From e97d7440fe9cf18cae43f20da0ed9731b2ee9212 Mon Sep 17 00:00:00 2001 From: "Daniel J. Egger" <38065505+eggerdj@users.noreply.github.com> Date: Tue, 27 Feb 2024 13:57:45 +0100 Subject: [PATCH] Qiskit Patterns (#16) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Elena Peña Tapia Co-authored-by: a-matsuo Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com> --- demos/qiskit_patterns/0_setup_instructions.md | 18 + .../qiskit_patterns/1_test_installation.ipynb | 121 ++ demos/qiskit_patterns/2_qiskit_patterns.ipynb | 1346 +++++++++++++++++ .../data/125node_eagle_depth_one.qpy | Bin 0 -> 198906 bytes .../data/125node_eagle_depth_zero.qpy | Bin 0 -> 32509 bytes demos/qiskit_patterns/data/125node_example.lp | 181 +++ .../qiskit_patterns/data/125node_example.png | Bin 0 -> 380852 bytes .../data/125node_example_ising.txt | 142 ++ .../data/125node_heron_depth_one.qpy | Bin 0 -> 210154 bytes .../data/125node_heron_depth_zero.qpy | Bin 0 -> 32719 bytes demos/qiskit_patterns/demo_src/graph.py | 21 + demos/qiskit_patterns/demo_src/map.py | 16 + demos/qiskit_patterns/demo_src/post.py | 149 ++ demos/qiskit_patterns/demo_src/run.py | 13 + demos/qiskit_patterns/demo_src/transpile.py | 4 + demos/qiskit_patterns/imgs/circuit.png | Bin 0 -> 693003 bytes demos/qiskit_patterns/imgs/eagle-heron.png | Bin 0 -> 74763 bytes demos/qiskit_patterns/imgs/exec-modes.png | Bin 0 -> 379485 bytes demos/qiskit_patterns/imgs/max-cut.png | Bin 0 -> 623222 bytes demos/qiskit_patterns/imgs/patterns.png | Bin 0 -> 198570 bytes demos/qiskit_patterns/requirements.txt | 8 + .../sampler_data/eagle_87ea531a.json | 1 + .../sampler_data/heron_215ebe55.json | 1 + 23 files changed, 2021 insertions(+) create mode 100644 demos/qiskit_patterns/0_setup_instructions.md create mode 100644 demos/qiskit_patterns/1_test_installation.ipynb create mode 100644 demos/qiskit_patterns/2_qiskit_patterns.ipynb create mode 100644 demos/qiskit_patterns/data/125node_eagle_depth_one.qpy create mode 100644 demos/qiskit_patterns/data/125node_eagle_depth_zero.qpy create mode 100644 demos/qiskit_patterns/data/125node_example.lp create mode 100644 demos/qiskit_patterns/data/125node_example.png create mode 100644 demos/qiskit_patterns/data/125node_example_ising.txt create mode 100644 demos/qiskit_patterns/data/125node_heron_depth_one.qpy create mode 100644 demos/qiskit_patterns/data/125node_heron_depth_zero.qpy create mode 100644 demos/qiskit_patterns/demo_src/graph.py create mode 100644 demos/qiskit_patterns/demo_src/map.py create mode 100644 demos/qiskit_patterns/demo_src/post.py create mode 100644 demos/qiskit_patterns/demo_src/run.py create mode 100644 demos/qiskit_patterns/demo_src/transpile.py create mode 100644 demos/qiskit_patterns/imgs/circuit.png create mode 100644 demos/qiskit_patterns/imgs/eagle-heron.png create mode 100644 demos/qiskit_patterns/imgs/exec-modes.png create mode 100644 demos/qiskit_patterns/imgs/max-cut.png create mode 100644 demos/qiskit_patterns/imgs/patterns.png create mode 100644 demos/qiskit_patterns/requirements.txt create mode 100644 demos/qiskit_patterns/sampler_data/eagle_87ea531a.json create mode 100644 demos/qiskit_patterns/sampler_data/heron_215ebe55.json diff --git a/demos/qiskit_patterns/0_setup_instructions.md b/demos/qiskit_patterns/0_setup_instructions.md new file mode 100644 index 0000000..ab9fefb --- /dev/null +++ b/demos/qiskit_patterns/0_setup_instructions.md @@ -0,0 +1,18 @@ +# Qiskit Patterns Lab Prep Work + +## Requirements + +- Laptop (Windows, MacOS or Linux), access to a terminal + +## Instructions + +1. Follow the instructions on https://docs.quantum.ibm.com/start/install#install-and-set-up-qiskit-with-the-qiskit-runtime-client +to install and set up a Python environment with Qiskit. Activate your environment. +2. Follow the instructions on https://docs.quantum.ibm.com/start/setup-channel#iqp to set up your access credentials to use +IBM Quantum systems. Only focus on the IBM Quantum Platform instructions, no need to worry about the IBM Cloud setup. +3. Clone this repository running `git clone https://github.com/qiskit-community/qopt-best-practices.git` +4. Navigate to the `demos/qiskit_patterns` directory using the terminal +5. Run `pip install -r requirements.txt` +6. Activate your jupyter environment running `jupyter notebook` in your environment, this should open a browser window +that shows the contents of the `qiskit_patterns` directory +7. Open `1_test_installation.ipynb` and follow the instructions to test that the installation was successful diff --git a/demos/qiskit_patterns/1_test_installation.ipynb b/demos/qiskit_patterns/1_test_installation.ipynb new file mode 100644 index 0000000..9bdee2a --- /dev/null +++ b/demos/qiskit_patterns/1_test_installation.ipynb @@ -0,0 +1,121 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "# Installation Test\n", + "\n", + "Run the cell below (press `Shift` + `Enter`) to check that all the imports work correctly. If you see the 🎉 emoji as the cell output, your installation was successful." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot\n", + "import networkx as nx\n", + "from qiskit_ibm_runtime.fake_provider import FakeVigoV2\n", + "from qiskit import qpy\n", + "from qiskit_aer import Aer\n", + "from qiskit_optimization.applications import Maxcut\n", + "print(\"Your installation works 🎉!\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you have followed the installation instructions (i.e. you have run `pip install -r requirements.txt`) and you get a `module not found` error, your jupyter environment might not be using the right Python kernel. You can try following the following instructions to register your kernel: https://saturncloud.io/blog/how-to-add-a-python-3-kernel-to-jupyter-ipython/." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "source": [ + "If you have not done so yet, you can use the cell below to check that your IBM Quantum Platform account registration has been successful. The backend retrieval step may take a couple of seconds." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "service = QiskitRuntimeService()\n", + "print(\"Your available backends are: \", service.backends())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "pycharm": { + "name": "#%% md\n" + } + }, + "source": [ + "If your service authentication fails (you get an `IBMNotAuthorizedError`), you can try saving your account again. Make sure to replace `\"\"` with your token in string format (example: `service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"1234abcd\")`)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "# Save an IBM Quantum account and set it as your default account.\n", + "QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"\", overwrite=True, set_as_default=True)\n", + "\n", + "# Load saved credentials\n", + "service = QiskitRuntimeService()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "ibm_tech_clean", + "language": "python", + "name": "ibm_tech_clean" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.0" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} \ No newline at end of file diff --git a/demos/qiskit_patterns/2_qiskit_patterns.ipynb b/demos/qiskit_patterns/2_qiskit_patterns.ipynb new file mode 100644 index 0000000..827f316 --- /dev/null +++ b/demos/qiskit_patterns/2_qiskit_patterns.ipynb @@ -0,0 +1,1346 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bc51e7bf-e582-49ba-93f8-035624d56ccf", + "metadata": {}, + "source": [ + "# Scaling Quantum Optimization with Qiskit Patterns\n", + "\n", + "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. Qiskit Patterns define a four-step process for running algorithms on a quantum computer:\n", + "\n", + "\n", + "\"Drawing\"\n", + "\n", + "\n", + " 1. Map classical problem to abstract quantum circuits and operators\n", + " 2. Optimize problem for quantum execution\n", + " 3. Execute on a quantum computer\n", + " 4. Post-process, return result in classical format" + ] + }, + { + "cell_type": "markdown", + "id": "8d3218ca-ce9e-40b4-a041-1b1d09bac8f5", + "metadata": {}, + "source": [ + "We will apply the patterns to the context of **combinatorial optimization** and show how to solve the **Max-Cut** problem using the **Quantum Approximate Optimization Algorithm (QAOA)**, a hybrid (quantum-classical) iterative method. " + ] + }, + { + "cell_type": "markdown", + "id": "1e943b1a-218a-468c-bb63-4269896ebebe", + "metadata": {}, + "source": [ + "# Part 1: (Small-scale) Qiskit Pattern for Optimization" + ] + }, + { + "cell_type": "markdown", + "id": "68fd0b4f-baa4-45dc-9f4c-d9cdff01a651", + "metadata": {}, + "source": [ + "The first part of the session will use a small-scale Max-Cut problem to ilustrate the steps required to solve an optimization problem using a quantum computer." + ] + }, + { + "cell_type": "markdown", + "id": "74b92ba5-c48a-405c-9c4b-04e985a7afbc", + "metadata": {}, + "source": [ + "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into to sets such that the number of edges traversed by this cut is maximum.\n", + "\n", + "\"Max-Cut\"/" + ] + }, + { + "cell_type": "markdown", + "id": "e2105a90-027f-44d7-97d1-c2c99373d488", + "metadata": {}, + "source": [ + "The workflow starts with a problem defined as a weighted graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "fb223414-87fc-4d6a-933c-db2ea3f37b4a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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t+PugmtwZvz3qCoHJZEJaWprbn+puu+023HbbbeW+161bN3z55Zc4ePCgW4FAqVQiNzcXer3eY5ezVNSf3d175lX1Z5fJZBUO3PHx8S4P6n5+fg06UBGRazQaDXr06IFu3brh8uXLSE9Px9WrV5GdnQ2LxeJsoiWRSKBSqRAWFobNmzfj3nvvxcCBA/l7pB55VCDIzc2F1WqtlckiUqkUgYGB5ZZmuUIul8NgMCAnJ6dOAkFV/dldHdRd6c9+48AdGxvr8id1X+/PTkS1TyaToUWLFmjRogWAv+cPWa1WZ5t5xxLzFStW4OzZsxg0aJDIVfsWjwsE7myjeSOz2Qyr1QqTyYTz58/j4sWLbq9TddyHzc3Ndb5xHW612Yor98wNBkO1+rO3bNnSpcvv7M9ORN5AJpNV+qFLp9Nh//79mDFjRj1X5ds8KhAUFhYCqP6SqW3btuHYsWPOY7Ru3bpcwnTsfmi322/6543f27hxI5YuXXrToF7ZYO5YunjjJ+7IyEi0aNHCpfvmbOlKRHQtEPz444/Iz893rjaguudRgeD6tdfV0b17d7Rp0waXLl1CcnIyCgsLcfHiRfj5+Tm3yayMVCqFTCaDVCp1Tl5x9Gd35b65SqXiLG8iolrQs2dPAMCBAwdw3333iVyN7/CoQODCgocqabVaKBQK6PV6tGrVCj///DN27dqFMWPGOPsMXD/wO/5540BeXFyMNm3a4IEHHqhRPURE5L6wsDC0atUK+/fvZyCoRx71kbY2GsCo1Wr4+fkhICAAXbt2RUFBASQSCUJCQhAUFOT8NO/Yf7uyT/Xesn6diKghcswjqOkHRXKdRwWC4OBgADW7UiCXyxEcHIz8/HznLYiq2tJWRCKROGshIqL6p9PpkJeXh4sXL4pdis/wqEAQHh4OqVRa6cS9yhgMhnL/HhoaCpPJhKNHj0Iul0Or1bp8LMe5w8PD3aqBiIhqT+fOneHn54f9+/eLXYrP8Kg5BFqtFnK5HBaLxa2lhz/99BPMZjPi4uIQGBgIg8GAgwcPoqioCPfdd59bHa6sVqvbIYKIiGqXn58funXrhgMHDmDSpElil+MTPOoKgb+/P6KiomCxWNx6nqPXwNGjR7F161YcPHgQYWFhuOuuu9ChQwe3jmU2m53zDYiISDw6nQ5Hjhypcmtxqj0edYUAADp06ICUlBTYbDaXrxK0bdu2wgZEycnJyM/PR0BAgEvHcSxN7NixI5cQEhGJTKfTYd68efjzzz/Ro0cPsctp8Dxu1LvtttvK7XJVE6GhodDr9S5fcTAajVCpVGjdunWNz01ERDXTvHlzaLVaziOoJx4XCBQKBbp06QK73V7jRkXBwcGQy+XIz8+/5WNtNhusVivat2/v8hUFIiKqOxKJBD179mQgqCceFwgAoGvXroiJialyRz5XOPoPFBYWVrlyQRAE53abOp2u2ucjIqLapdPpkJSUhLy8PLFLafA8MhDI5XL0798fSqUSpaWlNTpWSEgIBEFAQUFBpY8xGo2Qy+Xo169frey0SEREteP6NsZUtzwyEABAZGQk+vTpAwAoKyur9nFkMpmzUVFFVxuMRiNsNht69uyJ+Pj4ap+HiIhqX2hoqLONMdUtjw0EANCpUyfcddddsNvtMBgM1b59EBYWBqvViuLiYuf3HFsZW61WdOvWjbcKiIg8FNsY1w+PDgQSiQTdu3fHvffeC7lcDr1eD5vN5vZx/Pz8oNFonJMLbTYbSkpKAAC9evVCnz59uO0wEZGH0ul0yM/Px4ULF8QupUHz6EAAXAsFXbp0wZgxYxAdHQ2DwYDS0lK32xuHhobCaDSisLAQBoMBWq0Wo0aNwp133smeA0REHqxz585QKpW8bVDHvGYkjI6Oxrhx43DXXXdBqVTCYDBAr9fDbDZXGQ7sdjvMZjMEQYBarUZJSQl69OiBCRMmcM4AEZEXcLQxZiCoW14TCIBrPQruvPNOPPbYYxg0aBCio6Od8wv0ej2Ki4vLfen1ehgMBthsNmi1Wtx222347bff0LRpU64mICLyIjqdDseOHXN791pynURwYZZGcXExgoODUVRU5FE9/gVBgF6vR05ODnJzc1FQUODsSqhQKBAcHIzw8HBotVoEBQXBarVi2LBhuPfee/Gvf/1L5OqJiMhVycnJGDt2LD799FNOAneDO+O3x+1l4A6JRIKgoCAEBQWhRYsWt3y8n58fxo0bh6VLl2L69Olo1KhR3RdJREQ11qxZM4SHh+PAgQMMBHXEq24Z1IbRo0cDANatWydyJURE5CqJROJcfkh1w+cCQaNGjTBs2DCsXr2aW2oSEXkRnU6H8+fPIzc3V+xSGiSfCwQAMHHiROTn5+Pnn38WuxQiInKRYwvkgwcPilxJw+STgaBp06a4++678c0337DzFRGRlwgJCUHr1q1526CO+GQgAICEhARcuHCBSZOIyIs45hG425yObs1nA0G3bt3QqlUrfPPNN2KXQkRELmIb47rjs4FAIpFg0qRJ2Lt3L5KTk8Uuh4iIXNCpUye2Ma4jPhsIAGDgwIEIDw/nVQIiIi/BNsZ1x6cDgUKhwLhx4/DTTz85d0IkIiLPptPp8Oeff8JoNIpdSoPi04EAAEaNGgWpVIq1a9eKXQoREblAp9PBbDbj2LFjYpfSoPh8IAgKCsLw4cPx3XffcdMMIiIv0KxZM0RERPC2QS3z+UAAABMmTEBhYSF+/PFHsUshIqJbYBvjusFAACAuLg59+/bFypUrubaViMgL6HQ6XLx4ETk5OWKX0mAwEPwlISEBly5dYuIkIvICPXr0gEQiYXO5WsRA8JfOnTujbdu2WLFihdilEBHRLTRq1Aht2rThh7haxEDwF0ejooMHD+L8+fNil0NERLeg0+lw4MAB3uqtJQwE1+nXrx8iIyPZqIiIyAuwjXHtYiC4jlwux/jx47F161but01E5OE6dOgAf39/3jaoJQwENxg5ciT8/PywZs0asUshIqIqsI1x7WIguEFgYCBGjBiBtWvXsi0mEZGH0+l0OHbsGH9f1wIGggpMmDABJSUl+OGHH8QuhYiIqqDT6WCxWHD06FGxS/F6DAQViImJwb333stGRUREHq5p06ZsY1xLGAgqkZCQgJSUFOzevVvsUoiIqBJsY1x7GAgq0bFjR