
"\n",
"These tutorials aim to explain how to use Qiskit. We assume you have installed Qiskit; if not, please look at [qiskit.org](http://www.qiskit.org) or the install [documentation](https://qiskit.org/documentation/install.html). \n",
"\n",
"The focus of these notebooks is not on learning quantum computing. Instead we will focus on how to use Qiskit, and will go into details only when needed. For those interested in learning about quantum computing we recommend the [Qiskit Textbook](https://qiskit.org/textbook) that we and the community have put together, or the [Qiskit documentation](https://qiskit.org/documentation).\n",
"\n",
"\n",
"## Circuits\n",
"\n",
"This section gives you the tools to make your first circuits, execute them, and view the data.\n",
"\n",
"1. [Circuit basics](tutorials/circuits/01_circuit_basics.ipynb) - How to use the Qiskit quantum circuit.\n",
"\n",
"\n",
"2. [Plotting data in Qiskit](tutorials/circuits/2_plotting_data_in_qiskit.ipynb) - Illustrates the different ways of plotting data in Qiskit.\n",
"\n",
"\n",
"3. [Summary of quantum operations](tutorials/circuits/3_summary_of_quantum_operations.ipynb) - List of quantum operations (gates, reset, measurements) in Qiskit Terra\n",
" \n",
" \n",
"## Advanced Circuits\n",
"\n",
"1. [Advanced circuits](tutorials/circuits_advanced/01_advanced_circuits.ipynb) - Circuit building tools added including registerless declarations, composite gate updates and parameterized circuits.\n",
"\n",
"\n",
"2. [Operators overview](tutorials/circuits_advanced/02_operators_overview.ipynb) - Gives a summary of the features and uses of the Operator class.\n",
"\n",
"\n",
"3. [Advanced circuit visualization](tutorials/circuits_advanced/03_advanced_circuit_visualization.ipynb) - Details on drawing your quantum circuits.\n",
"\n",
"\n",
"4. [Transpiler passes and passmanager](tutorials/circuits_advanced/04_transpiler_passes_and_passmanager.ipynb) - How to use the transpiler passes, passmanger, and extend the transpiler with a new pass.\n",
"\n",
"\n",
"## Pulse\n",
"\n",
"1. [Building pulse schedules](tutorials/circuits_advanced/06_building_pulse_schedules.ipynb) - Building schedules of pulses.\n",
"\n",
"\n",
"2. [Pulse Scheduler](tutorials/circuits_advanced/07_pulse_scheduler.ipynb) - Scheduling pulse.\n",
"\n",
"\n",
"3. [Getting system information](tutorials/circuits_advanced/08_gathering_system_information.ipynb) - Obtaining system information.\n",
"\n",
"\n",
"4. [Pulse simulation](tutorials/circuits_advanced/09_pulse_simulator_duffing_model.ipynb) - Simulate a Duffing oscillator using the pulse simulator.\n",
"\n",
"\n",
"## High-Performance Simulators\n",
"\n",
"To really speed up development of quantum computers, we need better simulators with the ability to model realistic noise processes that occur during computation on actual devices. Qiskit provides a high-performance simulator framework called `Aer` for studying quantum computing algorithms and applications in the noisy intermediate-scale quantum regime. \n",
"\n",
"1. [Simulators](tutorials/simulators/1_aer_provider.ipynb) - Gives a summary of the Qiskit Aer provider containing the Qasm, statevector, and unitary simulator.\n",
"\n",
"\n",
"2. [Device noise simulation](tutorials/simulators/2_device_noise_simulation.ipynb) - Shows how to use the Qiskit Aer noise module to automatically generate a basic noise model for simulating hardware backends.\n",
"\n",
"\n",
"3. [Building noise models](tutorials/simulators/3_building_noise_models.ipynb) - Shows how to use Qiskit Aer noise module to construct custom noise models for noisy simulations\n",
"\n",
"\n",
"4. [Custom gate noise](tutorials/simulators/4_custom_gate_noise.ipynb) - Shows to implement simulations using custom noisy gates.\n",
"\n",
"\n",
"5. [Noise transformations](tutorials/simulators/5_noise_transformation.ipynb) - Noise approximation utility functions to construct approximate Clifford noise models out of a general noise model\n",
"\n",
"\n",
"6. [Extended stabilizer tutorial](tutorials/simulators/6_extended_stabilizer_tutorial.ipynb) - Gives an overview of the *extended stabilizer* Qasm Simulator method\n",
"\n",
"\n",
"7. [Matrix Product State simulator](tutorials/simulators/7_matrix_product_state_method.ipynb) - Gives an overview of the *matrix product state* Simulator method\n",
"\n",
"\n",
"## Quantum Device Noise Analysis\n",
"\n",
"This includes better characterization of errors, improving gates, and computing in the presence of noise. Qiskit `ignis` is meant for those who want to design quantum error correction codes, or who wish to study ways to characterize errors through methods such as tomography and randomized benchmarking, or even to find a better way for using gates by exploring dynamical decoupling and optimal control.\n",
"\n",
"1. [Hamiltonian and gate characterizations](tutorials/noise/1_hamiltonian_and_gate_characterization.ipynb) - Sequences to measure ZZ rates between qubits and to measure rotation and angle errors in the gates.\n",
"\n",
"\n",
"2. [Relaxation and decoherence](tutorials/noise/2_relaxation_and_decoherence.ipynb) - How to measure coherence times on the real quantum hardware\n",
"\n",
"\n",
"3. [Measurement error mitigation](tutorials/noise/3_measurement_error_mitigation.ipynb) - How to peform calibration experiments for measurement errors and fed those calibrations into a \"filter\" that can be utilized to mitigate errors in subsequent experiments.\n",
"\n",
"\n",
"4. [Randomized benchmarking](tutorials/noise/4_randomized_benchmarking.ipynb) - Randomized benchmarking (RB) is a technique used to measure the average gate error by measuring the outcomes of random Clifford circuits. This is used internally to report gate errors on our systems. \n",
"\n",
"\n",
"5. [Quantum volume](tutorials/noise/5_quantum_volume.ipynb) - How to run quantum volume measurements on the quantum hardware.\n",
"\n",
"\n",
"6. [Repetition Code](tutorials/noise/6_repetition_code.ipynb) - How to run a simple error correction code, known as the repetition code. This can be used to characterize bit flip errors in the hardware.\n",
"\n",
"\n",
"7. [Accreditation](tutorials/noise/7_accreditation.ipynb) - protocol devised to characterize the reliability of noisy quantum devices."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-08-09T15:31:26.743124Z",
"start_time": "2019-08-09T15:31:26.732618Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>© Copyright IBM 2017, 2021.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
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"source": [
"import qiskit.tools.jupyter\n",
"%qiskit_copyright"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
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"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
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"types_to_exclude": [
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"builtin_function_or_method",
"instance",
"_Feature"
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"nbformat_minor": 2
}
================================================
FILE: tox.ini
================================================
[tox]
minversion = 3.15
envlist = py310,py39,py38
[testenv]
no_package = true
install_command = pip install -c{toxinidir}/constraints.txt -U {opts} {packages}
deps =
-r{toxinidir}/requirements-dev.txt
[testenv:docs]
commands =
sphinx-build -W --keep-going -j auto -b html {toxinidir} {toxinidir}/_build/html/
[testenv:docs-clean]
deps =
allowlist_externals = rm
commands = rm -rf {toxinidir}/_build/
================================================
FILE: tutorials/algorithms/01_algorithms_introduction.ipynb
================================================
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# An Introduction to Algorithms in Qiskit\n",
"\n",
"This is an introduction to algorithms in Qiskit and provides a high-level overview to help understand the various aspects of the functionality to get started. Other tutorials will provide more in-depth material, on given algorithms, and ways to use them etc."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How is the algorithm library structured?\n",
"\n",
"Qiskit provides a number of [Algorithms](https://qiskit.org/documentation/apidoc/algorithms.html) and they are grouped by category according to the task they can perform. For instance [Minimum Eigensolvers](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.html#module-qiskit.algorithms.minimum_eigensolvers) to find the smallest eigen value of an operator, for example ground state energy of a chemistry Hamiltonian or a solution to an optimization problem when expressed as an Ising Hamiltonian. There are [Time Evolvers](https://qiskit.org/documentation/apidoc/algorithms.html#time-evolvers) for the time evolution of quantum systems and [Amplitude Estimators](https://qiskit.org/documentation/apidoc/algorithms.html#amplitude-estimators) for value estimation that can be used say in financial applications. The full set of categories can be seen in the Algorithms documentation link above.\n",