3To0IFLEImIPJxOp0NycjKys7PFLsWrMRBUYdKkSThy5AjOnj0rdilERFQJRxvjAwcOiF2KV2MgqMI999yDmJgYXiUgIvJgjRo1wu23387bBjXEQFAFmUyG8ePH45dffuGlKCIiDzZo0CBERERAEASxS/FaDAS3MGLECPj7+2P16tVil0JERJWYNGkSnnvuObHL8GoMBLegVqsxatQorF+/HqWlpWKXQ0RElZBKpZBIJGKX4bUYCFwwbtw4GAwGbN68WexSiIiI6gQDgQuioqIwYMAANioiIqIGi4HARZMmTUJ6ejr++OMPsUshIiI32e12ZGVlIS0tTexSPBYDgYvatm2LLl26cAkiEZEXMpvNWLx4MV5//XWxS/FYDARuSEhIwJ9//olTp06JXQoREd3AZrM5b+sKggCbzQabzQYA8Pf3x/333499+/bxSm8lGAjc0KdPH8TGxvIqARGRB5o7dy6+//57ANf2OJDJZJDJZACAI0eOYMWKFTh79ix+/PFHMcv0WAwEbpBKpZg4cSJ+++03ZGZmil0OERFd588//8TXX38NAEhNTcWCBQtw7733QqVSQafTYefOnXjuuecwcOBAkSv1TBLBhbZOxcXFCA4ORlFREYKCguqjLo9VWlqKoUOHYsSIEXjhhRfELoeIiP7yyy+/YMiQIYiKikJWVhZiY2PRq1cv9OvXD127dkV8fDyCg4OhVCrFLrXeuDN+y+uppgYjICAAo0ePxnfffYepU6dCrVaLXRIREQEYMGAAFAoFhg4diokTJ6J58+bQarUICAhgwyIX8JZBNYwdOxZGo9F5r4qIiMQnlUrRvHlzRERE4N5770WTJk2gVqsZBlzEQFANERERGDx4ML799lvnDFYiIhLflClTOMermhgIqikhIQGZmZn4/fffxS6FiIj+8vTTT+P9998XuwyvxEBQTa1bt8Ydd9yBFStWcLtNIiIPodFosGPHDrz88svIz88v9zNBENh+vgoMBDWQkJCAkydPIjExUexSiIjoL/v27cPGjRtx4cIFAIDVagVwrTeBVMphrzJcdlgDdrsdDz30EG677Ta89957YpdDREQAMjMzIZVKERkZWe77V65cwZ9//gkAuPPOOxEaGgq5vGEvtuOyw3oilUqRkJCA//73v0hPT0fjxo3FLomIyOdFR0c7/5ycnIzVq1dj06ZNyMjIQFhYGMrKynDhwgW8/PLLmDFjxk3BwVfxCkENGY1GDB06FPfddx9eeuklscshIqK/ZGVl4fnnn8fly5fRrVs3dOnSBXFxcYiKisL58+fxwQcfoFevXpg3b57YpdYZXiGoR/7+/njooYewcuVKPPnkkwgMDBS7JCIin2e32/HSSy9h//79WLp0Kbp164aQkBDnzzt37gyj0YjZs2c36EDgDs6uqAVjx46F1WrFDz/8IHYpREQE4MKFCzh8+DC++uorDBgwoFwYcLh69SqaN2+OsrIyESr0PLxCUAvCwsLw4YcfokuXLhAEgV2xiIhE1rJlS6SkpNwUBOx2O65evYpNmzZh9uzZeOedd6BSqUSq0rNwDkEtYRAgIvIs999/PyQSCe677z60b98eJpMJhw8fxs8//4xLly7hkUceweuvvw4/Pz+xS60z7ozfDARERNQgJScn4+2338aOHTsglUpx5coVhIaGYvDgwZg8eTL69u3b4D/IMRB4MLvdzsYYRET16NKlS0hOTkaHDh0QEREhdjn1iqsMPFRqaip+/vlntGrVCn369BG7HCIin9CsWTM0a9YMwLXbu45bvA396oC7+FG1Htntdhw6dAivvPKK2KUQEfkkR/tihoGbMRDUMZvN5twiuUmTJpg+fTr27t2LZcuWiVwZERHR3xgIallRURGKi4tht9shCAJkMhlkMhmys7Mxc+ZM9OnTB1qtFkajUexSiYiInBgIatncuXMxc+ZM5yWpP//8E6NGjUJUVBR++uknvPrqq9ixYwceeeQRsUslIvIZjm2PuV195TipsJb1798fw4cPR69evbBo0SIcOXIEvXv3xvLly3HPPfcgJiamwe+uRUTkaSwWC/75z39iwIABGDZsmNjleCReIahlgwcPRqdOnTB16lTcdttt2LJlC9atW4eHH34Y8fHxDANERCJQKpUoKirCnj17xC7FYzEQ1IFZs2ZBpVJh7ty5uO+++xAREcEZrUREIuvZsycOHDjgvH1A5TEQ1IFx48ZBqVRi7969YpdCRER/0el0KC4uxtmzZ8UuxSMxENSRzz//HNHR0WKXQUREf2nfvj0CAgKwf/9+sUvxSAwEdWTMmDHo0qULvvrqK2RnZwP4u0OWoy8BERHVH7lcju7duzMQVIKBoA6tWbMGL774In766ScAf++IKJPJYLVaceDAAaSkpCArK0vkSomIfINOp8Px48dRWloqdikeh1Pe69DYsWPh7++PsWPHAgCkUimuXr2KhQsX4qeffoLVakVKSgoaNWqEJ598Ei+99JLIFRMRNWw6nQ42mw2HDx/mnjI3YCCoQ6GhoZg8eTIAwGw2Y9myZfj8888BAH379kW7du3Qtm1bnDx5ErNnz0bLli0xYsQIESsmImrYYmNjERMTg/379zMQ3ICBoJ7s3r0bn376KXr37o3x48ejW7duzq0oe/fujfPnz+N///sfAwERUR2SSCTQ6XScR1ABziGoByaTCa+88gratGmDhQsX4t57771pX+rMzEw0b94cVqtVpCqJiHyDTqdDSkoKMjIyxC7FozAQ1IMrV66gsLAQ//znPyGVlv8rLygowOLFi/HLL7+gf//+7GRIRFTHunfvDqlUigMHDohdikdhIKgHrVq1QlFRERITE53fy83Nxd69e/Hyyy/jtddeQ0JCAoYPHy5ilUREviEwMBDt27fnbYMb8ONoPfl//+//Yd68eVi8eDG6du2KCxcu4Pfff0ezZs0wb948TJgwQewSiYh8hk6nw6pVq2C322+6cuur+LdQT2bMmIGPPvoI7dq1Q35+PsLDw/HLL78gKSnJGQa4LScRUf1wtDE+c+aM2KV4DF4hqCcSiQQDBw7EwIEDYTKZoFQqnT9zJFRugEREVD/atWsHtVqN/fv3o127dmKX4xF4haCeCYIApVLpbGMMgJeriIjqmUwmQ48ePTiP4DocieqZ4yqARCLhFQEiIhH17NkTJ06cgMFgELsUj8BAQEREPsnRxvjIkSNil+IRGAhE4rhlYDabxS6FiMgnxcbGonHjxrxt8BcGApFIJBKsXbsWkydPht1uF7scIiKfxDbGf2MgEFHLli2RlJSEffv2iV0KEZFPYhvjvzEQiKhTp05o164dVqxYIXYpREQ+6Y477oBUKuVVAjAQiEoikSAhIQGHDh1CUlKS2OUQEfkctjH+GwOByPr374+oqCh88803YpdCROSTdDodDh06BJvNJnYpomIgEJlMJsP48ePx888/IycnR+xyiIh8jk6ng16vx+nTp8UuRVQMBB5g5MiR8PPzw5o1a8QuhYjI57Rr1w4ajcbnbxswEHgAjUaDkSNHYt26dSgrKxO7HCIin+JoY3zgwAGxSxEVA4GHGD9+PEpKSvDDDz+IXQoRkc/R6XQ+38aYgcBDxMTEoF+/fli5ciUbFRER1TOdTge73Y7Dhw+LXYpoGAg8yKRJk5Camopdu3aJXQoRkU+JiYlBXFycT88jYCDwIO3bt0fHjh25BJGISAQ9e/ZkICDPMWnSJBw9etTnl78QEdU3nU6H1NRUpKeni12KKBgIPMw999yDmJgYrFy5UuxSiIh8iqONsa+uNmAg8DBSqRQTJ07Er7/+iqtXr4pdDhGRz9BoNOjQoYPP3jZgIPBAw4cPh0qlwurVq8UuhYjIp+h0Ohw8eNAn2xgzEHiggIAAjBo1CuvXr0dpaanY5RAR+QydToeSkhKcOnVK7FLqHQOBhxo3bhxKS0uxadMmsUshIvIZbdu2RWBgoE/eNmAg8FCRkZEYOHAgGxUREdUjmUyG7t27MxCQZ0lISEBGRgZ27NghdilERD5Dp9Ph5MmT0Ov1YpdSrxgIPFjbtm3RtWtXrFixQuxSiIh8hq+2MWYg8HAJCQk4ceIEEhMTxS6FiMgnxMTEID4+3uf6ETAQeLi7774bcXFxbFRERFSPdDqdz80jYCDwcI5GRdu2bUNGRobY5RAR+QSdToe0tDSkpaWJXUq9YSDwAsOGDYNGo8GqVavELoWIyCd069YNMpnMp24bMBB4AZVKhdGjR2Pjxo0oKSkRuxwiogZPrVb7XBtjBgIvMXbsWJjNZnz//fdil0JE5BN8rY0xA4GXCA8Px+DBg/Htt9/6zJuTiEhMOp0OBoPBZ9oYMxB4kYSEBGRlZWHbtm1il0JE1OD5WhtjBgIv0qpVK3Tv3h0rVqyAIAhil0NE1KBJpVL06NHDGQhMJhOys7ORkZGBzMxM5OTkwGw2i1xl7ZGLXQC5JyEhAS+88AJOnDiBTp06iV0OEVGDZbFYcPvttyM9PR1ffvkl9Ho9bDab8wOZRCKBXC5HaGgooqOjERcXh2bNmkEu986h1Tur9mG9evVC06ZN8c033zAQEBHVgaKiIpw6dQqJiYkoKipCbGwsMjMzoVaroVAoIJFIAACCIMBmsyErKwsZGRk4duwYgoOD0aFDB7Rr1w4ajUbkV+IeBgIv42hU9M477yAtLQ2xsbFil0RE1CDY7XacOHECe/fuhcFggEwmg0ajQW5uLiwWC/z9/W96jkKhcP7ZarWiqKgIO3fuxLFjx9CnTx/cfvvtzgDh6TiHwAsNHToUQUFB+Pbbb8UuhYioQSgqKsKGDRuwbds2GI1GBAYGQq1WO0OBKz1g5HI5NBoNNBoNDAYDtm7dis2bN3tN/xgGAi+kVCoxZswYbNq0CcXFxWKXQ0Tk1XJzc7F27VokJydDqVRCrVaX+1SvVqthsVhgsVhcOp5UKoVGo4FCocC5c+ewfv16FBYW1lH1tYeBwEuNHTsWVqsVGzduFLsUIiKvlZ+fjw0bNiA/P985iN8oICAAEonE7U/6fn5+UKvVuHr1KjZu3Ai9Xl9bZdcJBgIvFRoaivvuuw+rVq1yObUSEdHfjEYjNm3ahMLCQmg0GkilFQ+JUqkUKpUKBoPB7XM4bjnk5ORg8+bNsFqtNS27zjAQeLGEhARkZ2fjt99+E7sUIiKvs2/fPuTk5ECtVlcaBhwc8wKqQyqVIiAgABkZGTh8+HC1jlEfGAi8WIsWLaDT6fDNN9+wURERkRuuXLmC48ePw8/PDzKZ7JaPV6vVsNvtKCsrq9b55HI5ZDIZDh48iKtXr1brGHWNgcDLJSQk4OzZszh27JjYpRAReQW73Y7du3fDYrFAqVS69Bx/f3/IZLJqXyUAru1cazKZsGfPnmofoy6xD4GX0+l0aN68OVasWIGuXbuKXQ4RkcfLyMjA1atXoVKp3OoR4O/vjx07diAjIwNGoxERERHo27cvmjVr5tLzJRIJlEolUlJSkJubC61WW92XUCd4hcDLSSQSTJo0CTt37kRKSorY5RARebyTJ0/CZrO53WJ47969SExMRNu2bTFw4EBIpVKsXr0aqampLh/Dz88PFosFp0+fdrfsOsdA0AAMGTIEoaGhWLlypdilEBF5NJPJhPPnz5drQeyKjIwMXLx4EZ06dULPnj3RpUsXTJw4EcHBwfj9999dPo5EIoFMJsOZM2dgt9ur8xLqDANBA+Dn54cxY8Zg8+bNKCoqErscIiKP5WhDXFG/gaqcPXsWUqkUt99+u3MegVwuR6dOnZCWluZWkziFQoGysjKPa1bEQNBAPPTQQxAEAevWrRO7FCIij5Wbmwu73e7SyoLrZWVlISwsDKGhoeUaFEVHRwOAWysH5HI5rFYrcnNz3aqhrjEQNBAhISEYNmwYVq9e3aD25yYiqk25ubkQBMHtDYdKSkqg0WicbYwdv2cdOxq608XQ0fOAgYDqzIQJE5CXl4dffvlF7FKIiDyS0Wis1vOsViskEgnkcjkEQSh32wBAtTrGVreWusJlhw1Is2bN0Lt3b3zzzTcYOnSo12y5SURUVwRBgMlkQklJCUpKSpCTkwOLxYLi4mLY7XbY7XbYbLYq/+loSCQIApKTk2E2m523HBytiN2dkyAIgsdNKmQgaGAmTZqE6dOn49ChQ+jRo4fY5RARVZsgCDCbzc7B/MYvvV7v0s9sNpvzmO3atUN0dLTz07lUKoVMJiv3T0dXQce/S6VSaLValJSUQKFQQC6XQ61WA/j7VoHj1oGrHKsNPAkDQQNzxx13oFWrVlixYkW5QCAIAoqLi1FUVOT8n0MulyMkJOSmrT6JiGpDVYO5K4N6SUlJlZfiAwICoNFoyn2FhoYiPj4eGo0GgYGBN/08OTkZFy5cQFBQ0C33L7hebGwsdu/eDbPZjJYtWzoH84yMDABAZGSk238/KpXK7efUJQaCBkYikSAhIQGvv/46Tp8+DaPRiNTUVGRlZaGsrAw2m82574HjfpharUZ0dDSaNGmCli1butzKk4gaLovF4tbAXdFXVROcVSqVc5B2DNwhISGIi4u7aRCv7MudAd1BLpcjOTnZ7Q9BWq0WNpsNubm5aNeuHYBrtwtOnDiBmJgYBAUFuXwsx60CT+tUyEDQAHXp0gVdunTBmjVrnJe15HI55HI5/Pz8nP8jCIIAq9WK4uJiFBQU4MyZM9i1axfatWuHjh07olGjRiK+CiKqLqvVWq1P49f/vKrB3N/f/6bBOTg4GI0bN65w4L7xk7parRbtcrlWq4VMJnOrU2FeXh78/PzQtm1b7Nu3DzabDSEhIUhMTERRURGGDh3qVg1WqxVyuZyBgOqOxWLBoUOHcPjwYcTFxaGkpARarbbKyS4ymcx5RcBms8FoNOLAgQM4efIkevXqhY4dO1YrhRNVxmq1oqioCPn5+dBoNIiKiqry05rRaMTcuXOxZMkS2Gw2PPLII5g1axZiYmLqser6Y7PZqn2J3fEzk8lU6fGVSmWFg3ZUVFSFl9hvHNjVarXbLX89SVhYGJRKJcxms0uvo7i4GNnZ2dBqtXjooYfwxx9/4OTJkzAajQgPD8fYsWMRHx/vVg0WiwWBgYFuXVWoD977X5XKyc7Oxq+//orMzEzIZDJotVoUFhaiqKjI5RQqk8kQEBAAQRBQWlqKbdu24eLFixg4cKDHvXHJOxUUFGDu3Ln44YcfkJSUhLFjx2Lx4sUVvr8ca8VfffVVbNmyBR999BHCw8Mxffp0ZGVlYeHChR73vrTb7S5dSq9qUK9qe10/P78KB+qIiIhKP43f+OXubPiGxs/PD61bt8axY8du2Y+grKwMGRkZCA4ORnh4OACgf//+6N+/f7XPLwgCbDYb2rVr53EfthgIGoC0tDT88MMP0Ov1CAgIcKbe4OBgFBQUICwszK37ZRKJxNl8Izk5GevWrcOIESMQGhpaVy+BfITdbkdUVBQWLlyIBQsWwGAwVPrelEgkOHfuHH799Vc8/PDDmDhxIgDgnXfewZtvvoktW7ZgwoQJ1WoyU1ltBoOhRvfNS0tLKz2+QqGo8DJ6eHi4y/fM/fz8avw6CWjfvj0SExNhsVgq/Tu1WCxITU2FSqVydiOsDSaTyXn7wdMwEHi5zMxMbNq0CQaDAYGBgeV+MYaGhqKgoABFRUXVmg+gUCggk8mQm5uLDRs2YPTo0ZxXQDUSFhaGWbNmQSKRYMuWLdizZ0+5JWEOdrsdUqkUJ06cgEKhQPfu3Z0/6927N4KDg3Ho0KFKA0FSUhKys7Pdum9e1WAul8srHKDj4+Or/ER+/c84mHuOyMhIxMTEICUlpcJNjmw2G1JSUiCTyRAXF1drq7AcyyjbtGnjkb9LGQi8WElJCX744QeUlpbeFAaAa5fGAgMDkZ+fX+03n1QqhUajQX5+PrZs2YKxY8f6/CVHqhnHZK6QkBDo9foql5WZTCZYrdZya7xDQ0MRERGBy5cvV/q8jz/+GPv37wdw7T1c0aAdGxvr0mX2wMDAcpNxyftJJBL06dMHa9asgdFoLLf8TxAEpKWlwW63o2nTprV6Wb+0tBQBAQHo3bt3rR2zNjEQeClBELBz504UFhZCo9FU+ssqNDQUV65cgcFgcK44cJdUKkVAQAAyMzNx6NAh9OrVqyalUwMiCALKyspu+tQdFhaGli1bVvjL1PFeDQsLg8FgqDIQaDQaGI3Gco+RSqUICgpCSkpKpc977bXXIJFIoNFo4O/vz8GcbhIdHY3u3btj7969zln/wLW+AmVlZWjatGmtfvixWCwQBAG9evXy2NuvDAReKikpCWfPnoVSqawywQYEBMDf3x95eXnVDgQAnJ27Dh8+jGbNmtXqPTUShyAIMBqN1Vqedv1XRe1XR4wYgdmzZ1d43hsDwY3L2xytYqVSKcLDw6FQKJCZmen8udlshiAIVc4Qj4iIqM5fCfmY7t274/Lly0hPT4darUZ+fj6Ki4sRGxsLf3//WjuPzWZDWVkZmjdvjk6dOtXacWsbA4EXstls2LNnD+x2u0tNhMLCwpCeng6TyVSjpkMqlQp6vR779u3DqFGjqn0cqrkb+7NXZ3mawWCo8P498PfE0opmszdv3vyWl9iDg4Mrrd0RCEJDQ2E0Gm8KBI5WsQAQFxeHiIgI7NixA+PGjQNwbaXChQsX0Ldv33LHI3KXQqHAAw88gHXr1iEtLQ15eXmIjIxEYGBgrZ3DarWitLQUjRs3xv333+9xKwuux0DghS5fvoyCggKX214GBQXh9OnT2Lx5M/Lz81FUVASVSoXGjRujb9++Ll++kkgkUCqVSElJQW5ursc11fAm17d0dbUf+41fjk1VKhIQEHDToK3VatG0aVOX7psHBATU+S8urVYLi8VS7nWYTCb8/vvvAIAhQ4YgLi4ODz/8MJ544gn0798fffr0waeffoqkpCR8/fXXABgIqGYCAwPRpEkTHDp0COHh4TW6kno9R2i3WCyIi4vD8OHDPa5V8Y0YCLxQYmLiLS+Z3ujixYu4cuUKunbtiqioKBgMBhw+fBjLli3Do48+6lxjeyt+fn7Q6/U4ffo0+vTpU92X4NVc6c9+q0G9Jv3Zq+oA5+gC58mfQvLy8pCYmIjTp0/DZDLh008/RXh4OHr06IF+/fphzpw58Pf3x5AhQyCRSDBu3Djk5eVh1qxZyM7ORsuWLfH111+jefPmYr8UagDOnz+P119/Hd26dUOPHj1w9uxZmM3mGv1/ZLPZUFpaCrlcji5duuCuu+7yipbwEsHR2L4KxcXFCA4ORlFRkcc1AvE1BoMBS5cuhSAIbt3jSklJQUlJCcLDw52Df35+Pr744gu0adMGw4cPd6sGtVqNqVOnevTAU5Eb+7NX5765q/3ZbzVwV/blbX+n7tq8eTNGjBgBrVbr7DYYGBiIhx9+GNOmTcO6devg7+9frh2so4e8Uql0e1Maosrk5OTg0UcfRUhICJYsWQKVSoXz589jx44dKC4uBnCtTbMrkwsdreAduyiGhoaiX79+aNq0aV2+hFtyZ/zmFQIv49jL291LT/Hx8bh69SoKCgqg1WohkUgQGhoKrVaL3Nxct46lUChQVlaG4uLiel1L62jpWt1L7CUlt27peuPAHRQUhJiYGJeWponZn92bPPDAA1XuAz969OibvieTyaq1mxxRZUpLS/H8888DAObPn4+AgAAAQKtWrRAXF4dz587h+PHjyMvLcw7yMpkMcrkcEokEgiA4uw5arVbndsbR0dHo2LEjWrVq5RVXBa7HQOBlcnNzIQhCtT4h3dioSBAEGAwGt+cCyOVymEwm5OTkuBwIbDZbuS5w7myy4vhy/E9Zketbul4/cEdFRbn8Sd2b+7MTketsNhv+9a9/IS0tDcuWLbvplqlKpULnzp3RsWNHpKamIj09HVevXsXVq1dhMpnK7RgbEBCAqKgoREZGIjY2Fo0bN/baeS38DehlHIGgOm84R+vUvLw8NGrUCCdPnoRer3dpLoDdbofNZnP+02w2Y9euXTh27JhLg3pN+7Pf6hI8myURkSsEQcD777+Pffv24eOPP8Ztt91W6WOlUimaNGmCJk2aALj2e7C0tNR5RUAul0OlUjWYW1gMBF7GaDTWKH2GhYXh8uXLOHPmDH788UdotVpERkYiKyur3IDvWAvu+PON/P39ceLECVy+fLnCT91hYWEu3zdnS1ciqi/ffPMN1q5di1dffRU6nc6t5zo6tzZUDAReprJ1465SqVRQKpVYvXo1gGuNOQwGA6RSKWQyGaRSqbPZ0fXfu/GfZWVlGDBgAPr37++1l8eIyLds374d8+fPx5QpUzBy5Eixy/E4DAReRi6Xw4WFIZUyGo3Yvn07pFIp7rnnHqjVaoSGhiIkJMSt4zh27GIYICJvkJiYiFdffRWDBg3C9OnTxS7HIzEQeJmq9i24FavViu+++w4FBQVISEhAVFQUcnJykJWVhfz8fERGRrp0OcwRSByzcomIPFlaWhpefPFFtG3bFm+88UaDuedf2/i34mUcKwLcvUpgt9uxYcMGpKen48EHH0RsbCzkcjmio6PRvHlzKBQKpKamIiUlpcqleY5jSSQSdiokIo9XXFyM559/HoGBgfjwww85Z6kKvELgZcLDwyGVSp1byLpq27ZtOH/+PFq2bImysjIkJiaW+3mHDh1QUlKC7OxsJCcno1GjRggPD6/wHI6dwVztbkhEJAaz2YyXXnoJhYWFWL58eZV7bBADgdfRarVQKpUwm81uBYKrV68CuNam8/z58zf9vEOHDs5Z/4WFhcjJyUFxcTFCQ0MRFhZW7hKbxWJBWFhYrfX8JiKqbYIgYM6cOTh58iQWLVqEuLg4sUvyeAwEXsbPzw+tW7fGsWPH3OpHMGnSJJfP0ahRIwQFBSEvLw95eXkoLCxEeHg4GjVqBLvdDkEQ0L59++q+BCKiOrdo0SJs3boV7777Ljp27Ch2OV6Bcwi8UPv27SGXy6vcIKemHHvRt2jRAmq1GpmZmbh06RKKi4uhVCpx++2319m5iYhqYtOmTVi6dClmzJiBAQMGiF2O12Ag8EKRkZFo3LgxjEZjjZYgukKhUCAmJgbNmjWDVCpFQUEB0tLSnLcgiIg8ycGDBzF37lyMGjUKDz/8sNjleBUGAi8kkUjQt29fKJXKKlsC1yZ/f3+EhYVBq9Xi4sWLGD9+PN555x3k5+fXy/mJiG7l4sWL+Mc//oGePXvin//8J/ukuImBwEtFRkaiR48ezp226prZbIZEIsHQoUOxcuVKPP/88/jll18wcuRILF++vMotgYmI6lpubi6ef/55NG7cGO+++y53Hq0GBgIvdscddyA2NhalpaU1bmlcFYvFApPJhDZt2qBNmzbw8/NDQkICNm7ciBEjRmDhwoUYNWoUtm7dWuW2tkREdaGsrAwzZ86EzWYrt5UxuYeBwIvJ5XI88MADiIqKgsFgqJNQYLFYUFZWhubNm2PgwIHlLsEFBwdj1qxZ+O6779CmTRu8+uqrmDJlCo4fP17rdRARVcRut+Pf//43rly5ggULFiAiIkLskrwWA4GXU6vVePDBB9G4cWMYDIZam2goCAJKS0thNBrRsmVLDBs2rNIthuPj4/HBBx9g8eLFsNvtePzxx/Hyyy8jLS2txnUQEVXlww8/xO7du/Huu++iVatWYpfj1SSCC6NHcXExgoODUVRUhKCgoPqoi9xkNBqxZ88eJCYmwmq1IiAgoNr30KxWK0pLS6FUKtGjRw/ccccdLjdBstvt2Lp1Kz799FPk5+dj3LhxePzxx/m+IaJa9+233+LDDz/EK6+8glGjRoldjkdyZ/xmIGhgLl++jO3btztn/yuVSigUilvOthUEAWazGSaTCVKpFFFRURgwYAAiIyOrVYfRaMTKlSuxfPlyyOVyTJ06FQ899FClVxmIiNyxY8cO/OMf/8DDDz+MGTNmiF2Ox2Ig8HFmsxkXLlzAiRMnkJmZCZvNBkEQIJPJIJPJnOFAEARYrVYIggBBEODn54cmTZqgffv2aNasWa3M0s3Ly8OiRYvw/fffo3Hjxnj++efRt29fLgciomo7deoUpk2bhrvvvhtvv/02dy+sAgMBAbg24F+9ehXp6enIyclBZmYmSkpKnHMMJBIJgoODER0djfDwcMTHxyM0NLROarl48SLmz5+Pffv2oWvXrpg5cya7HRKR2zIyMjB58mTExsZi4cKFUCqVYpfk0RgIqFJWqxVWqxUSiQQymcytDZJqw969ezF//nwkJyfj/vvvxzPPPFPt2xJE5FuKi4vx+OOPw2w2Y/ny5QgJCRG7JI/HQEAezWaz4fvvv8eiRYtQUlKCSZMmYfLkyVw7TESVslgseO6555CUlITly5cjPj5e7JK8gjvjN2+8UL2TyWQYNWoUNm7ciEmTJmHFihUYOXIk1q9fX6cNlojIOwmCgLfeegvHjx/Hhx9+yDBQRxgISDQBAQF4+umnsX79euh0Orz99tuYOHEi9u3bJ3ZpRORBlixZgi1btuCNN95Aly5dxC6nwWIgINFFRUVhzpw5+PrrrxEUFITnnnsOzz33HC5evCh2aUQksi1btmDx4sV4+umnMXjwYLHLadAYCMhjtG3bFosXL8b777+PtLQ0TJgwAW+//TZ3VCTyUYcPH8abb76JESNGYMqUKWKX0+BxUiF5JIvFgrVr12LJkiWwWq2YPHkyEhISuMSIyEdcunQJU6ZMQbt27bBgwYJ6XxHVUHCVATUYxcXF+OKLL7BmzRqEhobi2WefxZAhQ9iIhKgBy8/Px+TJk6FSqbB06VJoNBqxS/JaDATU4KSmpuKTTz7B9u3b0bZtW7zwwgvo2rWr2GURUS0zGo2YNm0arl69iq+++gpRUVFil+TVuOyQGpy4uDi89957WLJkCQBg2rRp+Mc//oGUlBSRKyOi2mK32zF79mxcunQJCxYsYBioZwwE5FW6dOmC5cuX46233sKZM2cwZswYfPjhhyguLha7NCKqofnz5+OPP/7A22+/jTZt2ohdjs9hICCvI5VKMWTIEKxbtw5PPfUUvv/+e4wYMQIrV66ExWIRuzwiqoY1a9Zg5cqVeOmll3D33XeLXY5PYiAgr6VUKjFlyhRs3LgRgwYNwvz58zFmzBhs374dLkyNISIPsXPnTnzwwQdISEjA2LFjxS7HZ3FSITUYycnJmD9/Pvbu3YvOnTtj5syZaNeundhlEVEVzpw5g6lTp+LOO+/Ef//7X64gqmVcZUA+7cCBA5g3bx4uXLiAIUOG4JlnnkF0dLTYZRHRDTIzMzF58mRERUXh888/h7+/v9glNTgMBOTz7HY7Nm3ahIULF0Kv12PixImYMmUK1Gq12KUREYCSkhI89thjMBqNWL58OUJDQ8UuqUHiskPyeVKpFCNHjsSGDRvwyCOP4Ntvv8XIkSOxbt067qhIJDKr1YqXX34ZOTk5WLBgAcOAh2AgoAYtICAATz31FDZs2IBevXrhnXfewYQJE7Bnzx5OPCQSgSAIePvtt3H06FF88MEHaNasmdgl0V8YCMgnRERE4D//+Q9WrFiBkJAQPP/883jmmWdw/vx5sUsj8ilffvklNm3ahNdeew3dunUTuxy6DgMB+ZQ2bdpg0aJF+Oijj5CVlYWJEyfizTffRG5urtilETV4W7duxWeffYYnn3wS999/v9jl0A0YCMjnSCQS9OnTB2vWrMFLL72EHTt24MEHH8QXX3wBo9EodnlEDZIgCNizZw+GDRuGJ554QuxyqAJcZUA+T6/XY9myZVi1ahVCQkLw9NNP4/777+d6aKJaZLfbIZVKYbPZIJPJxC7HZ3DZIVE1pKen45NPPsFvv/2G1q1bY+bMmbjjjjvELouIqNq47JCoGho3box3330Xy5Ytg0KhwFNPPYUXX3wRV65cEbs0IqI6xysERBUQBAG//vorPvnkE2RnZ+Ohhx7C1KlT0ahRI7FLI/JI6enpsNlsUKlUCA8PB3Dt/yOJRCJyZb6NtwyIaonZbMaqVauwdOlSSCQSPP744xg3bhz8/PzELo3IYzz66KM4ffo0zp49izvuuAODBg3Cv/71LwB/zx0gcTAQENWygoICLF68GOvWrUNUVBRmzJiB/v3789MP+bwXX3wR33//PRYvXozs7GycOHECixYtwl133YXNmzcDYCgQEwMBUR25dOkSPv74Y+zatQsdO3bEzJkz0aFDB7HLIhJFSUkJhg8fjkmTJuGxxx4DcG3Vzt69e/Hkk08iKioKO3fu5BU1EXFSIVEdadasGebNm4fPPvsMRqMRU6ZMwSuvvIKMjAyxSyMSRUpKCi5evOj898DAQAwcOBArV65EWVkZnnjiCZhMJhErJFcxEBBVQ48ePbBixQq89tprOHr0KB566CF8/PHHKCkpEbs0onqj0WgwefJkbN26Fbt373Z+XyqVomfPnnjyySdx6NAh5OTkiFgluYqBgKiapFIphg8fjg0bNmDy5MlYs2YNRo4ciTVr1sBqtYpdHlG9GDBgAPz8/PD555/jwIEDzu/LZDIMHjwYhYWFXLrrJRgIiGpIpVJh2rRpWL9+Pfr06YP3338f48ePx65du7ijIjV4Op0Ob7zxBvbv34+33noLa9ascf4sOzsbUqkUAQEBIlZIruKkQqJalpSUhHnz5uHQoUPo3r07Zs6ciVatWrn8/LKyMiiVSs7KJo93fZ+BY8eO4aWXXkJBQQGkUinat2+Pn3/+GRMmTMBHH30kcqW+i6sMiEQmCAJ2796NBQsW4MqVKxg2bBimT5+OiIiIKp9ns9nw9ddfY+vWrejfvz+mTZtWTxUTVZ9jWWF+fj62bt2KPXv2QKFQoE2bNnjqqafELs+nMRAQeQir1Yr169dj8eLFkMvl+P777+Hn51dp/wKTyYTvvvsO58+fx5tvvolBgwZh1apV7JBIovrzzz8RHR2NyMjICn/OPgOei8sOiTyEXC7H2LFjsXHjRsydOxdyubzKZkZKpRKTJk3Cyy+/jODgYLRv356/aElUX331Fbp27YqPPvoIWVlZFT7G8R5NSkqqz9KolvE3DVE90Gg06Nat2y23fTWbzQCAN998ExqNBo8//jivypFoTp06hXfeeQcjR47EggULMGvWrHI9B663evVqjBgxAuvXr6/nKqm2MBAQeQi73Q4/Pz9kZ2fjgw8+wKxZs3DbbbeJXRb5KEEQcPr0aXTu3BnLli3Drl27sGXLFkydOhXHjx+H3W4v9/jY2Fi0bNnSrQm05Fk4h4DIQ9hsNshkMowZMwYXLlzA999/j/j4+Aofy13kqD4UFRUhMTERd911FwAgNTUVffv2hUqlwsKFC9G7d2/IZDIkJiYiNjYW/v7+UKlUIldN1+McAiIvY7fbIZPJcPToUaxbtw7//Oc/ERsbW+njHWHg119/xaefforffvutvkolHxIcHOwMA2azGXFxcUhKSkKjRo0wduxY/Pjjj/jjjz8wZMgQ/PbbbwwDXo6BgEhkR44cwdmzZwEA06dPx5AhQzBgwIAKJxPabDYAwNGjR/H4449j8ODB2LhxI0aPHo0RI0agqKioXmsn3+Hn5wer1Qq5XI49e/ZgwIABGD9+PIYMGYK+fftizJgxYpdINcRAQCQiu92O1atXo3379rj//vtx/PhxvPzyy9BqtTc9VhAEyGQyWK1WzJ49G+fOncOvv/6K3377DUePHkVGRgZ++eUXEV4F+Qq5XO4Mpf/3f/8HuVyOoUOHYuXKlSJXRrWBgYBIRFKpFO+99x42b96M7OxsmM1m7N27F2VlZeUeJwiCcxLXu+++iytXrmDGjBno378/AKBFixYwmUzOXvJsmUx1RSaToaysDA888ADUajXWrl0rdklUSxgIiDzA0KFDcfjwYfzvf//De++9h5dffhkAnDvFSSQSyGQyXL16Fd988w3uv/9+DBo0yPn83NxcNG3a1PnpjRMOqS5JJBLcc889OH78uNilUC1iICDyINOnT0dhYSGmT5+O/Px8PPfcc3j++eed+8lv3LgRgYGBGDBgQLnuhcnJydizZw+6d+8OgFcIqGays7OxZMkSCIJQ4XvJ398fs2bNQnh4uAjVUV2Ri10AEd2sbdu2MJlMGDRoEJo0aQKlUgkAMBqNsFgszlsFAFBSUoJFixahUaNGmDhxIgBeIaDqKy0txQsvvIDCwkKMHTsWwcHBFT6O77GGh4GAyEMplUrMmTOn3PcKCgpgNBrLdTz88ccfsWLFCue2s+wrT9Vls9nwr3/9C2lpaVi2bFmlYYAaJv7WIPIiDz74IARBwJdffomsrCzMmTMH77//PkaOHImRI0cCAMMAVYsgCHj//fexb98+vPfee+yS6YN4hYDIi3Tq1AnPPvssXnjhBcyfPx+pqal46aWX8MQTTwBgB0Oqvm+++QZr167Fq6++Cp1OJ3Y5JAK2LibyQlarFQcOHEB8fDzi4uIAlA8Ddrvd2USGVwzoVrZt24Z//vOfmDJlCp555hmxy6FaxNbFRA2cXC5H7969nWEAKD/JSyKRYP78+Zg4cSL2798vRonkJRITEzF79mwMGjQI06dPF7scEhEDAVEDJJFIMHToUKjVajz77LOYMWMGkpOTxS6LPExaWhpefPFFtG3bFm+88QavJvk43jIgasAEQcDvv/+Ojz/+GBkZGRg5ciSeeuophIaGil0aiay4uBiTJ08GAHz55ZdcUdBAuTN+MxAQ+QCz2Yy1a9diyZIlsNlsmDJlCiZOnOjsb0C+xWw245lnnkFycjKWL19e7tYTNSycQ0BE5fj5+WHixInYuHEjRowYgUWLFmH06NH46aefnHskkG8QBAFz5szBqVOnMG/ePIYBcmIgIPIhwcHBmDVrFr777ju0adMGs2fPxuTJk3Hs2DGxS6N6smjRImzduhX/+c9/0LFjR7HLIQ/CQEDkg+Lj4/HBBx9g8eLFEAQBU6dOxcsvv4zU1FSxS6M6tGnTJixduhQzZszAwIEDxS6HPAwDAZEP69q1K7766ivMmTMHJ0+exJgxY/DRRx+huLhY7NKolh08eBBz587FqFGj8PDDD4tdDnkgTiokIgDXNk5auXIlli9fDrlcjieeeAJjxoyBQqEQuzSqoYsXL+Kxxx5Dp06dMG/evHJ7YVDDxlUGRFRteXl5+Pzzz7Fx40Y0btwYM2bMwD333MOWyF4qNzcXkydPRmBgIL744guo1WqxS6J6xFUGRFRtYWFheOWVV/Dtt98iNjYW//jHPzBt2jScPn1a7NLITWVlZZg5cyZsNhsWLFjAMEBVYiAgogq1aNECn3zyCT755BMUFRXhkUcewezZs5GVlSV2aeQCu92Of//737hy5QoWLFiAiIgIsUsiD8dAQERVuvPOO/Htt9/ilVdewYEDBzBq1Ch89tlnKC0tFbs0qoQgCPjggw+we/duvPvuu2jVqpXYJZEXYCAgoluSyWQYNWoUNm7ciEmTJmHFihUYOXIk1q9fD5vNJnZ5dINvv/0Wa9aswf/7f/8PvXr1Ersc8hIMBETksoCAADz99NPYsGEDdDod3n77bUyYMAF79+4VuzT6y44dOzBv3jw88sgjGDVqlNjlkBdhICAit0VGRmLOnDn4+uuv0ahRI8yYMQPPPvssLly4IHZpPu3UqVP497//jX79+uHZZ58VuxzyMlx2SEQ1IggC/vjjDyxYsADp6ekYMWIEnnrqKYSFhYldmk/JyMjA5MmTERsbi4ULF3LjKgLAPgREJAKLxeLcUdFqteLRRx9FQkIC/P39xS6twSsuLsbjjz8Os9mM5cuXIyQkROySyEOwDwER1TuFQoEJEyZg48aNGDlyJJYsWYJRo0bhxx9/5I6KdchiseDll19GXl4ePvnkE4YBqjYGAiKqVUFBQXjxxRfx3XffoX379njttdfw6KOP4ujRo2KX1uAIgoC33noLx48fx4cffoj4+HixSyIvxkBARHUiLi4O7733Hr744gtIJBJMmzYNs2bNQkpKitilNRhLlizBli1b8MYbb6BLly5il0NejoGAiOpU586dsXz5crz11ls4d+4cxowZgw8++ABFRUVil+bVtmzZgsWLF+Ppp5/G4MGDxS6HGgBOKiSiemMymfDtt99i2bJlkMlkePzxxzF27Fj4+fmJXZpXOXz4MJ599lkMHToUr776KjeeokpxlQERebT8/Hx8/vnn2LBhA6KjozFjxgz069ePA5sLkpOT8dhjj6Ft27b4+OOPIZfLxS6JPBgDARF5heTkZCxYsAB79uxBp06dMHPmTLRv317ssjxWfn4+Jk+eDJVKhaVLl0Kj0YhdEnk4LjskIq/QvHlzLFiwAP/73/9gMBgwefJk/Pvf/0ZmZqbYpXkco9GIF154ASaTCQsWLGAYoFrHQEBEouvZsydWrlyJ2bNn4/Dhwxg9ejQ++eQTlJSUiF2aR7Db7Xj11Vdx6dIlLFiwAFFRUWKXRA0QAwEReQSpVIoRI0Zgw4YNeOSRR7Bq1So8+OCDWLt2rc/vqDh//nzs3LkTb7/9Ntq0aSN2OdRAMRAQkUcJCAjAU089hQ0bNqB3797473//i/Hjx2P37t1wYcpTg7N69WqsXLkSL730Eu6++26xy6EGjIGAiDxSREQE3njjDfzf//0fQkND8cILL+CZZ55BUlKS2KXVm507d+LDDz9EQkICxo4dK3Y51MBxlQEReTxBELBr1y7Mnz8fqampeOCBBzB9+nSEh4eLXVqdOXPmDKZOnYo777wT//3vfyGV8vMbuY/LDomoQbJarVi/fj0+//xzmEwmPProo5g0aRJUKpXYpdWqzMxMTJ48GVFRUfj888+5YyRVGwMBETVoer0ey5Ytw6pVq9CoUSM8/fTTGDp0aIP4FF1SUoLHHnsMRqMRy5cvR2hoqNglkRdjHwIiatACAwPx/PPPY+3atejUqRP+85//YNKkSTh06JDYpdWIYyvjnJwcLFiwgGGA6hUDARF5rcaNG+Pdd9/FsmXLoFQqMX36dLz44ou4fPmy2KW5TRAEvPPOOzh69Cg++OADNGvWTOySyMfwlgERNQiCIODXX3/FJ598gqtXr+Khhx7CtGnT0KhRozo7p8FgQE5ODnJzc5GTkwOTyQSbzQa5XA6NRoPw8HBotVpotdpbbuC0bNkyfPbZZ5gzZw7uv//+OquZfAvnEBCRzzKbzVi1ahWWLl0KiUSCxx57DOPHj6+1HRVtNhsuXbqEkydPIiUlBRaLBYIgQBAE5+ZMjj8LggCZTAZ/f3+0bt0a7du3R0RExE2bOP3000+YPXs2nnzySUydOrVW6iQCGAiIiFBQUIDFixdj3bp1iIqKwrPPPouBAwdWe0dFQRBw7tw57NmzB4WFhRAEAQqFAgqFAlKptMLjCoIAm80Gs9kMq9UKhUKBxo0bo2/fvoiIiAAAHD16FM888wwGDx6M119/nTs+Uq1iICAi+sulS5fw8ccfY9euXejYsSNeeOEFdOzY0a1jlJSUYMeOHUhKSoLdbodKpXJ722FBEGCxWGA0GuHv74+ePXtCq9XiiSeeQOvWrfHxxx9DoVC4dUyiW2EgICK6wcGDBzF//nwkJSVh4MCBeO655xATE3PL56Wnp2PLli0oKiqCv79/jW89CIKAsrIyWCwWpKen4+rVq1iyZAkCAwNrdFyiinDZIRHRDXr06IEVK1bgtddew7FjxzB69Gh8/PHH0Ov1lT4nJSUF33//PYqLi6HRaGplHoJEIoFKpUJhYSHUajUGDhzYIPonkPfju5CIfIZUKsXw4cOxYcMGTJkyBWvWrMHIkSOxZs0aWK3Wco/NysrCDz/8gNLSUmg0mlodtNPT02E0GhEeHo78/Hxs2rQJJpOp1o5PVB0MBETkc1QqFaZNm4YNGzagb9++eP/99zFu3Djs3LkTgiDAbDbjl19+gcFggEajqdWJftnZ2dDr9WjcuDECAgIQEBCAtLQ07N27t9bOQVQdnENARD4vKSkJ8+fPx8GDB3HHHXdg8ODBuHjxIgICAiCTyWrtPAUFBcjKykJkZGS5LoRGoxGCIGDUqFGIj4+vtfMRcQ4BEZEbWrVqhf/973+YP38+SkpKsHfvXpSUlMCFz0suKykpwdWrVxEaGnpTS2KlUgmr1Yrt27fDYrHU2jmJ3OHeuhkiogZKIpHgrrvugl6vx+HDh1FYWIji4mKEhYUhNDS0RnMITCYT0tPTodFoEBkZWeG5AwICkJeXh4sXL6JNmzY1eSlE1cJAQET0l5KSEly4cAGBgYHQarXIzc1Fbm4uCgoKEB4eXmkbZLPZjP379yMjIwOZmZkoKyvDsGHD0LFjR1itVqSkpMDPzw+NGzeu9NwymQyCICAxMZGBgETBWwZERH85e/YsTCYT/P39IZVKERERgRYtWiAgIACZmZm4dOkSDAbDTc8rLS3F7t27kZeX5+xACAB2ux0pKSmQSCSIj4+/5eREpVKJ9PR0ZGdn1/prI7oVBgIior+kpKQAQLmB29FuuGnTppBIJEhJSUFqairMZrPzMRqNBjNmzMAzzzyDe++91/n99PR0WK1WxMfHuzQ5UaFQwGq1IiMjoxZfFZFrGAiIiHDt0/zVq1crHbhVKhWaNm2K2NhYmEwmJCcnIysrq9zuhtfLz8+HwWBA48aNXW5o5NgQKScnp8avh8hdnENARASgsLAQJpPplnsUBAYGQqPRoKCgALm5uSgqKoJWq0VoaKjzyoLVaoXBYEB0dDTUarVbdUilUmRmZlb7dRBVFwMBERGurde22WxQKpW3fKxEIkFoaCiCg4ORm5uLnJwcFBQUICIiAgaDAVarFUFBQQgODna7DrlcjqKiItjtdrY0pnrFQEBEhGuf6gVBcKsroUwmQ2RkJEJCQpCdnY309HTk5uZCJpNVKww4OLZNZiCg+sRAQESEvycSuhsKAMDPzw+xsbEoLS2FSqXiNsbklRg/iYhw7VK9Y1JfdQUEBNTK9shSqbRWWyYTuYKBgIgIQKNGjSCXy2Gz2UStw2azISQkhLcLqN7xHUdEBCAoKAgqleqmbZDrm91uR3R0tKg1kG/iHAIiIlybQxAVFYVz585V6/mHDx+GyWSCXq8HAJw/f975527dusHf3/+Wx3DcrtBqtdWqgagmGAiIiP7StGlTJCUlVWvJ34EDB1BUVOT893PnzjnDRbt27VwKBCaTCX5+ftwCmUTBQEBE9JdWrVph9+7dMBqNCAgIcOu5zzzzTI3Pbzab0bp160o3USKqS5xDQET0F39/f7Rt29bZk6A+WSwWSKVSdOjQoV7PS+TAQEBEdJ2OHTtCpVKhtLS03s4pCALKysoQExODJk2a1Nt5ia7HQEBEdJ3Q0FD06tULdrsdFoulXs5ZVlYGf39/DBgwgMsNSTR85xER3aBTp05o0qQJysrKYLfb6/RcFosFNpsNPXv2RHh4eJ2ei6gqDARERDeQyWQYOHAgQkNDUVJSUmehwGKxoKysDK1bt0a3bt3q5BxErmIgICKqQKNGjTBixAiEhISgpKSk1jsYmkwmlJWVoWXLlhg8eDBbFZPoGAiIiCqh1WoxevRoREVFwWAwoKysrMarD+x2O/R6PaxWKzp06IChQ4fWeP8DotrAPgRERFUICQnB+PHjceDAARw5cgR6vR5KpRJ+fn5u7Ypot9thMplgsVgQHByMvn37olWrVm7vrEhUVxgIiIhuQaFQ4K677kLz5s2xd+9epKWlQa/XQyaTQaFQQC6X37Q6QBAE2O12WK1WWCwW2O12qFQqtG/fHjqdDhqNRqRXQ1QxBgIiIhfFxMTgoYceQk5ODk6dOoVz586hrKwMJpOpwsdLJBLI5XJotVp06NABbdq0cbsDIlF9kQgu3BArLi5GcHAwioqKEBQUVB91ERF5PLvdjqKiIuTm5iIvLw9msxk2mw0ymQwBAQEIDw+HVquFWq0Wu1TyUe6M37xCQERUTVKpFCEhIQgJCUHLli3FLoeoRrjKgIiIiBgIiIiIiIGAiIiIwEBAREREYCAgIiIiMBAQERERGAiIiIgIDAREREQEBgIiIiICAwERERGBgYCIiIjAQEBERERwcXMjx4aIxcXFdVoMERER1R7HuO3CxsauBQK9Xg8AiIuLq0FZREREJAa9Xo/g4OAqHyMRXIgNdrsdGRkZCAwMhEQiqbUCiYiIqO4IggC9Xo+YmBhIpVXPEnApEBAREVHDxkmFRERExEBAREREDAREREQEBgIiIiICAwERERGBgYCIiIjAQEBEREQA/j89VxvhtTWDXAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from demo_src.graph import generate_demo_graph, draw_graph\n", + "\n", + "demo_graph = generate_demo_graph()\n", + "draw_graph(demo_graph)" + ] + }, + { + "cell_type": "markdown", + "id": "12a9b2f4-570b-4f05-b77e-be1d261102ca", + "metadata": {}, + "source": [ + "Formally, this is an example of a classical combinatorial optimization problem with the form\n", + "\n", + "\\begin{align}\n", + "\\min_{x\\in \\{0, 1\\}^n}f(x)\n", + "\\end{align}\n", + "\n", + "Where the vector $x$ are the $n$ decision variables that correspond to every node of the graph. In this case, we have $n=5$, and each node can be 0 or 1 (included or not included in the cut). The minimum of $f(x)$ in this case will be when the number of edges traversed by the cut are maximal.\n", + "\n", + "As you can see, there is nothing relating to quantum computing yet. We need to reformulate this problem into something that a quantum computer can understand." + ] + }, + { + "cell_type": "markdown", + "id": "a06e4386-d7bd-4914-9baa-36a5cc60e3ab", + "metadata": {}, + "source": [ + "## Step 1. Map the classical inputs to a quantum problem\n", + "\n", + "The first step of the pattern is to map our classical problem (graph) into quantum **circuits** and **operators**. To do this, we take advantage of a series of mathematical reformulations, such as the QUBO notation.\n", + "\n", + "\n", + "
\n", + "In the QAOA methodology, we ultimately want to have an operator (Hamiltonian) that will be used to represent the cost function of our hybrid algorithm, as well as a parametrized circuit (Ansatz) that we use to represent quantum states with candidate solutions to the problem. We can sample from these candidate states and then evaluate them using the cost function.\n", + "
\n", + "\n", + "### Graph → QUBO\n", + "\n", + "The first step of the mapping is a notation change, can express our problem in Quadratic Unconstrained Binary Optimization notation:\n", + "\n", + "\\begin{align}\n", + "\\min_{x\\in \\{0, 1\\}^n}x^T Q x,\n", + "\\end{align}\n", + "\n", + "where $Q$ is a $n\\times n$ matrix of real numbers, $n$ corresponds to number of nodes in our graph, and $x$ is the vector of binary variables introduced above." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5947608b-f385-44bb-9bca-a7f632504a63", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Problem name: Max-cut\n", + "\n", + "Maximize\n", + " -2*x_0*x_1 - 2*x_0*x_2 - 2*x_0*x_4 - 2*x_1*x_2 - 2*x_2*x_3 - 2*x_3*x_4 + 3*x_0\n", + " + 2*x_1 + 3*x_2 + 2*x_3 + 2*x_4\n", + "\n", + "Subject to\n", + " No constraints\n", + "\n", + " Binary variables (5)\n", + " x_0 x_1 x_2 x_3 x_4\n", + "\n" + ] + } + ], + "source": [ + "from demo_src.map import map_graph_to_qubo\n", + "\n", + "qubo = map_graph_to_qubo(demo_graph)\n", + "print(qubo.prettyprint())" + ] + }, + { + "cell_type": "markdown", + "id": "a5b9e551-38a1-4543-b9f1-caaefb0ef3a9", + "metadata": {}, + "source": [ + "### QUBO → Hamiltonian\n", + "\n", + "We can reformulate the QUBO notation to express the problem as **a Hamiltonian, a function that represents the energy of a system**:\n", + "\n", + "\\begin{align}\n", + "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n", + "\\end{align}\n", + "\n", + "