"\n",
"Algorithms are configurable and often part of the configuration will be in the form of smaller building blocks, of which different instances of the building block type can be given. For instance with [VQE](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.html#qiskit.algorithms.minimum_eigensolvers.VQE), the Variational Quantum Eigensolver, it takes a trial wavefunction, in the form of a [QuantumCircuit](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.html#quantumcircuit) and a classical optimizer among other things.\n",
"\n",
"Let's take a look at an example to construct a VQE instance. Here [TwoLocal](https://qiskit.org/documentation/stubs/qiskit.circuit.library.TwoLocal.html#twolocal) is the variational form (trial wavefunction), a parameterized circuit which can be varied, and [SLSQP](https://qiskit.org/documentation/stubs/qiskit.algorithms.optimizers.SLSQP.html#slsqp) a classical optimizer. These are created as separate instances and passed to VQE when it is constructed. Trying, for example, a different classical optimizer, or variational form is simply a case of creating an instance of the one you want and passing it into VQE."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.algorithms.optimizers import SLSQP\n",
"from qiskit.circuit.library import TwoLocal\n",
"\n",
"num_qubits = 2\n",
"ansatz = TwoLocal(num_qubits, 'ry', 'cz')\n",
"optimizer = SLSQP(maxiter=1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's draw the ansatz so we can see it's a [QuantumCircuit](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.html#quantumcircuit) where θ\\[0\\] through θ\\[7\\] will be the parameters that are varied as VQE optimizer finds the minimum eigenvalue. We'll come back to the parameters later in a working example below."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 507.852x144.48 with 1 Axes>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ansatz.decompose().draw('mpl', style='iqx')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But more is needed before we can run the algorithm so let's get to that next."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How to run an algorithm?\n",
"\n",
"Algorithms rely on the primitives to evaluate expectation values or sample circuits. The primitives can be based on a simulator or real device and can be used interchangeably in the algorithms, as they all implement the same interface.\n",
"\n",
"In the VQE, we have to evaluate expectation values, so for example we can use the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html) which is shipped with the default Qiskit Terra installation."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.primitives import Estimator\n",
"\n",
"estimator = Estimator()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This estimator uses an exact, statevector simulation to evaluate the expectation values. We can also use a shot-based and noisy simulators or real backends instead. For more information of the simulators you can check out [Qiskit Aer](https://qiskit.org/ecosystem/aer/apidocs/aer_primitives.html) and for the actual hardware [Qiskit IBM Runtime](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/).\n",
"\n",
"With all the ingredients ready, we can now instantiate the VQE:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.algorithms.minimum_eigensolvers import VQE\n",
"\n",
"vqe = VQE(estimator, ansatz, optimizer)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can call the [compute_mininum_eigenvalue()](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.compute_minimum_eigenvalue.html#qiskit.algorithms.minimum_eigensolvers.VQE.compute_minimum_eigenvalue) method. The latter is the interface of choice for the application modules, such as Nature and Optimization, in order that they can work interchangeably with any algorithm within the specific category."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A complete working example\n",
"\n",
"Let's put what we have learned from above together and create a complete working example. VQE will find the minimum eigenvalue, i.e. minimum energy value of a Hamiltonian operator and hence we need such an operator for VQE to work with. Such an operator is given below. This was originally created by the Nature application module as the Hamiltonian for an H2 molecule at 0.735A interatomic distance. It's a sum of Pauli terms as below, but for now I am not going to say anything further about it since the goal is to run the algorithm, but further information on operators can be found in other tutorials."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.quantum_info import SparsePauliOp\n",
"\n",
"H2_op = SparsePauliOp.from_list([\n",
" (\"II\", -1.052373245772859),\n",
" (\"IZ\", 0.39793742484318045),\n",
" (\"ZI\", -0.39793742484318045),\n",
" (\"ZZ\", -0.01128010425623538),\n",
" (\"XX\", 0.18093119978423156)\n",
"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So let's run VQE and print the result object it returns."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{ 'aux_operators_evaluated': None,\n",
" 'cost_function_evals': 102,\n",
" 'eigenvalue': -1.857275020719397,\n",
" 'optimal_circuit': <qiskit.circuit.library.n_local.two_local.TwoLocal object at 0x7f96da26a470>,\n",
" 'optimal_parameters': { ParameterVectorElement(θ[0]): -2.403507257619715,\n",
" ParameterVectorElement(θ[5]): 1.7060524493254914,\n",
" ParameterVectorElement(θ[1]): 3.085467047665086,\n",
" ParameterVectorElement(θ[2]): -2.1949965223522487,\n",
" ParameterVectorElement(θ[3]): 4.276089268519914,\n",
" ParameterVectorElement(θ[4]): -3.098644972035885,\n",
" ParameterVectorElement(θ[6]): 0.032773583818940334,\n",
" ParameterVectorElement(θ[7]): 2.8861019033185396},\n",
" 'optimal_point': array([-2.40350726, 3.08546705, -2.19499652, 4.27608927, -3.09864497,\n",
" 1.70605245, 0.03277358, 2.8861019 ]),\n",
" 'optimal_value': -1.857275020719397,\n",
" 'optimizer_evals': None,\n",
" 'optimizer_result': <qiskit.algorithms.optimizers.optimizer.OptimizerResult object at 0x7f96da2a4d60>,\n",
" 'optimizer_time': 0.29071593284606934}\n"
]
}
],
"source": [
"result = vqe.compute_minimum_eigenvalue(H2_op)\n",
"print(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the above result we can see the number of cost function (=energy) evaluations the optimizer took until it found the minimum eigenvalue of $\\approx -1.85727$ which is the electronic ground state energy of the given H2 molecule. The optimal parameters of the ansatz can also be seen which are the values that were in the ansatz at the minimum value."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Updating the primitive inside VQE\n",
"\n",
"To close off let's also change the estimator primitive inside the a VQE. Maybe you're satisfied with the simulation results and now want to use a shot-based simulator, or run on hardware!\n",
"\n",
"In this example we're changing to a shot-based estimator, still using Qiskit Terra's reference primitive. However you could replace the primitive by e.g. Qiskit Aer's estimator ([qiskit_aer.primitives.Estimator](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html#qiskit_aer.primitives.Estimator)) or even a real backend ([qiskit_ibm_runtime.Estimator](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/stubs/qiskit_ibm_runtime.Estimator.html#qiskit_ibm_runtime.Estimator)).\n",
"\n",
"For noisy loss functions, the SPSA optimizer typically performs well, so we also update the optimizer. See also the [noisy VQE tutorial](https://qiskit.org/documentation/tutorials/algorithms/03_vqe_simulation_with_noise.html) for more details on shot-based and noisy simulations. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{ 'aux_operators_evaluated': None,\n",
" 'cost_function_evals': 200,\n",
" 'eigenvalue': -1.8574503552440247,\n",
" 'optimal_circuit': <qiskit.circuit.library.n_local.two_local.TwoLocal object at 0x7f96da2f4250>,\n",
" 'optimal_parameters': { ParameterVectorElement(θ[0]): -7.7940259581467375,\n",
" ParameterVectorElement(θ[5]): 0.28827257835035214,\n",
" ParameterVectorElement(θ[1]): -1.8091021117029589,\n",
" ParameterVectorElement(θ[2]): -2.460381278734678,\n",
" ParameterVectorElement(θ[3]): -7.725013961075425,\n",
" ParameterVectorElement(θ[4]): -1.3793338621798832,\n",
" ParameterVectorElement(θ[6]): -2.4148423942537587,\n",
" ParameterVectorElement(θ[7]): -1.8555574263247812},\n",
" 'optimal_point': array([-7.79402596, -1.80910211, -2.46038128, -7.72501396, -1.37933386,\n",
" 0.28827258, -2.41484239, -1.85555743]),\n",
" 'optimal_value': -1.8574503552440247,\n",
" 'optimizer_evals': None,\n",
" 'optimizer_result': <qiskit.algorithms.optimizers.optimizer.OptimizerResult object at 0x7f96da26a5f0>,\n",
" 'optimizer_time': 0.8142139911651611}\n"
]
}
],
"source": [
"from qiskit.algorithms.optimizers import SPSA\n",
"\n",
"estimator = Estimator(options={\"shots\": 1000})\n",
"\n",
"vqe.estimator = estimator\n",
"vqe.optimizer = SPSA(maxiter=100)\n",
"result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n",
"print(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note: We do not fix the random seed in the simulators here, so re-running gives slightly varying results."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This concludes this introduction to algorithms in Qiskit. Please check out the other algorithm tutorials in this series for both broader as well as more in depth coverage of the algorithms."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.23.0.dev0+f52bb33</td></tr><tr><td><code>qiskit-aer</code></td><td>0.11.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.7.1</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.19.2</td></tr><tr><td><code>qiskit-nature</code></td><td>0.5.0</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.5.0</td></tr><tr><td><code>qiskit-machine-learning</code></td><td>0.6.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.10.4</td></tr><tr><td>Python compiler</td><td>Clang 12.0.0 </td></tr><tr><td>Python build</td><td>main, Mar 31 2022 03:38:35</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>4</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Wed Dec 07 11:02:26 2022 CET</td></tr></table>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>© Copyright IBM 2017, 2022.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import qiskit.tools.jupyter\n",
"%qiskit_version_table\n",
"%qiskit_copyright"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.10.6 ('venv': venv)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.6"
},
"vscode": {
"interpreter": {
"hash": "f8729fd834348017bca17aea688b306f536a675180840f7307eb909fff39c285"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
================================================
FILE: tutorials/algorithms/02_vqe_advanced_options.ipynb
================================================
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Advanced VQE Options\n",
"\n",
"In the first algorithms tutorial, you learned how to set up a basic [VQE](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.html) algorithm. Now, you will see how to provide more advanced configuration parameters to explore the full range of capabilities of Qiskit's variational algorithms: [VQE](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.VQE.html), [QAOA](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.QAOA.html) and [VQD](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.VQD.html) among others. In particular, this tutorial will cover how to set up a `callback` to monitor convergence and the use of custom `initial point`s and `gradient`s."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Callback"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"Callback methods can be used to monitor optimization progress as the algorithm runs and converges to the minimum. The callback is invoked for each functional evaluation by the optimizer and provides the current optimizer value, evaluation count, current optimizer parameters etc. Note that, depending on the specific optimizer this may not be each iteration (step) of the optimizer, so for example if the optimizer is calling the cost function to compute a finite difference based gradient this will be visible via the callback.\n",
"\n",
"This section demonstrates how to leverage callbacks in `VQE` to plot the convergence path to the ground state energy with a selected set of optimizers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, you need a qubit operator for VQE. For this example, you can use the same operator as used in the algorithms introduction, which was originally computed by [Qiskit Nature](https://qiskit.org/ecosystem/nature/) for an H2 molecule."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.quantum_info import SparsePauliOp\n",
"\n",
"H2_op = SparsePauliOp.from_list(\n",
" [\n",
" (\"II\", -1.052373245772859),\n",
" (\"IZ\", 0.39793742484318045),\n",
" (\"ZI\", -0.39793742484318045),\n",
" (\"ZZ\", -0.01128010425623538),\n",
" (\"XX\", 0.18093119978423156),\n",
" ]\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next step is to instantiate the `Estimator` of choice for the evaluation of expectation values within `VQE`. For simplicity, you can select the [qiskit.primitives.Estimator](https://qiskit.org/documentation/stubs/qiskit.primitives.Estimator.html#qiskit.primitives.Estimator) shipped with the default [Qiskit Terra](https://qiskit.org/documentation/apidoc/terra.html) installation."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"from qiskit.primitives import Estimator\n",
"\n",
"estimator = Estimator()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You are now ready to compare a set of optimizers through the `VQE` callback. The minimum energy of the H2 Hamiltonian can be found quite easily, so the maximum number of iterations (`maxiter`) does not have to be very large. You can once again use `TwoLocal` as the selected trial wavefunction (i.e. ansatz)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization complete \n"
]
}
],
"source": [
"import numpy as np\n",
"from qiskit.algorithms.minimum_eigensolvers import VQE\n",
"from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SLSQP\n",
"from qiskit.circuit.library import TwoLocal\n",
"from qiskit.utils import algorithm_globals\n",
"\n",
"# we will iterate over these different optimizers\n",
"optimizers = [COBYLA(maxiter=80), L_BFGS_B(maxiter=60), SLSQP(maxiter=60)]\n",
"converge_counts = np.empty([len(optimizers)], dtype=object)\n",
"converge_vals = np.empty([len(optimizers)], dtype=object)\n",
"\n",
"for i, optimizer in enumerate(optimizers):\n",
" print(\"\\rOptimizer: {} \".format(type(optimizer).__name__), end=\"\")\n",
" algorithm_globals.random_seed = 50\n",
" ansatz = TwoLocal(rotation_blocks=\"ry\", entanglement_blocks=\"cz\")\n",
"\n",
" counts = []\n",
" values = []\n",
"\n",
" def store_intermediate_result(eval_count, parameters, mean, std):\n",
" counts.append(eval_count)\n",
" values.append(mean)\n",
"\n",
" vqe = VQE(estimator, ansatz, optimizer, callback=store_intermediate_result)\n",
" result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n",
" converge_counts[i] = np.asarray(counts)\n",
" converge_vals[i] = np.asarray(values)\n",
"\n",
"print(\"\\rOptimization complete \");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, from the callback data you stored, you can plot the energy value at each objective function call each optimizer makes. An optimizer using a finite difference method for computing gradient has that characteristic step-like plot where for a number of evaluations it is computing the value for close by points to establish a gradient (the close by points having very similar values whose difference cannot be seen on the scale of the graph here)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false,
"tags": [
"nbsphinx-thumbnail"
]
},
"outputs": [
{
"data": {
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fsHLlSo4++mgefvhh/uEf/mHI5+rq6mLRokU9H5/97Gf55S9/yete97qeY1paWjj11FP5+c9/3rDXXMnKMwnDZNWqVa6aZngRERGRMHryySc5/PDDm72MUBnoPTWzB51zqwY6Xj3ZdbJj92ay+W7a4tFmL6XuotEYLa3zmr0MERERkQlDIbtO3vuTc1mXLDR7GQ3z2SVv4LwzPtPsZYiIiIhMCArZdTLfncrMfZs56cCZzV5K3X1x6728uHt9s5chIiIiMmEoZNdJV8tlPL+9k6+de1qzl1J3X/3vo+guZJu9DBEREZEJQ9NF6iQZi5LNl5q9jIZIAplid7OXISIiIjJhKGTXSdKLks0Xm72Mhkg6o7uUa/YyRERERCYMhew6ScXDG7ITZmQVskVERESqppBdJ4lYhGwhnO0iKSJkS+GdnCIiIiL119raWtVxV111FQsXLmTlypUcdthhXHHFFZRKfqZ6+9vfzgEHHMDKlStZuXIl//7v/w5AR0cHV1xxBcuXL+e4447j+OOP57/+678AKJVKvO997+Ooo47q2ejm+eefH/T5ly1bxooVK1i5ciUrVqzgxhtvHOUr9+nCxzpJelFyhRKlkiMSsWYvp64SFlXIFhERkYb527/9W/7u7/6OUqnEq1/9an77299yxhlnAPDFL36RN73pTX2Of+c738mBBx7IM888QyQSYdu2bXznO98B/N0iN23axKOPPkokEqG9vZ2WlpYhn//OO+9k1qxZPP3005x99tmcf/75o35NCtl1koz5m9B0F0qkQrYhTdI8tYuIiIhMVL/4CGx5rL7nnLcCXvu5+p4TyOVyZLNZpk+fPugx69ev549//CM/+tGPiET8pozZs2fz93//9wBs3ryZ+fPn99y3aNGiqp9/7969Qz53LdQuUifJmP9WhrEvOxnx6HbhbIURERGR5vvyl7/MypUrmT9/PocccggrV67sue9DH/pQT7vIY489xrp16zjmmGN6QnR/f/7nf87Pf/5zVq5cyQc/+EEefvjhYZ//jDPO4KijjuK0007j05/+dF1eU1Mq2WZ2MXAVcDhwonNuzSDHfQd4PbDVOXfU2K2wduVKdrYQxpAdI4NCtoiIyITUgIpzvZXbRfL5PG9605v48Y9/zJvf/GZg/3aR/v3Vn/nMZ7j22mvZunUrmzZtYtGiRTz99NPccccd3HHHHZx11llce+21nHXWWYM+f7ldZP369Zx11lmcfvrpVfeUD6ZZlezHgYuAu4c57rvAOQ1fTR2UK9mZXPhCdiISpxvX7GWIiIhIyMViMc455xzuvnvwiHjEEUfwyCOP9Fwc+fGPf5y1a9eyd+/enmMSiQSvfe1r+eIXv8jHPvYxbrjhhqqef/ny5cydO5cnnnhiVK8DmhSynXNPOueeruK4u4GdY7CkUUt6QSU7hBvSJKMJsgrZIiIi0mDOOe69916WL18+6DEHHXQQq1at4hOf+ATFol/czGazOOdnlYceeohNmzYB/qSRRx99lKVLl1b1/Fu3buX555+v+vih6MLHOglzu0gqmiBrgHNg4ZqcIiIiIo3R1dXV56LDD3zgA3zgAx8Y8Ngvf/nL/PCHPySfz3P00Ufznve8Z8hzf+tb3+JDH/oQBx10EDNnziSVSvGFL3wB8IPyu971Lrq7/d2qTzzxRK688sohz3fGGWcQjUbJ5/N87nOfY+7cubW81AE1LGSb2e3AvAHu+rhzrj4DCPs+3+XA5QBLliyp9+mH1ROyQ3jhY8JLkDXDFXJYLNHs5YiIiMgEUG7nGM5VV13FVVddNeB93/3udwe8fcqUKXzzm98c8L5zzjmHc86pvtv4hRdeqPrYWjQsZDvnVjfq3IM839XA1QCrVq0a896Gck92dxjbRbwUzoxc924SsdH/ZiciIiISdmoXqZMwV7KTXgqAbHYPiVaFbBEREaldeQpIpYsvvpiPf/zjY/L8r3jFK3paSMp+8IMfsGLFioY8X7NG+F0IfBWYDdxiZmudc39mZguAbznnzg2OuwY4HZhlZu3AJ51z327GmocT5p7sZMzfJSmb3c3UJq9FREREJqaPf/zjYxaoB3L//feP6fM1JWQ7564Hrh/g9k3AuRVfXzqW6xqN3s1owtcukoilAeju3tPklYiIiIhMDNrxsU56R/iFr5KdivvD2DO5vcMcKSIiIiKgkF035XaRTAhDdiLmh+zu7n1NXomIiIjIxKCQXScJL7ztIsl4GwDZnEK2iIiIVO8zn/kMRx55JEcffTQrV67k/vvv5/TTT2fNmjV9juvq6uItb3kLK1as4KijjuLUU0+lo6MDgPb2ds4//3wOPvhgDjzwQK688sqeCxjvuusupk6dysqVKzn88MP5p3/6pzF/jYNRyK6TSMSIexG6Q1jJTiWmAJDNdzR5JSIiIjJR/P73v+fmm2/moYce4tFHH+X2229n8eLFAx77la98hblz5/LYY4/x+OOP8+1vf5tYLIZzjosuuogLLriAZ555hmeeeYZMJsOHP/zhnse+6lWvYu3ataxZs4Yf/vCHPPTQQ2P1EoekkF1HqVg0lD3ZiXLIznU2eSUiIiIyUWzevJlZs2aRSPgb2c2aNYsFCxYMeuzChQt7vj700ENJJBLccccdJJNJ3vGOdwAQjUb58pe/zPe///2eSndZS0sLxx9/PM8++2yDXlFtNCe7jpKxSDjbRRLTAMjmFbJFREQmms//8fM8tfOpup7zsBmH8fcn/v2Qx5x99tn88z//M4cccgirV6/mkksu4bTTThvw2P/7f/8vZ599Ntdddx1nnXUWl112GQcffDDr1q3j+OOP73PslClTWLZs2X5heseOHfzhD3/gH/7hH0b34upEIbuOkrFoOOdkJ/3p2Nl8pskrERERkYmitbWVBx98kN/97nfceeedXHLJJXzuc58b8NiVK1fy3HPP8atf/Yrbb7+dE044gd///vdVPc/vfvc7jj32WCKRCB/5yEc48sgj6/kyRkwhu46SXjjbRZKJIGQXFLJFREQmmuEqzo0UjUY5/fTTOf3001mxYgXf+973Bj22tbWViy66iIsuuohIJMKtt97KMcccw3XXXdfnuL1797JlyxYOPfRQ7r//fl71qldx8803N/ql1Ew92XUU2naR8mY0RYVsERERqc7TTz/NM8880/P12rVrWbp06YDH3nvvvezatQuAXC7HE088wdKlSznrrLPo6uri+9//PgDFYpEPfvCDXHnllaRSqca/iFFQyK6jRCwayjnZXsQj6hyZQnezlyIiIiITREdHB5dddhlHHHEERx99NE888QRXXXUVAK973etYtGgRixYt4uKLL2b9+vWcdtpprFixgmOPPZZVq1bxxje+ETPj+uuv57rrruPggw9m5syZRCKRpm7PXi21i9RRMhZlT1eu2cuoOzMjAXQXFbJFRESkOscffzz33XfffrffddddAx7/tre9bcDbFy9ezE033QTAfffdx6WXXspDDz3Ecccd19OKMh4pZNdR0ovwcgjbRQCSzsiWFLJFRESkeU455RRefPHFZi+jKmoXqaNUPJzTRQBSRMgW881ehoiIiMiEoJBdR2GdLgKQsAhZp5AtIiIiUg2F7DoK63QRgKRFyZYKzV6GiIiIVMk51+wlhMZI3kuF7DpKhnRbdfBDdrcL52sTEREJm2QyyY4dOxS068A5x44dO0gmkzU9Thc+1lEiFqW7UMI5h5k1ezl1lYzE6HBdzV6GiIiIVGHRokW0t7ezbdu2Zi8lFJLJJIsWLarpMQrZdZSM+f8w0F0okYxFm7ya+kpEYuwgnK0wIiIiYROLxTjggAOavYxJTe0idZT0/GCdyYWvrSIZiZNF/+QkIiIiUg2F7DoqV6/DOMYvGY2TbfYiRERERCYIhew6KreLhHHCSDKaIGuAZmWLiIiIDEshu45S5Up2CCeMJL0k3WaQzzR7KSIiIiLjnkJ2HSXDHLKjSbKRCKVcZ7OXIiIiIjLuKWTXUSLM7SKxNADd2d3NXYiIiIjIBKCQXUdhvvAxUQ7Z3XuavBIRERGR8U8hu47KI/y6Q9gukoq1AJBVyBYREREZlkJ2HYV5ukiiJ2TvbfJKRERERMY/hew6KreLZEJYyU7GWwHI5vY1eSUiIiIi459Cdh2FerpIvA1QyBYRERGphkJ2HYW5XSSZmAJAtrujySsRERERGf8UsuuofOFjKCvZiWkAdOc1J1tERERkOArZdRSJGHEvEsoRfuVKdkYhW0RERGRYCtl1lvQidIexXSQ5FYBsQduqi4iIiAxHIbvOkrFoKNtFejajUcgWERERGZZCdp2FNWSnvBQA2UK2ySsRERERGf8UsussGYuEcrpIIpoAIFtUyBYREREZjkJ2nSVj0VBuRuNFPDwH2WJ3s5ciIiIiMu4pZNdZ0gtnuwhAEsgWc81ehoiIiMi4p5BdZ8l4lGwhfO0iAEkiZEsK2SIiIiLDUciuM3+EX0gr2Rahu1Toc9sL2ztxzjVpRSIiIiLjk0J2nYV1ughA0qJkXb7n65d2dHH6/7uL36/f0cRViYiIiIw/Ctl1FtbpIgBJ88iUen+B2Nnlt47s6FQLiYiIiEilpoRsM7vYzNaZWcnMVg1yzGIzu9PMngiO/ZuxXudIJGPRUG6rDpAwj27X+9ryRf+XiUIpnL9UiIiIiIxUsyrZjwMXAXcPcUwB+KBz7gjgJOC9ZnbEWCxuNELdLhKJkaW3/7ocsvMF9WSLiIiIVPKa8aTOuScBzGyoYzYDm4PP95nZk8BC4ImxWONIJT2/XcQ5N+Trm4iS0Thb6a1a54t+uM4VVckWERERqTQherLNbBlwLHD/EMdcbmZrzGzNtm3bxmxt/SViUQC6QzjGLxmNkzUg6MvOB68xr5AtIiIi0kfDQraZ3W5mjw/wcX6N52kF/hd4v3Nu72DHOeeuds6tcs6tmj179miXP2LJIGSHsWUkGU3QbQb5DFDRLqKQLSIiItJHw9pFnHOrR3sOM4vhB+z/cc79bPSrarxUT8gOX/BMRpNkLOKH7ERrT5tIuW1ERERERHzjtl3E/IbmbwNPOuf+tdnrqVYy5r+loaxke6mgkt0F9IZrVbJFRERE+mrWCL8LzawdOBm4xcxuC25fYGa3Boe9EngrcKaZrQ0+zm3GemvR0y4SwjF+iViKXMQo5joAtYuIiIiIDKZZ00WuB64f4PZNwLnB5/cAE248R28lO3zBMxVrAaA7u5s0lSFb7SIiIiIilcZtu8hElfTCe+FjIpYGINvtX3+aC6aL5EI4SUVERERkNBSy6ywR5ukisVagN2SrJ1tERERkYArZdRbqCx/jQcjO7QPUky0iIiIyGIXsOkuGeYRfv5BdCMJ1QT3ZIiIiIn0oZNdZmDejScSnANAdTBfJaVt1ERERkQEpZNdZKsQhO5WYCkAm1wmoXURERERkMArZddbTkx3CiRvJpB+yuwvlzWg0wk9ERERkIArZdRbqEX5xf052Nt8/ZIfvFwoRERGR0VDIrrNIxIhHI6G88DEVTQGQLWQAyBWCnuwQVu1FRERERkMhuwESsUg4K9leAugN2apki4iIiAxMIbsBkrEo3YXwhexkNAlAtpgFesN1oaSebBEREZFKCtkNkIxFyORCGLK9csjOAb0hW+0iIiIiIn0pZDdA0ouGsic7YhHiDrLFbqB3TrbaRURERET6UshugFQ8SjaE7SIACYvQXcoDkC9ohJ+IiIjIQBSyG8CvZIczZKeIkA1CdqGkCx9FREREBqKQ3QD+dJFwBs+kRcm6AqB2EREREZHBKGQ3QDIW3kp2wqJknf/a1C4iIiIiMjCF7AbwR/iFs7qbisR6Q7bmZIuIiIgMSCG7AZJeODejAUhEYmRd33CtkC0iIiLSl0J2A4S5XSQZiZM1B6VST5tIvuhwTi0jIiIiImUK2Q2QjEXIhDVkR+N0m0EhS66igq2+bBEREZFeCtkN4FeyS6Gs7iajCTIWgXymT5uIWkZEREREeilkN0AyFgUI5cWPCS/pV7LzXeQLJSLm315QJVtERESkh0J2A/SE7BDOyk56SbKRIGQXHS1xD6BP64iIiIjIZKeQ3QDJmP+2hnFr9ZTXQtYMl+siVyyRTvi/UKhdRERERKSXQnYDJD0/eIZxwkgilqJgRja7F6Cnkq2QLSIiItJLIbsByu0iYdxaPRlrAaArswdAlWwRERGRAShkN0BPu0gIK9nlkN0ZVLLTsaAnu6ALH0VERETKFLIboFzJDuOs7GS8DYBMtm8lu1BSJVtERESkTCG7AcJcyU7EWwHoyu0D1JMtIiIiMhCF7AZIeOHtyU4lpgCQ7fZDdjruv1a1i4iIiIj0UshugFS8vBlNCCvZiakAZHOdALQkVMkWERER6U8huwF6p4uEL2Qng3aRTL4L6P2FQiFbREREpJdCdgMkvXJPdviCZ8pLAdBd8EN2OqaQLSIiItKfQnYDhLmSnYgmAOguZABI97SLqCdbREREpEwhuwFCvRmNlwQgW+wGoEXtIiIiIiL7UchugGjEiEWNbAgvfExG/ZCdK2aBykq2QraIiIhImUJ2gyS9KJlcCEN2UMnuLvWtZOfULiIiIiLSQyG7QRKxaDhH+AU92blSHoB0eTOagirZIiIiImUK2Q2SikdC2ZNtZiQxul05ZKsnW0RERKQ/hewGSXrRUE4XAUgQIecKALQk/JBdKKldRERERKSsKSHbzC42s3VmVjKzVYMckzSzP5rZI8Gx/zTW6xyNZCy8ITtpUbqDkJ0K2kVyahcRERER6dGsSvbjwEXA3UMc0w2c6Zw7BlgJnGNmJ43B2uoiGQtnuwhAyjzy+L9AxKMRYlFTu4iIiIhIBa8ZT+qcexL8/t4hjnFAR/BlLPiYMD0JyViUju5Cs5fREImIRzd+qPZDdkQhW0RERKTCuO7JNrOoma0FtgK/ds7d3+QlVS3hRUNbyU5GYnSbAxxe1IKQPWF+/xERERFpuIZVss3sdmDeAHd93Dl3YzXncM4VgZVmNg243syOcs49PsjzXQ5cDrBkyZKRLbqOkrEI3WHtyY7E6TZIkCcWtIvkVMkWERER6dGwkO2cW13Hc+02szuBc/D7uQc65mrgaoBVq1Y1vayajEXJhDVkRxPstQhJcsSCSnZBIVtERESkx7htFzGz2UEFGzNLAa8BnmrqomrgX/gYzpCdiMbpNmNKNIeZ2kVERERE+mvWCL8LzawdOBm4xcxuC25fYGa3BofNB+40s0eBB/B7sm9uxnpHIhULcU+2lyJrRmvU35BG7SIiIiIifTVrusj1wPUD3L4JODf4/FHg2DFeWt0kY1GyhSLOuSGnqExESS9JNmLMi5RDdkTbqouIiIhUGLftIhNdMhbFOUJZ4e1fyY57GuEnIiIiUkkhu0ESnv/WhrFlJBlroduMlkgWAC9i6skWERERqaCQ3SDJWBQglGP8krE0RTPSkW4AbUYjIiIi0o9CdoOUQ3YoK9nxVgAS0QygdhERERGR/hSyGyQZC9pFCuGrZCdifsiO96lkq11EREREpEwhu0GSnl/JzuTCF7JTiTYA4pEuwB/hp0q2iIiISC+F7AbpbRcJX8hOxKcA4FlvJTuMU1RERERERkohu0FS8XK7SPjCZzLuV7Ij5k8XievCRxEREZE+FLIbJOGFt5Kd9JIARINKthc18gX1ZIuIiIiUKWQ3SJjbRcoh2yraRQolVbJFREREyhSyG6Q8XaQ7jCP8gpCN5YCgJzuEbTEiIiIiI6WQ3SA9lewQjvBLRv2Q7fBDtj8nW+0iIiIiImUK2Q0yGdpFSj2VbI3wExEREamkkN0gSc9/azO58IXPRDQBQIk8UO7JdpRKqmaLiIiIgEJ2w3jRCF7EQtkukvJSABQoAH7IBsjr4kcRERERQCG7oVKxaCjbRWKRGOag2FPJNgAK6ssWERERARSyGyoRi5IN4XQRMyPmjLz5v0D0VLLVly0iIiICKGQ3VDIWoTuElWyAqDPy9A3Z2lpdRERExKeQ3UDJWDSUPdnFksMrRXtCdrynkq12ERERERFQyG6oZCwSynaRfLFE1EXIUQLniHl+T3ZeG9KIiIiIAArZDZX0wnnhY75YIlKK0m1AMY8XUU+2iIiISCWF7AZKhnS6SL7oMOeRiUQg31Vx4aPaRURERERAIbuhkrEImZC2i1jJo9sM8hni5XYRVbJFREREAIXshkrEoqGcLpIrlKAUI2vWr5KtkC0iIiICCtkNFdbNaPLFEs7tH7I1wk9ERETEp5DdQMlYhGwIJ27ki84P2RG/XUQ92SIiIiJ9KWQ3UJini5RKiaAnu6tnW3WN8BMRERHxKWQ3UHm6iHPhqvDmiiVKpXjQLtJbyS6UFLJFREREQCG7oZKxCCUXvjaKfKFEwSXImuFynRU92eF6nSIiIiIjpZDdQMlYFGDIrdXvfGorezL5sVpSXeSLjmIpgTMjl+vo3VZd7SIiIiIigEJ2QyXKIXuQvuyX92Z5x3cf4Md/fGkslzVq+VKJfCkFQDa3r3dbdU0XEREREQEUshsq6flvbzY3cPh85uUOADbuzozZmuohXyiRc0kAst17NSdbREREpB+F7AYarl3k2a37ANi0Oztma6qHfNFR6KlkdxCLqCdbREREpJJCdgOlhmkXeWarX8nesneCVbKLJZyLA5DNd/a0ixRUyRYREREBFLIbqqeSnR84fD4bhOzNE6ySnSuWcKUYAFltqy4iIiKyH4XsBkrGgp7sQSrZ67f5IXtHZ25CbVqTL5bA+SG7u5DBi/iVbLWLiIiIiPgUshsoOUS7yO6uHNs7chwytxXwJ41Uq1hy/OnlffVZ5AjkCxWV7EIXZkY8GlElW0RERCSgkN1APZXsAeZHl1tFXnXwbAA276k+ZN/0yEbO+be72bavuw6rrF2+6KAU9GQX/HXHoqY52SIiIiIBhewGSniDV7Kf6QnZswDYvKf6ix+f3dpBycGurlwdVlm7XLGEcx4A2aIfsj1VskVERER6KGQ3ULldpHuAkP3s1g6SsQirls0Aaqtkb9jpB/KuXHP6uPPFUm8lu+hX02PRCPmSerJFREREQCG7ocrtIplBQvaBs1ppTXhMSXo1TRhp39UFQFd3oT4LrVG+WCJiQU920a+mx9UuIiIiItJDIbuBhhrh9+zWDg6a41/0uGBaqqZKdvuu5layC0VHzBIAZEt5AGKe2kVEREREypoSss3sYjNbZ2YlM1s1zLFRM3vYzG4eq/XVSywawYvYfj3ZXbkCG3dnODgI2fOmJqvuyc7mi2wNLnjsatLYv1yxRCwaI0pFyI5G/AsiRURERKRplezHgYuAu6s49m+AJxu7nMZJxqL7VbLXb+0E6Klkz5+aYkuVlexNu3vDeDPbReLRCEnzyJb8NcSiEXKqZIuIiIgATQrZzrknnXNPD3ecmS0CXgd8q/GraoxkLEK20Lfi/Ow2f8Z1b8hOVr0hzYZdFSG7WRc+FhyxaISERel25ZBtahcRERERCYz3nux/Az4MDJvezOxyM1tjZmu2bdvW8IVVK+FF9wvPz27tIBoxls5sAfyQDdVtSFO+6BEGvqByLOSLJWKekYrEyOKgmCcWjVBQu4iIiIgI0MCQbWa3m9njA3ycX+XjXw9sdc49WM3xzrmrnXOrnHOrZs+ePaq111MyFqG7X7vIs1s7WDozTdzz3/75U1MAbKpiwkj7rgyxqBGNGJ1Nahfxe7IjJCMxsmaQ99ekdhERERERn9eoEzvnVo/yFK8E3mBm5wJJYIqZ/dA59xejX93Y8Xuy969kly96BJg/za9kb9k7/MWP7bsyLJiWYmdnrqlzsuPRCIlIjGwkEoTsCB1NCv0iIiIi4824bRdxzn3UObfIObcMeDNwx0QL2OCH7Mq2jlyhxAs7unr6saG3XaSaMX7tu7pYND1FOh4l07SQ7fdkJ6OJoJLdRVw7PoqIiIj0aNYIvwvNrB04GbjFzG4Lbl9gZrc2Y02NkoxF+lSyX9zRSbHk+oTsdNxjaipW1YY0G3ZmWDQtTTruNW2EX75YIha1ipDtV7LzBfVki4iIiEDzpotcH1SpE865uc65Pwtu3+ScO3eA4+9yzr1+7Fc6eql+I/ye3doBwEGz2/ocN39qcthKdjZfZHtHd08lu1kj/HKFoCfbS/ZUsj1NFxERERHpMW7bRcIiEYv2GeFXDtnL57T0OW5+FRvSlHd6XDwj7YfsJvZkx6IREl6S7khFu0hJIVtEREQEGnjho/iSXrTPdJFnt3WwcFqKdLzvWz9vaopH2/cMea7y+L5F01Ok4h57Mvn6L7gKhZIjFjVSXpqMGdz9Rd6yK8XqbBZ+9pOmrKkhpi+DMz7a7FWIiIjIBKSQ3WD9e7KfebmjTz922YKKDWmSseiA5ypvRLNoepp0LMrm3dVtxV5v5XaRRHoW3dEY7HqRA7pyzC0V4aUXmrKmuuveC5ldcNIVkJrW7NWIiIjIBKOQ3WCVI/xKJcdz2zs4efnM/Y6bV7EhTXmTmv7ad/ltGXPaEqQTTW4X8SIkk1PJenF4/xq++vN1XPdgO4+9/8+asqa6e+j7cNNf+2FbIVtERERqpJ7sBvO3VffbRTbuzpDNlwauZE8bfkOa9l0ZFk5PEYmYP8KvadNFHPFohFQ0RXexm5IrhW+EX2KK/2d2b3PXISIiIhOSQnaDJb0oxZIjXyz1XPR48AAhu1zJHmpDmvZdGRZN98N4Ou41bcfH8gi/hJcAoLvYHUwXCdEIv2QQsrsVskVERKR2CtkNVu6vzuSLveP7BgjZ5Q1phqpkbww2ogFIx6N0F0oUS2MfbMvTRZJRf83ZQpZYNEKx5Cg1YT0NkZjq/6lKtoiIiIyAQnaDJWP+W5wNQvas1jjT0vH9jitvSLNlkFnZXbkC2ztyLJqeDo7vDe9jrXJONviV7FjUf52hGeOXDEK2KtkiIiIyAgrZDVauZHfnSzyzdR/LZ+9fxS4balb2xp7JIn4lOxWMAGzGhjT5oiPu9VayM4UM8XLIDkvLSLldJDv0WEURERGRgShkN1g5ZJcr2QO1ipQNtetje8X4PoCWoJLdjAkjA/Vkx6Lm31cISSU7oZAtIiIiI6eQ3WDlkN2+K8PebGHAix7L5k1NDRGy/Y1oFlf0ZMPYh+xSyQWb0fjTRSDoyfbKleyQhOxYEqJxtYuIiIjIiChkN1i5J/vxjX5F9KA5bYMeu2Bqkp3BhjT9te/KEPcizGr1q8fldpFMfmzbRco91/626v5assUssYj/OnNhCdng92XrwkcREREZgao2ozGzLwHfcc6ta/B6QqdcyX6sJ2QPVckOxvjtybJsVt8NaTbs6mLRNH9GNvS2i3R2j20luxD0XMei1nPh4z/e+48UC3HSB2T5qzuuJu6F43e3RdPTfCWzW7+JioiISM2q3fHxSeBqM/OA/waucc6pWbUKSc8Pw+s27aU14TF3SmLQY8sb0mweIGS378qwaEa65+tUk9pFyu0gsWiEg6YdxBsPfiN7c3vZvCfDxm27WdAyi7ZkbEzX1Agv7X2Ju2KOju7dTGn2YkRERGTCqSpkO+e+BXzLzA4F3gE8amb3Av/lnLuzkQuc6MrtIht3Zzhm8TTMbNBjy5XsgSaMtO/KcNTCqT1fp5vULpKrCNmJaIKrTrkKgNvWbeH3v3+Q97/xVI5cMHWIM0wMP336p3zqD58i071XIVtERERqVvW/hJtZFDgs+NgOPAJ8wMx+3KC1hUK5XQQG3umx0vyekN334sfO7gI7O3M94/ugee0i5RF95ZF9ZWEb4ZeO+f9qkMnta/JKREREZCKqtif7y8B5wG+Azzrn/hjc9Xkze7pRiwuDypA9VD829G5I07+S3X98H/S2i2TGul0kGNEX8/pW5Hs2ownJhY8pz/+FRiFbRERERqLanuxHgU845zoHuO/EOq4ndMrtIgAHDbERTdn8qcn9dn3sP74PettFmtmTXckL2Zzscsjuync1eSUiIiIyEVUbsh8BDu3XT7wHeFEXQA6tlko2+CF70+7+IXv/SnY0YiS8CF255vVkVyp/HZYRfmkvaBcpdUOxANFq/1MRERERqT5kfx04Dr+ibcBRwDpgqpld4Zz7VYPWN+HFohGiESMaMRZXTAcZzPxpKR5p7/t7S/uuLhJehFmt8T63p+PRJlSyh+7JLoSkJ7unXcTM35AmPaPJKxIREZGJpNoLHzcBxzrnVjnnjgeOBZ4DXgN8oVGLC4ukF+HAWS1EI4NPFimbP2X/DWnad2VYND2132SSdNwbN+0i5R7tsPRk91SyIxHt+igiIiI1qzZkH1K5EY1z7gngMOfcc41ZVrik4l5VrSLgV7KBPn3ZG3Z1DVgFT8WjY94u0nPhY3TgCx/D0i6SigU92WaQVUeUiIiI1KbadpEnzOwbQHlc3yXBbQkg35CVhcjnLlrBkpnDt4pA3zF+5Q1p2ndlWLl42n7HtjSjXaQU7PjohXuEX0+7SMS0tbqIiIjUrNqQfRnwHuD9wdf3An+HH7DPqP+ywmX1EXOrPnZ+vw1p9mXz7O7K97nosSwVjzZvhF9kkOkiIalkJ6P+30PG1C4iIiIitRs2ZAeb0NzqnDsD+NIAh3TUfVWT2PypvVurg79TJNBnI5qydNxj677sfrc3Uk9PdsjnZEcjUZKRuH/hoyrZIiIiUqNhe7Kdc0WgZGYTf6/sCSAVjzIt3bshTftO/8/FA1Sy0/EoXWO84+NwI/zC0i4CfstIV0Q92SIiIlK7attFOoDHzOzXQM+GNM659zVkVZPcvCm9G9JsCDaiGbiSPf5G+IWlkg2QiqXVLiIiIiIjUm3I/lnwIWNgwbRUz4Y07bsypGJRZrTE9zvOH+E3xtNFBq1kh2vHR4CUlyYT9VTJFhERkZpVFbKdc98zsxSwxDn3dIPXNOnNm5pk7YbdgL8RzUAzsqFZleyBR/hFI4ZZuCrZ6ViajBdTJVtERERqVtWcbDM7D1gL/DL4eqWZ3dTAdU1qC6b2bkjTvisz6E6R6XiUQsmRG8Pqcfm5+o/wMzNikQi5kPVkZyJRXfgoIiIiNat2M5qrgBOB3QDOubXAgQ1ZkTBvau+GNBt2dg3Yjw3+JjfAmI7xG6wnG/zqdpgq2f6Fj1G1i4iIiEjNqg3Zeedc/6QRnjQ1zpRnZT/98j72ZguDhuyWeBSAzjHsyx6sJxv86nYhZCE7EzG1i4iIiEjNqr3wcZ2Z/R8gamYHA+8D7mvcsia3cshe88JOgAE3ogF/3B8wpn3Z+WKJiPk92P3FouFqF0nH0mRA7SIiIiJSs2or2X8NHAl0A9cAe+nd/VHqrLwhzR9f2AUMPL4P/OkiMPbtIgNVscFvIQlbu0jGSqpki4iISM2qnS7SBXw8+JAGK29Is26j36Ez0EY00Lx2kcFCdih7sl0Jl93D/nV7ERERkcFVFbLN7BDg74BllY9xzp3ZmGXJvClJnuraR0sQuAdSbhcZ20p2ab/xfWVeCCvZRRz5QpZ4IQfe/rPKRURERAZSbU/2tcB/At8CxnYw8yS1YFqKp7bsY9H09IAzsqG3XWSse7IHr2RHyBXC05Od8vw2nUwkQrx7L3izmrwiERERmSiqDdkF59w3GroS6WNecPHjYP3Y4M/JBsZ018dcYaiebKNQCk8lO+35bToZM6Zm90CLQraIiIhUp9oLH39uZu8xs/lmNqP80dCVTXILgpA92EY0UBmyx7aSHfcGr2SHrV0EoEtj/ERERKRG1VayLwv+/FDFbQ5tSNMw5Q1phq5kN6tdZOD2lVg0Qj6M7SIW0YY0IiIiUpNqp4sc0OiFSF8LppXbRQavZCdjEcwgM16mi3gRMpn8mK2l0VKxikq2ZmWLiIhIDYZsFzGzD1d8fnG/+z470ic1s4vNbJ2Zlcxs1RDHvWBmj5nZWjNbM9Lnm4hOXDaDT51/JGccNnvQY8yMdCxK5xhWsnNDzMmORcI1wq+yJ1vtIiIiIlKL4Xqy31zx+Uf73XfOKJ73ceAi4O4qjj3DObfSOTdoGA8jLxrhrScvI+FFhzwuFffGtl2kUCI+xHSRMIXs3nYRVbJFRESkNsO1i9ggnw/0ddWcc08Cg46mk+ql49ExbxdJxAZvFymEaFv13gsf1ZMtIiIitRmuku0G+XygrxvBAb8yswfN7PIxeL4JJx0f23aRfGmIdpGokQtjJTuWVLuIiIiI1GS4SvYxZrYXv2qdCj4n+Do51APN7HZg3gB3fdw5d2OV6zvVObfRzOYAvzazp5xzA7aYBCH8coAlS5ZUefqJz69kj227yOBzssPVLpKOBT3ZsaTaRURERKQmQ4Zs59zQDcFDP3b1SB9bcY6NwZ9bzex64EQG6eN2zl0NXA2watWq8PQsDCMd98Z0M5phR/iFqF0kGU1iGJlYArrVLiIiIiLVq3YzmjFnZi1m1lb+HDgb/4JJqZCOR8fNtupe1MgXwlPJNjOSXpIuL6FKtoiIiNSkKSHbzC40s3bgZOAWM7stuH2Bmd0aHDYXuMfMHgH+CNzinPtlM9Y7no19yB5qW/VIqHqywe/LzkQ9XfgoIiIiNal2x8e6cs5dD1w/wO2bgHODz58DjhnjpU04Yz3CLzfUZjTRCIVSeNpFIAjZ+YwufBQREZGajNt2EalOSxNG+MWH6MkulhzFEAXtdCxNJhJVu4iIiIjURCF7gkvHo3Tlizg3NsF2qOkiMc8P32GaMJLyUmQiwY6PY/Qei4iIyMSnkD3BpeIezkE2PzbBNl90xLzBe7L9Y8IVsrtwUMxBIdvs5YiIiMgEoZA9wbUk/CmLYzHGzzk3ZE+2FylXssNT8U15KTLlfZfUMiIiIiJVUsie4FKxcshu/MWP5YsaB+3J9sJXyU57aTIueG918aOIiIhUSSF7gkvH/QExYxKygwr1UNNFIFwhO+WlyLjgXwlUyRYREZEqKWRPcOn42LWLlGdgDzUnG8LXLtJVyvlfaNdHERERqZJC9gTXG7IbX8nO94TswUf4VR4XBikvRaaY87uytSGNiIiIVEkhe4Iby3aR/DCV7HL4zoVoa/V0LI3D0W2mdhERERGpmkL2BJcaw3aRfGGYnuwQXviY8lIAZMx04aOIiIhUTSF7gusd4df4SnZPT/Ygc7JjkfD1ZKe9NABdkYgq2SIiIlI1hewJLh0b+3aRwbdV928vhLGSnWhTT7aIiIhUTSF7giu3i2TGol1kuJ7soMKdC2XIblW7iIiIiFRNIXuCi3sRYlGjcxxc+BjGEX7pmN8ukomn1S4iIiIiVVPIDoFULEqmipD9iRse490/eHDEz5Mb7sLHkI7wA8jEU6pki4iISNW8Zi9ARi8d96qaLvL4xr3sy+ZH/Dw9Pdne0D3ZYQzZXfEUdOxu7mJERERkwlDIDoF0IlrVhY/bO7pHFYALpeHmZAc92SGak91TyfYSkN3U5NWIiIjIRKGQHQLp+PAh2znH9o5uvMjIO4SqbxcJUU92MMIv48XULiIiIiJVU8gOgXRs+HaRzlyRbL6EWQnnHGYDt3wMpdodH8sV7zBIxYJKdjTmX/joHIzgvRMREZHJRRc+hkA6MfyFj9v3dQN+RhzpTO3ekD1IT7YXvnaReCROxCJ0RaLgipDvavaSREREZAJQyA6BdDw67Ai/7R3dPZ93do9spvZkHOFnZqS8FJlym402pBEREZEqKGSHQCrmDV/JrgjZHSMM2bni5BvhB/7Fj5ly8V6zskVERKQKCtkh0JKIDtuTva0j1/N5Z/cI20UK5W3VB/62iUYMs/CF7LSXpqscsnXxo4iIiFRBITsEUtW0i+wbfSW7p11kkDnZ4Fezw7StOgSVbBe8JlWyRUREpAoK2SGQjnnkCiWKpcF7oXd01jFkD1LJBr/KXQhRTzYEIZvgl5js7qauRURERCYGhewQSMejAEO2jGzfl+tp8xjphY/lnmwvMlQl20LXLpLyUmRKwXumdhERERGpgkJ2CKQT5ZA9eMvI9o5uFs/wZz6PppIdj0aGnLEdi0ZCF7LTsTRdpaCnXe0iIiIiUgWF7BDorWQPHbKXzWwBRl7JLhRLg87ILotFIz07Q4ZFykuRKXaDRVXJFhERkaooZIdAKuZv3Dlku0hHjsUz0piNZk6269lwZjChbRcpZCA5RZVsERERqYpCdgi0BO0ig83KzuaLdHQXmN2WoCXu0THCEX65YmnIix4hnO0iPSE7MUWb0YiIiEhVFLJDoNwuMtgYv23B+L5ZrXFaE97IK9mFErEhLnqEcsgOV7tIOpYmU8hQSrapXURERESqopAdAuV2kcwg7SLl3R5ntSZoSURHdeHjsO0iXjgr2QDZhNpFREREpDoK2SHQMsx0kR3Bbo8zWxO0JrxRhGw3bLtIPKQ92QBdiVZVskVERKQqCtkhkBqmXaS3kh2nZRTtIpO5Jxsgk2hRT7aIiIhURSE7BNLxWtpFRlPJLhEfZoSfF430bFoTFj0hO5ZSu4iIiIhURSE7BFKxodtFtnfkaEt4JGNR/8LHIUb9DSVfRSU7HjXyhXBVstNeGoBMLOG3i5TC9fpERESk/hSyQyAaMZKxyKAhe1tHN7PaEoDfv905whF++cLwPdmxaIRCyEJoT0+2lwAc5DqauyAREREZ9xSyQyId9wbdjGb7vm5mtcYBRtUukqtmukgIR/ilYkG7iOe/h7r4UURERIajkB0S6Xh0iHaRbma1+pXstoRHrlAiN4KWjkJp+J5sf1v1cFayM1G/910XP4qIiMhwFLJDIh2P0jVIG8j2jlxPyG5J+EFxJBNGqmkXiXvhG+HX05Md8XvfdfGjiIiIDEchOyRScY+u/P4hO1cosSeT3y9kj6RlpJoLH71IiEf4RYLXrnYRERERGUZTQraZXWxm68ysZGarhjhumpldZ2ZPmdmTZnbyWK5zImmJRwcc4bezs7wRjd9P3FquZI9gwkj1c7LD1ZNdrmR3lTtlVMkWERGRYTSrkv04cBFw9zDHfQX4pXPuMOAY4MlGL2yiGqwnu3JGNoyyXaRYIjZcT3YI20Vi0RieeWQIfnnI7m7qekRERGT885rxpM65JwHMBg9sZjYVeDXw9uAxOSA3BsubkFJxb8CQvS0I2bPbypVsv6+4YwRj/KrbVj187SLgTxjJELwutYuIiIjIMMZzT/YBwDbgv83sYTP7lpm1NHtR41U6Fh1whN/2fXWsZBeqaxcpOSiWwtUykvJSZEp5iMTULiIiIiLDaljINrPbzezxAT7Or/IUHnAc8A3n3LFAJ/CRIZ7vcjNbY2Zrtm3bVodXMLGkE4O1i/jF/56QHR/5hY/+nOzhR/gBoatmp700XYUuSE5RJVtERESG1bB2Eefc6lGeoh1od87dH3x9HUOEbOfc1cDVAKtWrQpXGbUK5Z5s51yfNpztHd2kYtGeCnZbMgjZ2ZH1ZMeHrWT7z50rlkgG272HQcpLkSlkIDlVlWwREREZ1rhtF3HObQE2mNmhwU1nAU80cUnjWjruUSw5cv0qyNs7upkV9GPDyNtFiiVHyVFVuwj4rSVh0hOyE1O0GY2IiIgMq1kj/C40s3bgZOAWM7stuH2Bmd1acehfA/9jZo8CK4HPjvliJ4h03K8aZ/q1jFTu9gh+CI57ETpqHOFXbv+oNmQXwtaTHUuRyWfULiIiIiJVadZ0keuB6we4fRNwbsXXa4FB52hLr3LI7swVmZbuvX1HR45F09N9jm1NeDVXsntD9nA92UG7SMgq2WkvzZbCFr+S3bG+2csRERGRcW7ctotIbVLBBY39N6TZ3tHdM76vrCURpbPGEX7lDWbi3nDbqofzwseUlwoufJyqSraIiIgMSyE7JFqCSnblhJFiybGzM9enXcQ/1qt5ukit7SJh2/Wx74WP6skWERGRoSlkh0Sq3C5SUaHe2Zmj5NgvZI+kXaTc/jFcyPYifrtI2CrZaS/de+FjrgNKtW/mIyIiIpOHQnZIpMvtIvne8Nx/S/Wylkb2ZAftIv2nnEx0KS9Fd7GbYqLVv0EtIyIiIjIEheyQGKhdpDdk9+3Jbk167Ks5ZPvtH9Vsqw5QCGG7CEAm5v+pWdkiIiIyFIXskEgNFbLb+rWLxEdTya62Jzt8lWyATCzp36BKtoiIiAxBITskyu0iXRXhefu+vluql/ntIrX1FOdqHeEXspCdjvljEDOx4L3UxY8iIiIyBIXskCjPye7K961kx6MRpiT7jkNvTUTpzBVwrvqWjvIOjsNvqx7eHR8BMtGYf4PaRURERGQICtkhkfAiRKzvjo/bO3LMbI1j1rf63JLwcK5va8lwenqyh5mTHeYRfgBd0eAXFrWLiIiIyBAUskPCzEjH+7aB9N9Svawl4QfFWvqyq+/JDucIv55KdiR4/apki4iIyBAUskMkFY/uN8Kv/2QR8OdkAzVtSFP9tuohv/CxJ2SrJ1tEREQGp5AdIi3x6H7TRYauZNfeLjJcT3bvturhahcpX/jYVcqDl4RuhWwREREZnEJ2iKQq2kVKJceOjtx+4/ugt5K9rztf9bk1wi+oZJd3fVS7iIiIiAxBITtE0hXtInsyeQolN2Alu3UEleyeEX7DXvgY8p7sQgaSU3Tho4iIiAxJITtE0hXtIoPt9gjQkvDH/Y3swsfqerLDNie7Z7pIoQuSU9WTLSIiIkNSyA6RdDxKV1Cd3haE7NlDVLJruvAxmHsdi1Q7JztcPdlexCMeiatdRERERKriDX+ITBTpuEdX0C6yo8Pf7XFm3Ub4VTcnOxoxIha+dhGAVCxFJh+0i2x8CH52ebOX1AAGx18GS09p9kJEREQmNIXsEEnHoz2b0QzVLpKORzGrLWRXu626f0yEfCmEIdtL+e0iB62GzY/AhvubvaT627cFunYoZIuIiIySQnaIpOPRnosZt3d0E40Y09P7h2wzoyXu0VHTCL/q2kXAH/MXtnYR8EN2ppCB497mf4TRzR+AR38CxQJE9eNBRERkpNSTHSKpuEcmX6RUcmzfl2NGS5xIZODKc0siSkeNI/y8iA16vkoxLxLOdpFyyA6zZadCrsOv1IuIiMiIKWSHSEvcnxqSLRQH3YimrDXh1bwZzXAzssu8iIUyZKe99OQI2QAv3tPcdYiIiExwCtkhkg5CdleuOOiW6mWtCa/mbdWr6ccGvyc7bCP8IOjJznc1exmN1ToHZh0KLyhki4iIjIZCdoik4n4PbVd3ke0duQHH95W1JLya52THh5ksUhb3IqHbVh0mSbsI+NXsF3/v92WLiIjIiChkh0i5XaQrX2BbR/eAW6r3HFtrJbtQfbtILGoUQlrJnjQhO7cPtqgvW0REZKQUskMkFYTsl/d2kyuUhm0X6czV2i5SbcgO54WP6dgk6MmG3r5stYyIiIiMmEJ2iKSDdpGXdvp9wzNbhqpkR2u68DFXc0+22kUmrNY5MOsQhWwREZFRUMgOkfKFj+1ByK5ru0hNlWzr2YY9TFJeinwpT75U/ejDCUt92SIiIqOikB0i5ZD94o4gZA/VLhL3yBVK5KoMw7WM8Atru0jKSwFMjmq2+rJFRERGRSE7RPq3iww1XaQ16R9b7YSRWkf4hTFkp2NpADL5SRCyl6ovW0REZDQUskOkfOHjhp1dmMGMlsEr2S0JP2RX2zKSK9R64WM4e7JhklSy2+aqL1tERGQUFLJDpNwusq+7wPR0HG+IUNwahOxqJ4zUNic7nDs+lkN2VyHkG9KUqS9bRERkxBSyQyQWjRAPgvVQ/djQW8muvl1EPdmTqpINFX3ZjzZ7JSIiIhOOQnbIlFtGZg3Rjw3QmvCP66hyjF8tPdleJJztImkv6MmeLCFbfdkiIiIjppAdMuVdH2cOE7Jrr2RX35Md94ycKtkTn/qyRURERkwhO2R6K9nDtIsEk0g6stW3i8QnebtIuZLdlZ8kPdkAS18JL6kvW0REpFYK2SFTHuM3XLtIW7K26SK1bqteCGG7SCo2ySrZ4Pdld+9VX7aIiEiNFLJDpjxhZKgZ2TDCdhGvlm3Vw1fJnnTtIuCHbFDLiIiISI0UskOmHLJntQ3dLhKLRoh7ETqqHOGXK5TwIlX2ZEf9EX7OhauanYwmgUkWstvmwcyDFbJFRERqpJAdMtW2i4A/K7uWEX7Vzsn2ohGcg2IpXCE7GomSjCYnV8gGv5qtvmwREZGaKGSHTLrKEX4ALYkonQ0Y4Vfu3Q7jGL+Ul5pcFz6C+rJFRERGQCE7ZNI9I/yGbhcBf8JINRc+lkqOQqmWzWj8MB7WvuxJWckGtYyIiIjUQCE7ZI5fNoMzD5tDwosOe2y17SL5kh+Wq5+T7R9XCGHITsfSky9kqy9bRESkZk0J2WZ2sZmtM7OSma0a5JhDzWxtxcdeM3v/GC91wnnDMQv4zttPqOrYlkR1lexy20ctc7IrHxcmk7KSDb192aXq2otEREQmO69Jz/s4cBHwzcEOcM49DawEMLMosBG4fiwWN1m0Jj027Bq+v7hcka69Jzt8leyUl6KrMMl6ssEP2Q/+NzzyY5i+tNmrqb/UdJh7ZLNXISIiIdKUkO2cexLArLrQBpwFrHfOvdiwRU1CrfHq2kXKvdWxKqeLhL0ne2/X3mYvY+wtexVYFG58T7NX0jjvfxymLW72KkREJCSaVcmu1ZuBa5q9iLBpSXhVTRcpt33UsuOj/7hwhuxJ2S7SNheuuBc6tzV7JfW3+RH41SdgT7tCtoiI1E3DQraZ3Q7MG+CujzvnbqzhPHHgDcBHhznucuBygCVLltSw0smrNRGlM1fAOTfkvyrkC35YrrknuxC+nux0LE0mPwlDNsCcw4HDm72K+ktN9/8M4y8QIiLSNA0L2c651XU61WuBh5xzLw/zfFcDVwOsWrUqfOmuAVoSHs5BV67Ys836QPLF2qaLlNtFylNJwmTS9mSHWcts/8/Orc1dh4iIhMpEGOF3KWoVaYhysB6uLztX44WP8Z5KdjhDdqaQCd2W8ZNaepb/Z+f25q5DRERCpVkj/C40s3bgZOAWM7stuH2Bmd1acVwL8BrgZ81YZ9i1BiF73zAhu+aebC/cI/yKrki+lG/2UqReoh6kZqhdRERE6qpZ00WuZ4BxfM65TcC5FV93AjPHcGmTSrWV7FrbRbyI9XlcmKS9NACZQoZ4dPhdNWWCaJmtkC0iInU1EdpFpEHKlezhNqQpt33UOic7rCP8gMk5YSTMWmZDh0K2iIjUj0L2JNbaU8keeoxfrXOy4164R/gBdOV18WOotMxSJVtEROpKIXsSa0lEgWraRUa2rXohpD3ZoEp26LTOUcgWEZG6UsiexKptFymMcIRfGNtF0jG/J1tj/EKmZTZkd0Mh1+yViIhISChkT2INH+E3gpC9bV83z23rqPlxY0WV7JBqCcb4dWmMn4iI1IdC9iSWjkcxq75dpOrpIqOYk/3eHz3Euf/+O9Zu2F3zY8dCT0+2Ktnh0rMhjVpGRESkPhSyJzEzoyXuVTEnO9hWvcoLH3t2fKyxJ/v57Z388fmd5IuOd37vATbsHH9BtqeSPVm3Vg+rljn+nwrZIiJSJwrZk1xLIlr3OdkjHeF33YMbiBj84C9PJFco8Y7vPsCervG16YvaRUKqRbs+iohIfSlkT3KtCW/4EX4jnJNdy3SRYsnxvw9u5PRD53DK8ll8862reHFHJ1f8z4M9zz8elC98VMgOGbWLiIhInSlkT3KtCW/4zWhq7MmORoxoxGq68PF3z2xjy94sFx+/CICTl8/kcxcdzX3rd/Cx6x/DufExDjAZTWKYQnbYJNogmoCOrc1eiYiIhERTtlWX8aMl4dW9XcQ/traQfe2D7UxPxzjr8Lk9t73x+EW8tLOLr/zmGZbOSPPXZx1c9fkaxcxIekld+Bg2ZsGsbLWLiIhIfShkT3ItCY+dnUMHxnyxRMT8CnW1YtFI1T3Zu7ty/Hrdy7zlpCX7XVz5/tUHs2FnF1/69Z9YMjPN+SsXVr2GRkl5KVWyw0i7PoqISB0pZE9yrQmPztzwc7JrqWKDH7KrrWTfuHYTuWKJi49fvN99Zsa/vHEFG3dn+NC1j7JgWooTls2oaS31lvbSCtlh1DJb7SIiIlI36sme5FoSUTqyw7SLFFzVW6qXxaJGvlBdH/VP12zgqIVTOGLBlAHvT3hRvvnW45ndluBff/WnmtbRCKlYSiP8wqhltirZIiJSNwrZk1xLFdNFCqUSsSpnZJfFohHypeEr2es27WHdpr0DVrErTUvHOeeoeTz40i6y+aHX22gpL6We7DAqt4uMk4tsRURkYlPInuRa4x65YmnIMXn5Yqnq8X1l8Wikqs1orl3TTjwa4fyVC4Y99uQDZ5IrlJq+G6R6skOqZQ4Uc9C9t9krERGREFDInuRak35b/lATRnIFN7Ke7GHmW+cKJW5cu5HXHDmXaen4sOc84YAZRAx+v35HTWupN4XskOqZla0JIyIiMnq68HGSa0n43wId3QWmtwwcdPPFUu092d7wI/x+8+TL7OrK98zGHs7UVIwjF0zlD881N2SnvTTrd6/nrJ+e1dR1NMrJC07m/ce/n1mpWc1eytgq7/rYsRVmLm/uWkREZMJTyJ7kWoOQPdSEkfwIpot4keFH+P10zQbmTUnyqoNnV33ekw6cwffue5FsvkgyFq1pTfVy6WGX9myvHjaZQoZbnr+F21+6nfcc8x4uPfxSYpFYs5c1NrTro4iI1JFC9iRXrmQP1S6SL5aIeSPpyR48ZL+8N8tv/7SNK05fXtP87ZOXz+S/fvc8D720i1OWN6fSunLOSlbOWdmU5x4LV+y5gs8/8Hm+uOaL/OyZn/GRV3yEk+af1OxlNV7rHP9PhWwREakD9WRPcq0JvxrcMcSEkVxxBD3Zng154eP/PtROycGbhpkq0t+qZX5f9h+a3JcdZsumLuPrZ32dr575VbLFLO/61bv44F0fZHPH5mYvrbHSM/0/1ZMtIiJ1oJA9yfX0ZA8xKztfKBGL1H7hY2GQSrZzjuvWtHPishkcMKulpvNOScZYsXAqf3huZ02Pk9qYGacvPp0bzr+B9658L79t/y1vuOENrN26ttlLa5xoDFLTVckWEZG6UMie5FrijWkX8bdVH7iS/eCLu3hueydvWlXdBY/9nXTgTB7esItMrrnzsieDpJfk3ce8mxsvuJFCqcBv23/b7CU1Vsts6NSujyIiMnoK2ZNca8V0kcGM5MLHoXqyv/f7F2lNeLxuxfyazll20vKZ5IuOh17aNaLHS+0Wti5kQesCXtr7UrOX0lgtc9QuIiIidaGQPclVc+HjSHqyvejAI/zWb+vg5kc38RcnLe157lqdsGwG0Yg1fV72ZLN4ymI27NvQ7GU0VnnXRxERkVFSyJ7k4l6EuBehY4gRfoWRzMkeZDOab9y1noQX4Z2vOqDmtZa1JrygL1sheywtbVvKS/tewoV52/GW2QrZIiJSFwrZQmvCG74nu8Zt1Qfqyd6ws4sbHt7IpScuYVZrYkRrLTvpwJk80r6briF+OZD6WjJlCZ35TnZkQ/zLTctsyOyCYr7ZKxERkQlOIVtoSUTpHGKEX34E7SLxqFEo9a1kf/Pu9ZjB5a8+cETrrHRy0Jf94Ivqyx4ri9v8cYuhbhlp1dbqIiJSHwrZQkvcY98QI/xyxRIxb3TtIi/vzfLTB9p50/GLmT919Lslrlo6HU992WNqSdsSgHBf/KhdH0VEpE4UsqWqdpGae7K9SJ/NaK6++zmKznHFactHvM5KLQmPoxepL3ssLWxdSMQivLRPIVtERGQ4CtlCS8Kjc4je5nxhBD3ZESNXLOGcY0dHNz+6/yXOX7mAJTPTo11uj5MOnMmj7XuG/AVB6icWjbGgZQEb9oa4XUQhW0RE6kQhW2hNeMPMyR7BturB8YWS4zv3Pk+2UOQ9px80qnX2d/LymRRKjjXqyx4zS6YsCXkle5b/p0K2iIiMkkK2DNku4pwjVyzhjaBdBGBHR47v3/ci5x41n4PmtI56rZWOXzqdWFR92WNpcdtiXtob4jF+iSkQTShki4jIqClki98uMsh0kR2dOQCSsZFVsr99z3Ps6y7w3jPqW8UGSMc9jlk0bdi+7Oe2dYQ3FI6xJW1L2Jffx+7u3c1eSmOYBbOyNV1ERERGRyFbaE1E6cwVBgyiV9/9HBGDs4+YV9M540EP9/d//yKrD5/DEQum1GWt/Z104Ewe27hnwHaXUsnxqZuf4Mwv/ZbrHmxvyPNPNkumBBNGwt4yokq2iIiMkkK20JLwcA66cn2r2Vv3Zfn+71/ggmMX1tzqUa5kdxdKDalil528fCbFkuOBF3b2uT2bL/LeHz3Et+95nljU+OXjWxq2hsmkJ2SHfYxfx9Zmr0JERCY4hWyhJeEB7FcN/vqd68kXHX9z1sE1n7Pcw33qQbM4dsn00S9yEMct8fuy/1DRl72zM8dbvnU/v1y3hU+87nDe8oql3PPsdjK5wTfckeosal2EYSHfkGaO2kVERGTUFLKF1gFC9uY9GX70x5e4+PhFLJ3ZUvM5p6djAFx5ZuOq2ACpeJRjF0/v6ct+cUcnb/zGfTy2cQ9f+z/H8c5XHcjqw+fSXShxz7MKTqMVj8aZ3zJ/crSLqI9fRERGQSFbeirZlRNGvnbnszjnRhySTz90Dnd88DROOnBmXdY4lJMOnMFjG/fwu2e2cdHX72NXV44fvfMVnLtiPgAnHjCDtoTHb558ueFrmQwWT1kc/naRYjd072v2SkREZAJTyBZaElGgt5LdvquLnzywgUtOWMyi6SPbPCYaMQ6cXd+RfYM5aflMSg7e+u0/0pLw+NkVp7Bq2Yye++NehFcfOpvbn9xKqaTq5GgtaQv7rGxtSCMiIqOnkC20JfzWjvIYv6/+5lnMjCvPqL0XuxmOWzKdqakYxyyays/ec8qA4f41h89le0c3j27c04QVhsuStiXs6d7Dnu6QvpcK2SIiUgdNCdlmdrGZrTOzkpmtGuK4vw2Oe9zMrjGz5Fiuc7IoV7I7uwu8sL2T6x5q5y2vWMK8qRPj7U7GotzxwdO47opTmNWaGPCY0w+dTTRi3P6EWkZGqzxhJLQXPypki4hIHTSrkv04cBFw92AHmNlC4H3AKufcUUAUePPYLG9yqbzw8d9/8wyxqHHF6cubvKrazGxNDLn1+7R0nFVLp3O7+rJHbUlbyMf4KWSLiEgdNCVkO+eedM49XcWhHpAyMw9IA5sau7LJqXzh46Ptu7lh7UYuO3kZc9omRhW7FqsPn8tTW/bRvqur2UuZ0Ba1LQLgxX0vNnklDZIOLtbtUMgWEZGRG7c92c65jcD/A14CNgN7nHO/au6qwikdj2IG1z3YTjIW5fJXH9jsJTXE6iPmAvCbJ7XRyGgkvSRz03PZsDek7SJeHJLTVMkWEZFRaVjINrPbg17q/h/nV/n46cD5wAHAAqDFzP5iiOMvN7M1ZrZm2zb9z7EWZkZL3KPk4B2vXMbMQfqaJ7oDZrVw4OwWtYzUwZIpIZ8w0jpHIVtEREalYSHbObfaOXfUAB83VnmK1cDzzrltzrk88DPglCGe72rn3Crn3KrZs2fX4yVMKi2JKG0Jj3e9KpxV7LLVh8/lD8/tYF82P+RxHd0F1m7YPTaLmoCWtC0J74WP4Pdla9dHEREZhXHbLoLfJnKSmaXNzICzgCebvKbQumTVYj75hiOZlo43eykNtfrwueSLjrv/NHiAKpUcV/zwQS742r08u1UbkgxkyZQl7MzuZF8upO9PeddHERGREWrWCL8LzawdOBm4xcxuC25fYGa3Ajjn7geuAx4CHgvWenUz1jsZfODsQ3nT8YuavYyGO27JNKalY0Pu/vjd+17gd8/4IfwHvw/pxX2jVJ4wEtpqdsts6FTvvoiIjFyzpotc75xb5JxLOOfmOuf+LLh9k3Pu3IrjPumcOyxoM3mrc667GeuV8PCiEc48dA53PL2VQrG03/1PbdnL5375FKsPn8OFxy7kugfbh20tmYwWty0GwjzGbw5kdkFRf/ciIjIy47ldRKQhzjp8Lru78jz00u4+t2fzRd7/47VMSXp87o1Hc9kpy+jMFbn+4Y3NWegw9mXz3Pl0c6qtPSE7rBc/tszy/+za0dx1iIjIhKWQLZPOqw+ZRSxq+00Z+dKvnuapLfv44puOYVZrgpWLp3HMoql8774XcM41abWD+487n+Ud//0AT27eO+bPnY6lmZOaE+JKtjakERGR0VHIlkmnLRnjpANn9gnZ9z67nf/63fO89aSlnHHYnJ7b33byMtZv6+S+9eOrolkqOW582N+b6aZHmrNH0+Ipi8Pdkw3Qob5sEREZGYVsmZRWHz6X57Z18ty2DnZ35fjgTx9h+ewWPnbu4X2Oe93R85nREuf7v3+hOQsdxB+e38GWvVnakh43rd3UlEr7krYQz8puDX7R0hg/EREZIYVsmZTOOtwPUbc/+TIfv/5xtnd085U3H0sqHu1zXDIW5ZITFvPrJ15m4+5MM5Y6oBse3khrwuOjrz2cjbszPPTSrjFfw5IpS9ie2U5XPoTb1Jd7stUuIiIiI6SQLZPSoulpDpvXxtfuXM8tj23mA2cfwlELpw547Fte4Y+r+58/jI9xftl8kV88toU/O3Ieb1i5gIQX4ca1Y98yEuqLHxNTIBpXyBYRkRFTyJZJa/Xhc9mTyXPiATP4q1cvH/S4RdPTrD58Lj9+YAPZfHEMVziw3zy5lX3dBS48diGtCY/VR8zllkc3kx9gJGEjlWdlh/LiR7NgVrZCtoiIjIxCtkxabzp+Ea86eBb/+ufHEI3YkMdedsoydnbmuOXRzWO0usHdsHYjc9oSnLx8JgDnH7OAHZ057n12bPuHl0wJQnYYK9mgXR9FRGRUFLJl0lo2q4Uf/OUrWDQ9PeyxpyyfyfLZLQ25AHJ3V44v/PIpNuwcvrd5V2eOu57eyvkrF/T8YnDaobOZElwAOZZaYi3MTM4M8YSROQrZIiIyYgrZIlUwMy47ZRmPtO9h7YbddTvvn17ex/lfu5ev37WeD177yLBTQm55bDP5ouOCYxf23Jbworz2qPnctm7LmLezLJmyJJztIhC0i2i6iIiIjIxCtkiVLjpuEa0Jr27V7F8/8TIXfu1eOruLvP2UZfzx+Z3csHbo3SVveHgjh8xt5Yj5U/rcfv7KBXTmivzmybGd67y4bXH420XG4UZEIiIy/ilki1SpNeHxxuMWcvMjm9nR0T3i8zjn+I87nuHyH6zhwNmt3HTlK/nH1x/BMYun8ZlbnmJPJj/g417a0cWaF3dxwbELMevbQ/6KA2cypy3BjcOE9Hpb0raErV1byRTGz3jDummZDYUsdO9r9kpERGQCUsgWqcFbT15Krljixw+MrA+5K1fgyh89zP/71Z94wzELuPbdJ7NgWopIxPjMBUexs7Obf/3V0wM+thygz1+5cL/7ohHj9Ucv4K6ntw0a0hth6ZSlAOHsy+7ZkEZ92SIiUjuFbJEaHDSnjVMPmsXX7nyWb/52PblC9WPz2nd18aZv/J5bH9/MR197GP92yUqSsd7Nb45aOJW/OGkpP/jDizy+cU+fxzrnuH7tRl5xwAwWTksNeP7zVy4gVyxx2+NbRvbiRmDxFH9W9oa9IQzZPRvSqC9bRERqp5AtUqMvvOloTlk+k3/5xVOc85W7+e2fhq50Pr+9k6tuWsc5//Y7Nuzq4jtvP4G/Om35fi0fAB88+1BmtMT5xA2PUyr19gI/vnEvz23r5MJj969ilx29aCrLZqa58ZGxaxkJ9YY0LbP9P1XJFhGREVDIFqnRgmkpvnXZCfz3O07AObjsO3/k8u+v6TOCzznH3X/axv/97gOc+aW7+J/7X+Q1R8zlpitP5YxD5wx67qmpGB8793DWbtjNT9f0Voevf3gj8WiE166YP+hjzYw3HLOA+9bvYOvebH1e7DCmxKcwPTE95CF7bC8mFRGRcPCavQCRieqMQ+dwyvKZfPue5/mPO55l9b/+lr86bTmz2xJ8774XeHZrB7Na47zvzIN5y0lLmNOWrOq8Fx67kB8/sIHP/fIpzj5ynj8D+5FNnHX4HKamYkM+9g0rF/DvdzzLzx/dzF+eekA9XuawFk9ZHM4xfmm1i4iIyMipki0yCgkvyntOP4jffPA0zj5yHv/+m2f4hxseJxWL8q9/fgz3fuRM/vY1h1QdsMGvSH/q/KPYly3whV8+xb3rd7C9o3vACx77O2hOG0cumMJNYzhlZGnb0nFRye7sLvCNu9bv188+Yl4cktPULiIiIiOiSrZIHcyfmuKrlx7L5a86kEKpxMrF0wbsua7WofPa+MtTD+Dqu5/j8U17mJL0OOOw2VU99vyVC/jsrU/xwvZOls1qqfo5X9rRxS2PbWbpzDTnHDmPyDBbzZctnrKYnz/3czL5DHu6jOe2dfDc9k6eDz4yuSKXv/pATj909qjek6Hc9+x2Pvy/j9K+K8OXb4/wT284kjefsHj0z9cyWyFbRERGRCFbpI5WLJpat3P9zVkHc9PaTTy+cS+XnriEhBcd/kHA64/2Q/ZNj2zifWcdPOSxXbkCv3hsC9c+uIE/PLez5/bD5rXxwbMPZfXhc4YMqjs7czy7MQHAqq/9Pblcb8U+FjWmp+PkCiUuvynPgbNaOOuIucxuTVT1OqrRXShyx1Nbefil3cxojfOWE+aw5oVd/ONdd3LtM1M556h5xKKj+Ae71iTxjudY8NKdLGhdwKK2RbTEqv/FRUREJi8bbhvniWjVqlVuzZo1zV6GyKj98vHNvOd/HuK6K07huCXTq37cn3/z96zbuIcVi6aydEYLS2amWToz3fP5s1v3ce2adm5+dDMd3QWWzkxz8fGLuODYhTz44i6+/Os/8cKOLo5ZNJUPnn0orzp4Vk/Yds5x//M7+dH9L/HLx7eQj75M64FfASs06m0YV6YmprKgxQ/ch884nPOWn8e8lnnNXpaIiDSBmT3onFs14H0K2SLj295sninJoS947G/tht18774XeHFHJy/t7GJ7R26/Y9LxKOeumM+fr1rMCcum96lYF4olfvbQRr7ym2fYuDvDictm8N4zD+KZl/dxzR9fYv22TtqSHm88bhGXnriEA2cnyZeG3gRnd1eer935DD9+oJ10PMK7T1vOpScuZeveLC/s7OTF7V28uLOTF3Z08eKOToolx6JpaRZOT7F4eppFM1Isnp5iVmuC//rdc1z34EYOmJXmMxeuYOXiafs93++e2caH//dRSkXHZy5awerD5wKwozPHrY9u5oa1G3ly8z68iLF0Zpr12zqJRyOsPmIuF69ayInLZmC/+hiZx/+Xzce/lY2FDjYW9rGp0EF7voP2/D5eLOzFgGOj83h1ZAlHFudSKkI2XyQZizKrNc6s1gTT0nEG6r7JFx1b92XZvDvL5r1Ztu/rZlo6zqLpSRZOTzO3LUG0yradEZmyEJaeAtOWNO45RERCTCFbZJLr6C7w0o4uXtrZyYs7upjZmuC1R82jJTF0x1h3ochPH9jAV+94lq37/K3kj1syjUtPXMLrj15AKl5dC0ulZ7fu4zO3PMmdT+/f69yW8DhgdgvLZrbgRY32nRle2tnFln4jCSMG73r1gfzt6kP6bOjTX/uuLt7zPw/xaPse/s8rlrB1b5a7nt5GoeRYsXAqbzxuIW9YuZAZLXGe3uL/AvGzh9rZmy2wbGaaTy5+iDOe+udBz7/Bi3Jjays3tLXwsucxrVjk9R2dXLivk0PyY7fz5qhNWwJLT4Vlr4Slr4Tpy6Bfm1Cp5MgVS+SLJbL5Etl8ka5ckUy+SCZXJJMvkCuUaEl4TE3Fej7akrHG/qIgItJECtkiMirZfJHb1m3hkLltHD5/Sl3O+btntvHA8ztZPCPNAbNaWDarhZkt8QF7wLP5Iht3+4G7fVeGYxdP46iF1fW/dxeKfOrmJ/jhH15i7pQEFxy7kDcet4hD5rYNeHw2X+QXj2/mmvs38McXdhKjgOH/nJyejrNsVpplM/31LpiaZGoqRmsywnNdj3D3ltu4d8vdFEoFEtEEOKPkHCXncA7/T8CAiBkRMywCUTMqX7UDiiUXPNZ/XCNEcEQoEcERpdTzOh2Go+/fQ+UKYs7/iJf/LJVvs0FHVo32GlSr+Mz63lCz8tvpel6x0bt3q3/iyvUO9lSV70m9f42wKs/oaNz/ww3jlZkkp2aGmY5U7xff8/cz8GvreW8m+e9uh89vIxbRkLgex1wKR1885k+rkC0ik97Le7PMaq2t/eLZrftYt2kvS2e2cMDMFqamh2/b2ZXdxa3P38qWzoG3t88VinjRCJEaUme+WGJnZ45C0VEolSiWHIWS6/mz5BwRDDM/vFf+CX6oLDpHqV9wd/0+T+b30Nb9Mm35bXilHGa9gdbwx0s6oGiOvEHOHHlzdOP/mTP/lwmH37vf5/OqXy37/cJR/sT1uX2wMw79vvbGav8s1u/2Sq7PJ44Bz13xHg/y6KrWNfBjRqLi15EhnnL49fpWd3qs7hriX7zcgJ+OSlW/RLnBn6+aX4rCYPnsVjz9K1Gv498Ox711zJ9WIVtEREREpM6GCtn6dwYRERERkTpTyBYRERERqTOFbBERERGROlPIFhERERGpM4VsEREREZE6U8gWEREREakzhWwRERERkTpTyBYRERERqTOFbBERERGROlPIFhERERGpM4VsEREREZE6U8gWEREREakzhWwRERERkTpTyBYRERERqTOFbBERERGROlPIFhERERGpM4VsEREREZE6U8gWEREREakzc841ew11Z2bbgBcbdPpZwPYGnVvCQd8jMhx9j8hw9D0iQ9H3x/ix1Dk3e6A7QhmyG8nM1jjnVjV7HTJ+6XtEhqPvERmOvkdkKPr+mBjULiIiIiIiUmcK2SIiIiIidaaQXburm70AGff0PSLD0feIDEffIzIUfX9MAOrJFhERERGpM1WyRURERETqTCG7BmZ2jpk9bWbPmtlHmr0eaS4zW2xmd5rZE2a2zsz+Jrh9hpn92syeCf6c3uy1SnOZWdTMHjazm4OvDzCz+4OfJT8xs3iz1yjNY2bTzOw6M3vKzJ40s5P1c0QqmdnfBv+fedzMrjGzpH6OjH8K2VUysyjwNeC1wBHApWZ2RHNXJU1WAD7onDsCOAl4b/A98RHgN865g4HfBF/L5PY3wJMVX38e+LJz7iBgF/CXTVmVjBdfAX7pnDsMOAb/e0U/RwQAM1sIvA9Y5Zw7CogCb0Y/R8Y9hezqnQg865x7zjmXA34MnN/kNUkTOec2O+ceCj7fh/8/xoX43xffCw77HnBBUxYo44KZLQJeB3wr+NqAM4HrgkP0PTKJmdlU4NXAtwGccznn3G70c0T68oCUmXlAGtiMfo6MewrZ1VsIbKj4uj24TQQzWwYcC9wPzHXObQ7u2gLMbda6ZFz4N+DDQCn4eiaw2zlXCL7Wz5LJ7QBgG/DfQUvRt8ysBf0ckYBzbiPw/4CX8MP1HuBB9HNk3FPIFhklM2sF/hd4v3Nub+V9zh/foxE+k5SZvR7Y6px7sNlrkXHLA44DvuGcOxbopF9riH6OTG5BP/75+L+QLQBagHOauiipikJ29TYCiyu+XhTcJpOYmcXwA/b/OOd+Ftz8spnND+6fD2xt1vqk6V4JvMHMXsBvMTsTv/92WvDPvqCfJZNdO9DunLs/+Po6/NCtnyNSthp43jm3zTmXB36G/7NFP0fGOYXs6j0AHBxczRvHv+jgpiavSZoo6K39NvCkc+5fK+66Cbgs+Pwy4MaxXpuMD865jzrnFjnnluH/zLjDOfcW4E7gTcFh+h6ZxJxzW4ANZnZocNNZwBPo54j0egk4yczSwf93yt8j+jkyzmkzmhqY2bn4/ZVR4DvOuc80d0XSTGZ2KvA74DF6+20/ht+X/VNgCfAi8OfOuZ1NWaSMG2Z2OvB3zrnXm9mB+JXtGcDDwF8457qbuDxpIjNbiX9hbBx4DngHfhFMP0cEADP7J+AS/KlWDwPvxO/B1s+RcUwhW0RERESkztQuIiIiIiJSZwrZIiIiIiJ1ppAtIiIiIlJnCtkiIiIiInWmkC0iIiIiUmcK2SIi45yZFc1sbcXHR4Z/1IDnucvMVtV7fVU87wVmdsRYP6+ISDN5wx8iIiJNlnHOrWz2IkbhAuBm/A00REQmBVWyRUQmIDM7x8yurfj6dDO7Ofj8G2a2xszWBZtYDHeuE8zsPjN7xMz+aGZtZpY0s/82s8fM7GEzOyM49u1m9h8Vj7052GgHM+sws88E5/mDmc01s1OANwBfDKrwy+v7ToiIjE8K2SIi41+qX7vIJcDtwCvMrCU45hL83d8APu6cWwUcDZxmZkcPdmIziwM/Af7GOXcMsBrIAO8FnHNuBXAp8D0zSw6zzhbgD8F57gbe5Zy7D3+L8A8551Y659aP4PWLiEw4CtkiIuNfJgio5Y+fOOcKwC+B88zMA14H3Bgc/+dm9hD+VstHAkP1Qx8KbHbOPQDgnNsbnPtU4IfBbU/hb+19yDDrzOG3hQA8CCyr8XWKiISGerJFRCauHwNXAjuBNc65fWZ2APB3wAnOuV1m9l1guAp0LQr0LdBUnjvvnHPB50X0/xgRmcRUyRYRmbh+CxwHvIveVpEpQCewx8zmAq8d5hxPA/PN7ASAoB/bA34HvCW47RBgSXDsC8BKM4uY2WLgxCrWuQ9oq+F1iYhMeArZIiLjX/+e7M8BOOeK+O0Zrw3+xDn3CH6byFPAj4B7hzqxcy6H38/9VTN7BPg1fnX660DEzB7D79l+u3OuOzjf8/iTQv4deKiK9f8Y+FBwAaUufBSRScF6/2VPRERERETqQZVsEREREZE6U8gWEREREakzhWwRERERkTpTyBYRERERqTOFbBERERGROlPIFhERERGpM4VsEREREZE6U8gWEREREamz/w+LKWUFpwilFAAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import pylab\n",
"\n",
"pylab.rcParams[\"figure.figsize\"] = (12, 8)\n",
"for i, optimizer in enumerate(optimizers):\n",
" pylab.plot(converge_counts[i], converge_vals[i], label=type(optimizer).__name__)\n",
"pylab.xlabel(\"Eval count\")\n",
"pylab.ylabel(\"Energy\")\n",
"pylab.title(\"Energy convergence for various optimizers\")\n",
"pylab.legend(loc=\"upper right\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, since the above problem is still easily tractable classically, you can use [NumPyMinimumEigensolver](https://qiskit.org/documentation/stubs/qiskit.algorithms.minimum_eigensolvers.NumPyMinimumEigensolver.html#numpyminimumeigensolver) to compute a reference value for the solution."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reference value: -1.85728\n"
]
}
],
"source": [
"from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n",
"from qiskit.opflow import PauliSumOp\n",
"\n",
"numpy_solver = NumPyMinimumEigensolver()\n",
"result = numpy_solver.compute_minimum_eigenvalue(operator=PauliSumOp(H2_op))\n",
"ref_value = result.eigenvalue.real\n",
"print(f\"Reference value: {ref_value:.5f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"You can now plot the difference between the `VQE` solution and this exact reference value as the algorithm converges towards the minimum energy."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pylab.rcParams[\"figure.figsize\"] = (12, 8)\n",
"for i, optimizer in enumerate(optimizers):\n",
" pylab.plot(\n",
" converge_counts[i],\n",
" abs(ref_value - converge_vals[i]),\n",
" label=type(optimizer).__name__,\n",
" )\n",
"pylab.xlabel(\"Eval count\")\n",
"pylab.ylabel(\"Energy difference from solution reference value\")\n",
"pylab.title(\"Energy convergence for various optimizers\")\n",
"pylab.yscale(\"log\")\n",
"pylab.legend(loc=\"upper right\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradients\n",
"\n",
"In Qiskit's variational algorithms, if the provided optimizer uses a gradient-based technique, the default gradient method will be finite differences. However, these classes include an option to pass custom gradients via the `gradient` parameter, which can be any of the provided methods within Qiskit's [gradient](https://qiskit.org/documentation/stubs/qiskit.algorithms.gradients.html) framework, which fully supports the use of primitives. This section shows how to use custom gradients in the VQE workflow.\n",
"\n",
"The first step is to initialize both the corresponding primitive and primitive gradient:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"from qiskit.algorithms.gradients import FiniteDiffEstimatorGradient\n",
"\n",
"estimator = Estimator()\n",
"gradient = FiniteDiffEstimatorGradient(estimator, epsilon=0.01)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, you can inspect an SLSQP run using the [FiniteDiffEstimatorGradient](https://qiskit.org/documentation/stubs/qiskit.algorithms.gradients.FiniteDiffEstimatorGradient.html) from above:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value using Gradient: -1.85728\n"
]
}
],
"source": [
"algorithm_globals.random_seed = 50\n",
"ansatz = TwoLocal(rotation_blocks=\"ry\", entanglement_blocks=\"cz\")\n",
"\n",
"optimizer = SLSQP(maxiter=100)\n",
"\n",
"counts = []\n",
"values = []\n",
"\n",
"\n",
"def store_intermediate_result(eval_count, parameters, mean, std):\n",
" counts.append(eval_count)\n",
" values.append(mean)\n",
"\n",
"\n",
"vqe = VQE(\n",
" estimator, ansatz, optimizer, callback=store_intermediate_result, gradient=gradient\n",
")\n",
"\n",
"result = vqe.compute_minimum_eigenvalue(operator=H2_op)\n",
"print(f\"Value using Gradient: {result.eigenvalue.real:.5f}\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pylab.rcParams[\"figure.figsize\"] = (12, 8)\n",
"pylab.plot(counts, values, label=type(optimizer).__name__)\n",
"pylab.xlabel(\"Eval count\")\n",
"pylab.ylabel(\"Energy\")\n",
"pylab.title(\"Energy convergence using Gradient\")\n",
"pylab.legend(loc=\"upper right\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initial point\n",
"\n",
"By default, the optimization begins at a random point within the bounds defined by the ansatz. The `initial_point` option allows to override this point with a custom list of values that match the number of ansatz parameters.\n",
"\n",
"You might wonder... *Why set a custom initial point?* Well, this option can come in handy if you have a guess for a reasonable starting point for the problem, or perhaps know information from a prior experiment.\n",
"\n",
"To demonstrate this feature, let's look at the results from our previous VQE run:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{ 'aux_operators_evaluated': None,\n",
" 'cost_function_evals': 9,\n",
" 'eigenvalue': -1.8572750175655812,\n",
" 'optimal_circuit': <qiskit.circuit.library.n_local.two_local.TwoLocal object at 0x13ef7dd20>,\n",
" 'optimal_parameters': { ParameterVectorElement(θ[0]): 4.296519450348719,\n",
" ParameterVectorElement(θ[3]): 6.092947832767056,\n",
" ParameterVectorElement(θ[1]): 4.426962358395531,\n",
" ParameterVectorElement(θ[7]): 0.36021017470898664,\n",
" ParameterVectorElement(θ[4]): -2.598326651673288,\n",
" ParameterVectorElement(θ[5]): 1.5683250498282322,\n",
" ParameterVectorElement(θ[2]): 0.5470777607659094,\n",
" ParameterVectorElement(θ[6]): -4.717616147449751},\n",
" 'optimal_point': array([ 4.29651945, 4.42696236, 0.54707776, 6.09294783, -2.59832665,\n",
" 1.56832505, -4.71761615, 0.36021017]),\n",
" 'optimal_value': -1.8572750175655812,\n",
" 'optimizer_evals': None,\n",
" 'optimizer_result': <qiskit.algorithms.optimizers.optimizer.OptimizerResult object at 0x13010b6a0>,\n",
" 'optimizer_time': 0.3502693176269531}\n"
]
}
],
"source": [
"print(result)\n",
"cost_function_evals = result.cost_function_evals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, you can take the `optimal_point` from the above result and use it as the `initial_point` for a follow-up computation.\n",
"\n",
"**Note:** `initial_point` is now a keyword-only argument of the `VQE` class (i.e, it must be set following the `keyword=value` syntax)."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{ 'aux_operators_evaluated': None,\n",
" 'cost_function_evals': 1,\n",
" 'eigenvalue': -1.8572750175655812,\n",
" 'optimal_circuit': <qiskit.circuit.library.n_local.two_local.TwoLocal object at 0x1411b9780>,\n",
" 'optimal_parameters': { ParameterVectorElement(θ[0]): 4.296519450348719,\n",
" ParameterVectorElement(θ[1]): 4.426962358395531,\n",
" ParameterVectorElement(θ[4]): -2.598326651673288,\n",
" ParameterVectorElement(θ[5]): 1.5683250498282322,\n",
" ParameterVectorElement(θ[3]): 6.092947832767056,\n",
" ParameterVectorElement(θ[2]): 0.5470777607659094,\n",
" ParameterVectorElement(θ[6]): -4.717616147449751,\n",
" ParameterVectorElement(θ[7]): 0.36021017470898664},\n",
" 'optimal_point': array([ 4.29651945, 4.42696236, 0.54707776, 6.09294783, -2.59832665,\n",
" 1.56832505, -4.71761615, 0.36021017]),\n",
" 'optimal_value': -1.8572750175655812,\n",
" 'optimizer_evals': None,\n",
" 'optimizer_result': <qiskit.algorithms.optimizers.optimizer.OptimizerResult object at 0x1411e3f10>,\n",
" 'optimizer_time': 0.05097508430480957}\n",
"\n"
]
}
],
"source": [
"initial_pt = result.optimal_point\n",
"\n",
"estimator1 = Estimator()\n",
"gradient1 = FiniteDiffEstimatorGradient(estimator, epsilon=0.01)\n",
"ansatz1 = TwoLocal(rotation_blocks=\"ry\", entanglement_blocks=\"cz\")\n",
"optimizer1 = SLSQP(maxiter=1000)\n",
"\n",
"vqe1 = VQE(\n",
" estimator1, ansatz1, optimizer1, gradient=gradient1, initial_point=initial_pt\n",
")\n",
"result1 = vqe1.compute_minimum_eigenvalue(operator=H2_op)\n",
"print(result1)\n",
"\n",
"cost_function_evals1 = result1.cost_function_evals\n",
"print()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cost_function_evals is 1 with initial point versus 9 without it.\n"
]
}
],
"source": [
"print(\n",
" f\"cost_function_evals is {cost_function_evals1} with initial point versus {cost_function_evals} without it.\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"By looking at the `cost_function_evals` you can notice how the initial point helped the algorithm converge faste
gitextract_bmptrtaj/
├── .github/
│ ├── CODE_OF_CONDUCT.md
│ ├── CONTRIBUTING.md
│ ├── ISSUE_TEMPLATE/
│ │ ├── bug-report.yml
│ │ ├── documentation.yml
│ │ └── feature-request.yml
│ └── PULL_REQUEST_TEMPLATE.md
├── .gitignore
├── .mergify.yml
├── CODE_OF_CONDUCT.md
├── CONTRIBUTING.md
├── INSTALL.md
├── LICENSE
├── README.md
├── azure-pipelines.yml
├── conf.py
├── constraints.txt
├── index.rst
├── requirements-dev.txt
├── start_here.ipynb
├── tox.ini
└── tutorials/
├── algorithms/
│ ├── 01_algorithms_introduction.ipynb
│ ├── 02_vqe_advanced_options.ipynb
│ ├── 03_vqe_simulation_with_noise.ipynb
│ ├── 04_vqd.ipynb
│ ├── 05_qaoa.ipynb
│ ├── 06_grover.ipynb
│ ├── 07_grover_examples.ipynb
│ ├── 09_IQPE.ipynb
│ ├── 10_pvqd.ipynb
│ ├── 11_VarQTE.ipynb
│ └── 12_gradients_framework.ipynb
├── circuits/
│ ├── 01_circuit_basics.ipynb
│ ├── 1_getting_started_with_qiskit.ipynb
│ ├── 2_plotting_data_in_qiskit.ipynb
│ └── 3_summary_of_quantum_operations.ipynb
├── circuits_advanced/
│ ├── 01_advanced_circuits.ipynb
│ ├── 02_operators_overview.ipynb
│ ├── 03_advanced_circuit_visualization.ipynb
│ ├── 04_transpiler_passes_and_passmanager.ipynb
│ ├── 05_pulse_gates.ipynb
│ ├── 06_building_pulse_schedules.ipynb
│ ├── 07_pulse_scheduler.ipynb
│ └── 08_gathering_system_information.ipynb
└── operators/
├── 01_operator_flow.ipynb
└── 02_gradients_framework.ipynb
Condensed preview — 45 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (7,124K chars).
[
{
"path": ".github/CODE_OF_CONDUCT.md",
"chars": 3214,
"preview": "# Contributor Covenant Code of Conduct\n\n## Our Pledge\n\nIn the interest of fostering an open and welcoming environment, w"
},
{
"path": ".github/CONTRIBUTING.md",
"chars": 1468,
"preview": "# Contributing\n\nIf you would like to contribute to the Qiskit IQX tutorials, there are a number of ways to \nget involved"
},
{
"path": ".github/ISSUE_TEMPLATE/bug-report.yml",
"chars": 1838,
"preview": "name: 🐛Bug Report\ndescription: Create a report to help us improve 🤔.\nlabels: [\"bug\"]\nbody:\n - type: markdown\n attrib"
},
{
"path": ".github/ISSUE_TEMPLATE/documentation.yml",
"chars": 712,
"preview": "name: 📚 Documentation\ndescription: Create a report to help us improve our documentation 📖.\nlabels: [\"documentation\"]\nbod"
},
{
"path": ".github/ISSUE_TEMPLATE/feature-request.yml",
"chars": 901,
"preview": "name: 🚀Feature request\ndescription: Suggest an idea for this project🌟.\nlabels: [\"enhancement\"]\nbody:\n - type: markdown\n"
},
{
"path": ".github/PULL_REQUEST_TEMPLATE.md",
"chars": 413,
"preview": "<!--\n⚠️ If you do not respect this template, your pull request will be closed.\n⚠️ Your pull request title should be shor"
},
{
"path": ".gitignore",
"chars": 247,
"preview": "\n__pycache__/\n.cache/\n\n# ignores any checkpoints folder anywhere\n.ipynb_checkpoints/\n\n# editor files\n.vscode/\n.idea/\n\n# "
},
{
"path": ".mergify.yml",
"chars": 403,
"preview": "queue_rules:\n - name: automerge\n conditions:\n - check-success=Qiskit.qiskit-tutorials\n\npull_request_rules:\n - "
},
{
"path": "CODE_OF_CONDUCT.md",
"chars": 398,
"preview": "<!-- Copyright Contributors to the Qiskit project. -->\n\n# Code of Conduct\nAll members of this project agree to adhere to"
},
{
"path": "CONTRIBUTING.md",
"chars": 582,
"preview": "<img src=\"images/gallery_shot.png\" >\n\n# Contributing\n\n## What makes a good tutorial?\n\n\n## Adding a tutorial\n\n\n## Setting"
},
{
"path": "INSTALL.md",
"chars": 4284,
"preview": "# Qiskit Tutorials\n\n## Installation and setup\n\n### Get the tutorials\n\nFor the full experience, you can start by download"
},
{
"path": "LICENSE",
"chars": 11357,
"preview": " Apache License\n Version 2.0, January 2004\n "
},
{
"path": "README.md",
"chars": 4891,
"preview": "# Qiskit Tutorials\n\n[]("
},
{
"path": "azure-pipelines.yml",
"chars": 1228,
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},
{
"path": "conf.py",
"chars": 3034,
"preview": "# This code is part of Qiskit.\n#\n# (C) Copyright IBM 2018, 2023.\n#\n# This code is licensed under the Apache License, Ver"
},
{
"path": "constraints.txt",
"chars": 35,
"preview": "docplex==2.15.194\ndecorator==4.4.2\n"
},
{
"path": "index.rst",
"chars": 470,
"preview": "================\nQiskit Tutorials\n================\n\nQuantum circuits\n================\n\n.. nbgallery::\n :glob:\n\n tuto"
},
{
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"chars": 137,
"preview": "qiskit>=0.38.0\njupyter\nsphinx\nnbsphinx\nqiskit_sphinx_theme\nnetworkx\nscikit-learn\nmatplotlib\nqiskit[visualization]\nqiskit"
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About this extraction
This page contains the full source code of the QISKit/qiskit-tutorial GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 45 files (6.6 MB), approximately 1.7M tokens. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.