\n", + "First, a variable change, we convert the binary variables $x_i$ to variables $z_i\\in\\{-1, 1\\}$ by doing\n", + "\n", + "\\begin{align}\n", + "x_i = \\frac{1-z_i}{2}.\n", + "\\end{align}\n", + "\n", + "Here, for example, we see that if $x_i$ is $0$ then $z_i$ is $1$. When we substitute the $x_i$'s for the $z_i$'s in the QUBO above, we obtain the equivalent formulations for our optimization task (the details of the computation are shown in Appendix A below):\n", + "\n", + "\\begin{align}\n", + "\\min_{x\\in\\{0,1\\}^n} x^TQx\\Longleftrightarrow \\min_{z\\in\\{-1,1\\}^n}z^TQz + b^Tz\n", + "\\end{align}\n", + "\n", + "Now, to obtain a quantum formulation of the problem, we promote the $z_i$ variables to a Pauli $Z$ matrix, i.e., a $2\\times 2$ matrix of the form\n", + "\n", + "\\begin{align}\n", + "Z_i = \\begin{pmatrix}1 & 0 \\\\ 0 & -1\\end{pmatrix}.\n", + "\\end{align}\n", + "\n", + "When we substitute these matrices in the QUBO above we obtain the following Hamiltonian\n", + "\n", + "\\begin{align}\n", + "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n", + "\\end{align}\n", + "
\n", + "\n", + "We refer to this Hamiltonian as the **cost function Hamiltonian**. It has the property that its gound state corresponds to the solution that **minimizes the cost function $f(x)$**.\n", + "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min f(x)$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "01a2d8eb-b63b-40bc-93c5-0b547c06b194", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Offset: -3.0\n", + "Cost Function Hamiltonian: SparsePauliOp(['IIIZZ', 'IIZIZ', 'ZIIIZ', 'IIZZI', 'IZZII', 'ZZIII'],\n", + " coeffs=[0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j])\n" + ] + } + ], + "source": [ + "from demo_src.map import map_qubo_to_ising\n", + "\n", + "cost_hamiltonian, offset = map_qubo_to_ising(qubo)\n", + "print(\"Offset:\", offset)\n", + "print(\"Cost Function Hamiltonian:\", cost_hamiltonian)" + ] + }, + { + "cell_type": "markdown", + "id": "33f71b0d-4a2a-4082-8c1a-ce9d2b769048", + "metadata": {}, + "source": [ + "### Hamiltonian → Quantum Circuit" + ] + }, + { + "cell_type": "markdown", + "id": "00431c46-30c2-40f9-99df-40baf8da98f6", + "metadata": {}, + "source": [ + "The Hamiltonian $H_c$ contains the quantum definition of our problem. We will now create a quantum circuit that will help us *sample* good solutions form the quantum computer. The QAOA is inspired from quantum annealing and proceeds by applying alternating layers of operators in the quantum cirucit.\n", + "\n", + "
\n", + "Losely speaking, the idea is to start in the ground state of a known system, $H^{\\otimes n}|0\\rangle$ above, and then steer the system into the ground state of the cost operator that we are interested in. This is done by applying the operators $\\exp\\{-i\\gamma_k H_C\\}$ and $\\exp\\{-i\\beta_k H_m\\}$ with the right angles $\\gamma_1,...,\\gamma_p$ and $\\beta_1,...,\\beta_p~$. \n", + "
\n", + " \n", + "The quantum circuit that we generate is **parametrized** by $\\gamma_i$ and $\\beta_i$ , so we can try out different values of $\\gamma_i$ and $\\beta_i$ and sample from the resulting state.\n", + "\n", + "

\n", + " \"QAOA\n", + "

\n", + "\n", + "\n", + "In this case we will try an example with 1 QAOA layer that contains two parameters: $\\gamma_1$ and $\\beta_1$.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7bd8c6d4-f40f-4a11-a440-0b26d9021b53", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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EViUWi2FjYwOxmG8/REQtBd/RiciqFAoFPv74YygUCqFLISIiM2GgJCIiIiKTMFASERERkUkYKImIiIjIJAyURGRVLi4uGDlyJFxcXIQuhYiIzEQqdAFEdG/x9/fHG2+8IXQZRERkRmyhJCKrqqysxLVr11BZWSl0KUREZCYMlERkVVlZWUhISEBWVpbQpRARkZnwkjcREenQaDRQqVRCl2EQiUQCkUgkdBlE9yQGSiIi0qFSqbB161ahyzBIQkICpFL+WSMSAi95ExEREZFJGCiJiIiIyCS8NkBEVhUZGYnjx48LXQYREZkRWyiJiIiIyCQMlERkVTk5OZg5cyZycnKELoWIiMyEgZKIrKq8vBznz59HeXm50KUQEZGZMFASERERkUkYKImIiIjIJAyURERERGQSBkoisipfX18sWbIEvr6+QpdCRERmwnEoiciq3NzcEB8fL3QZ1AwVFhaioqKCH0aImiAGSiKyqsLCQuzZswdxcXFwd3cXuhyysPz8fKSmpiIrKwtZWVkoKiqCSqWCVCqFp6cngoODERQUhOjoaLRq1are/RQWFuLNN99EeXk5XnvtNYZKoiaGgdIKFAoFVq5cie+++w4ymQze3t546KGHsGzZMjz//PP49NNPsX79esyZM0foUoksrqCgAKtWrULnzp0ZKFsolUqFU6dO4ddff8X58+frXU+hUCA9PR0AIJFI0Lt3bwwfPhxRUVEQiUTa9WrDZF5eHgDggw8+wOuvv15nHSISFgOlhZ05cwbx8fGQy+VwcnJChw4dkJeXh3Xr1uHKlSu4desWAKBr167CFiqQzs+Ng2fnYHhGB8OlfRuUXruOb3s/I3RZRGSknJwcbNiwAdnZ2TrLRCIR3NzcIJFIUFVVhZKSEu0ylUqFo0eP4ujRo+jevTsef/xxeHh46IRJLy8vPPvsswyTRE0MA6UFKRQKjBkzBnK5HPPmzcPixYvh4uICAFi5ciUWLFgAqVQKkUiE6OhogasVRo9FU1FxqwS3zmXC1tVR6HKIyEhqtRo//vgjvv32W6hUKu18Hx8fxMbGIiIiAoGBgbC3t9cuKy4uRlZWFlJTU7F//34UFxcDAE6fPo358+dj8uTJ2LlzZ50w+dprr6F169bWPTkiahADpQU9//zzkMlkmDNnDlavXl1nWVJSEjZv3oyzZ88iKCgIrq6uAlUprG/7PIPSq9cBAGP3vQ0bJ/sGtiCipkatVuPDDz/E/v37tfMCAgIwbdo0REdHQyzWP6CIq6srunTpgi5dumDChAk4evQovvrqKxQVFaGsrAyffPKJdl2GSaKmjcMGWUhaWhq2bNkCLy8vLF++XO86PXr0AAB06dJFO682gPbu3Rt2dnYt/rJObZike4ejoyP69OkDR0e2SLcEGo0GH3/8sTZMikQiPPjgg1i+fDm6du1ab5j8JxsbGwwaNAirV69Gz5496yxzdnZmmCRq4thCaSHJyclQq9WYOnUqnJ2d9a7j4OAAoG6gvHz5MrZu3YpevXrB1tYWhw8ftkq9RNbSrl07rF+/XugyyEz27t2LvXv3Aqi5sea5555D3759jd6fUqnUXuKuVVpaiqKiIgZKoiaMLZQWUvsGGxsbW+86MpkMQN1AOWjQIOTn52Pbtm2Ii4uzbJFEAlCpVCgtLa3Tz46aJ4VCgf/85z/a6WeeecakMPnPG3BqP3QDwIYNG1BVVWV8sURkUQyUFpKTkwMAaN++vd7lSqVS2/r490DZ2MtDRM1VRkYGhg4dioyMDKFLIRN98sknKC8vBwAMGTIE/fv3N3pf+u7mXr58OUJCQgAAeXl5+P77700vmogsgpe8LaSsrAwAtG+2/7RlyxYoFAq4uLggKCjIorX07NkTcrncoseoj41GjMXoLcixm4vwsHBUi9RCl2G08ePHG7T+9es1/WZ37tyJU6dONWqbcePGGVxXUzPusRfg5OyKfHk+AgICdKabGltb23r7fwNAbm4u/vjjDwCAh4cHZsyYYfSx9IXJ2j6TTz/9NF566SUolUr8+uuvePDBB2FnZ6d3P+Hh4WzFJDKBj48PTp48adS2DJQW4uPjg8LCQpw+fRoxMTF1luXn52P+/PkAgOjoaIvfeCOXy5Gbm2vRY9THViQB2ghy6GYjLz8PVZrme/m39sNTY9V+yCovL2/0tkL9/JqT+n+X+NUqFXJzc3Wmm5r6Qlut3bt3a78fPXq00TdZ3S1MAjV3i/fr1w8HDx5EWVkZjh49iiFDhujdV15eHiorK42qg4hMw0BpIXFxcUhLS8OKFSswfPhwhIeHAwBOnDiB6dOnQ6FQALDOgOY+Pj4WP0Z9bDRioPk2vlmFn69fs26hdHJyMmj92hDp4ODQ6G39/f0NrqupEUsk2q/+/v46002Nra1tvctUKhUOHDigXW/w4MFGHaOhMFlr+PDhOHjwIABg37599QZKPz8/tlASmcCUvMBAaSG140xeu3YNHTt2RGRkJCoqKnD58mXEx8cjMDAQu3btqtN/0lKMbb42h+o7FfgqZJpgx28OLmVcgo1j8x1/88SJEwatf/HiRSQnJyM+Ph6RkZGN2mbt2rVGVNa0LHvvKxSXlsHXxxcymUxnuqlRKpXYunWr3mW5ubnaluZu3boZ/KECaHyYBIDQ0FC0adMGBQUFyMzMhFKphFSq++fr0qVLeucTkeXxN89CAgICkJKSgvnz5+PAgQPIzs5Ghw4dsHHjRjzxxBPajubWCJRNWfD4QXAO8AYA2Hu6QmwjRfQLCQCAUtkNZH57UMjyyAJCQ0Oxa9cu7VOjqPnJzMzUfh8aGmrw9oaESaBmbMuQkBAUFBSguroaMpkMgYGBRtVORJbBQGlBUVFR2L59u8780tJSZGdnQywWo1OnTgJU1nSETxkGn34d68zrvmAKAEB+JJWBsgWSSqVwd3cXugwywdWrV7XfGxrsDA2TtYKDg3HkyBEANaNoMFASNS0MlAJITU2FRqNBeHi43o7s3377LQDgwoULdaYDAwN1niDR3P2SsFjoEsjKZDIZ1qxZg7lz5zbJu5upYXfu3NF+36pVq0ZvZ2yYBAA3Nzft9/WNnkFEwmGgFMC5c+cA1H+5e8KECXqnH3nkEXz++ecWrY3I0kpLS5GSkoInnnhC6FLISDNmzMD48eNRVVUFb2/vRm+nUChw8+ZNAIY/m7tHjx5Ys2YNbG1t6336GBEJh4FSAA0FSo1GY81yiIgM4ujoaNQwQWFhYVi4cCE++eQTzJ8/36BHKRp7TCKyDgZKATQUKImIWqrIyEisWLGCTwUjamEYKAVQ+5xvIqJ7EcMkUcvD32oisipvb28kJiYa1PeOiIiaNrZQEpFVeXp6YurUqUKXQUREZsQWSiKyquLiYuzZswfFxcVCl0JERGbCQElEVpWXl4dFixZpxyIkIqLmj4GSiIiIiEzCQElEREREJmGgJCIiIiKTMFASkVXZ2dkhIiICdnZ2QpdCRERmwmGDiMiqgoKCsGnTJqHLICIiM2ILJRERERGZhIGSiKwqPT0d/fv3R3p6utClEBGRmTBQEpFVaTQaVFdXQ6PRCF0KERGZCftQEhGRDolEgoSEBLPtb9XGLSgpK4OLkxPmPzVJZ9ocJBKJWfZDRIZjoCQiIh0ikQhSqfn+RGgAqDU1X6VSqc40ETVvvORNRERERCbhx0IisqrAwEAkJyfD399f6FKIiMhMGCiJyKrs7e0REhIidBlERGRGvORNRFaVn5+PpUuXIj8/X+hSiIjITBgoiciqioqKsG3bNhQVFQldChERmQkDJRERERGZhIGSiIiIiEzCQElEREREJmGgJCKrEovF6NatG8Rivv0QEbUUfEcnIqtSq9X4448/oFarhS6FiIjMhIGSiIiIiEzCQElEREREJmGgJCIiIiKTMFASkVW5uLhg5MiRcHFxEboUIiIyEz7Lm4isyt/fH2+88YbQZRARkRmxhZKIrKqyshLXrl1DZWWl0KUQEZGZMFASkVVlZWUhISEBWVlZQpdCRERmwkveREREemg0GqhUKqHLMIhEIoFIJBK6DLoHMVASERHpoVKpsHXrVqHLMEhCQgKkUv5pJ+vjJW8iIiIiMgkDJRERERGZhO3iRGRVkZGROH78uNBlEBGRGbGFkoiIiIhMwkBJRFaVk5ODmTNnIicnR+hSiIjITBgoiciqysvLcf78eZSXlwtdChERmQkDJRERERGZhIGSiIiIiEzCQElEREREJmGgJCKr8vX1xZIlS+Dr6yt0KUREZCYch5KIrMrNzQ3x8fFCl0HULKnVaojFbAuipoeBkoisqrCwEHv27EFcXBzc3d2FLofI4tRqNQoKCpCVlYX8/HxUV1dDLBbDyckJ7du3R1BQEJycnBrcT3p6OjZu3IgXX3wRfn5+VqicqPEYKInIqgoKCrBq1Sp07tyZgZJatKysLPz66684duwY7ty5c9d1AwICMHToUAwePFhvuExPT8fy5ctRUVGBN998E0uWLEHr1q0tVTqRwdhubiUKhQJJSUkIDQ2Fvb092rZti8TERJSVlWHWrFkQiUR49913hS7T6lyDfdF1/iSM2r4Mk89/gqkZm/DA7lWITnwIUgc7ocsjIjLYlStX8Oqrr2LhwoXYt29fg2ESAGQyGb788ks888wz+PLLL1FRUaFd9vcwCdSEz1atWlmqfCKjsIXSCs6cOYP4+HjI5XI4OTmhQ4cOyMvLw7p163DlyhXcunULANC1a1dhCxVA2OShiHxsJK7+ehJXvkuBRqmCT7+O6P7Swwgc0w87Ri+CqqJK6DKJiBpUXV2NrVu3Ytu2bVCr1dr5Dg4O6NChA4KDg9GuXTvY29tDrVajsLAQmZmZuHz5MjIzMwEAlZWV+Pnnn3Hq1CnMnj0bYrG4Tpjs3Lkz5s+fD1tbW0HOkag+DJQWplAoMGbMGMjlcsybNw+LFy+Gi4sLAGDlypVYsGABpFIpRCIRoqOjBa7W+rJ3/I4/13+P6pK/PsGnf/krirPy0eWF8QibMhQXP/tFwAqJiBpWWlqKFStWICMjQzsvICAA8fHx6N+/P+zt7fVuN2TIEAA1LZS7d+/Gvn37UFVVhYKCAixZsgRSqRRKpRIAwyQ1bbzkbWHPP/88ZDIZ5syZg9WrV2vDJAAkJSWhS5cuUCqVCAwMhKurq4CVCuPm2St1wmStrB+PAADcI9tZuySyMEdHR/Tp0weOjo5Cl0JkFmVlZVi6dKk2TEokEkyYMAFvvfUWhg0bVm+Y/LuAgAA89thjWLFiBSIiIrTzGSapuWCgtKC0tDRs2bIFXl5eWL58ud51evToAQDo0qWLdt63336LhIQEtG/fHo6OjoiMjMTLL7+M0tJSq9TdFDj5eQIAym/cFrYQMrt27dph/fr1aNeOHxao+VOr1Xj77beRnZ0NoGZYrKVLlyIhIQFSqeEXAX19fTFlyhRIJJI684cMGcIwSU0aA6UFJScnQ61WY+rUqXB2dta7joODA4C6gXL16tWQSCRYtmwZdu7ciaeffhobNmzAyJEj6/TLaalEYjG6vDAe6molMr8/JHQ5ZGYqlQqlpaVQqVRCl0Jksl27diE1NRUA4OLigtdeew1BQUFG7y89PR1vvfWWzu/H559/jqKiIpNqJbIk9qG0oL179wIAYmNj611HJpMBqBsof/rpJ3h7e2unBw8eDG9vb0ydOhWHDh3CoEGDLFRx09D7jUfRulcETi37CsVX8oQuh8wsIyMDM2bMwJdffonIyEihyyEymlwuR3JysnY6MTER/v7+Ru/vn3dzd+7cGba2tjh16hRKSkrw6aefYu7cuSbXTWQJDJQWlJOTAwBo37693uVKpRKHDx8GUDdQ/j1M1urZsycAIDc31+A6evbsCblcbvB25mCjEWMxejd6/W5JkxE1636kb/oV59Z/b8HKmo7wsHBUi5pvy/P48eMNWv/69esAgJ07d+LUqVON2mbcuHEG19XUjHvsBTg5uyJfno+AgACd6ZauOZ6/ra1tvd2VAOD7779HVVXNKBQjRoxAp06djD6WvjA5f/583LlzB5cuXUJJSQmOHTuGrKysu7aAhoeHa2siMpSPjw9Onjxp1LYMlBZUVlYGACgvL9e7fMuWLVAoFHBxcWnwEsm+ffsAAFFRUQbXIZfLjQqi5mArkgBtGrdu13kT0WXueGQk78XRpA8tW1gTkpefhypN8738W/tz3li1vw/l5eWN3laon19zUv/vEqZapUJubq7OdEvXHM/fzq7+sXBLS0tx5EjNzYOOjo6YMmWK0cepL0za2trC1tYWEyZMwKeffgoA2L17N5588sl695WXl4fKykqjayEyFgOlBfn4+KCwsBCnT59GTExMnWX5+fmYP38+ACA6Ohoikaje/eTm5uLVV1/FyJEjjRqr0sfHx+BtzMVGIwYa0fjWdd5EdH1xIi5v2YfD8zbcfZ/ODoh6YhTax/eGa5AvRBIxSq9dx7Xdp5C6YRsqbhbXu61ILMb4kxvg5OuJ0yv/iz/XfFvvumJbKSKmj0DQ2P5oFR4AiZ0NyvJvIu/gnzj//o8ovXq93m3dwvwx7uA7AICfH3wV14+l1buun69fs26hbMwj4/6uNkQ6ODg0eltTLiM2FeL/3WQhlkjg7++vM93SNcfzv9tNMAcOHEB1dTWAmm5Jtf3hDXW3MFlr4MCBSE5ORnl5OQ4fPoxp06bVO0qCn58fWyjJaKbkBQZKC4qLi0NaWhpWrFiB4cOHIzw8HABw4sQJTJ8+HQqFAsDdBzQvLS3F2LFjYWtrq/2Eaihjm6/NofpOBb4KmXbXdbrMHV8TJr85gENz3wc0mnrXdQ32xfDkV+Ac4I2cn48hY/NeqJVKeHcPR4cnRiFsciz2TH8Lij8y9G7vP7QbnHw9UZyVj9CJQ+oNlPZebhi++WV4dg5G7oGzOPPvr1FdVgGPDu0ROikWoROH4MDTa3Ft1wm924dNGYaqkjtQVVQhbHLsXQPlpYxLsHFseFiRpurECf2vQX0uXryI5ORkxMfHN7oP5dq1a42orGlZ9t5XKC4tg6+PL2Qymc50S9ccz1+pVGLr1q16l/3555/a7+Pi4ozaf2PCJFDz4at///7Ys2cPKisrkZ6ejm7duund56VLl4y6u5zIVLzL24KSkpLg6emJa9euoWPHjujcuTPCwsLQu3dvBAcHY+jQoQDq9p/8u/LycowZM0b7PFhfX19rlm8VkY+ORLekySiV3UB+yp8IfmgAghMGav/5DvprsHeJgy2GffESHH088NuMt7D/iX/j4ue/4NJ/9uDwv97Hzw+8ArFUimFfLIC9p/4xPcMeHorirHyceP0LuAb6wKdfR73rDfloHjw7B+PI/A+we/KbuPDRDmRs/g3HXvkUPw6bh4pbxRi84QW0Ctft+yWSShAyfhCyfzqKzO9SEDgmBlKn5hsYzS00NBS7du1CaGio0KUQGUWj0WifbOPq6go/Pz+D99HYMFmrQ4cO2u9rj03UlDBQWlBAQABSUlIwatQo2NvbIzs7Gx4eHti4cSN27NiBS5cuAdAfKKurqzF+/HicPHkSO3furPNm0pJ4dQ0BADgHeGPguucw6N3EOv+6JCZo1w2bMgxuof648NEOyH47rbOvm2ev4NTyzXDwboVOz4zVWW7v5Ya2cT1w5ZsDkP12GuU3biPs4WE66wUM7wGfvh2Qte0ILv1nj87y0qvXcTTpQ0gd7NB1/iSd5W1H9ISDdytc+WY/Lm/ZDxsnBwSN7W/Q69KSSaVSuLu7sxWFmq2bN2+ipKQEABAUFHTXLkv6GBoma49Ti4GSmiK+o1tYVFQUtm/frjO/tLQU2dnZEIvFOncG1o5d+dtvv+Hnn39G796Nv0u6uTn0wns49MJ7jVo3cHRfANAb8mpd/nofer/xKNqP6ouTb26qsyxkwmCIJGJc+eYANCo1Mr9LQcSMEfjdxbHO03oCR8f87zi76z1O7t4/UJarQMCw7hDbSqGuUmqXhU0ZipKcAhT8XnOZ++a5TIRNHoqMzb816jxbOplMhjVr1mDu3LlN9u5eorspLCzUfm/olSNjwiQAtGnTBiKRCBqNBrdv3za4ZiJLYwulQFJTU6HRaBAWFqbTufrZZ5/FN998g7lz58LR0RG///679t+NGzcEqlh4rSLaoarkDkqy6x8CSVVehaLLeXBp3wbSf/RLDJsyFAW/p6FUVvMaXv56P6QOdggeN6DucSLbAgBunsu6az03z2dB6mAH16C//qA4tHGH/5CuuPLNAe28y1/vR+teEXALa5o3HlhbaWkpUlJS7qknP1HL4u7ujokTJ+LBBx9EdHR0wxv8T1VVFdauXWtwmAQAsViMsWPHIiEhAcOG6V5ZIRIaA6VAzp07B0D/5e6dO3cCAN566y3ExMTU+bdjxw6r1tmU2Lo4oLpY97nf/1RdWrOOjfNfgdK7ZwRahQXg8tf7tfMKL+Tg5rkshE0ZWvc4zjUBv6FjVZfWDH9j6/rXB4LQSbEQiUW4/M1fx8n8LgWqqmqETR76z10QUTPk5eWFhx56CJMnT0b37t0bvZ2trS0SExNhZ2dn1LO5J0+ejAkTJmj73xM1JbzkLZC7BcraZ8JSXVUl5bBxaXhoDhtnR6hVKlTcKtHOC5syFKqqatw6nwWXwL+GRcjbfwadnxsH96j2KEyrGYi+qjaQujqi6nb9rWg2zjW1VP0teIZNjkXhhRyIxOI6x7l+Ih0h4wfh1LKvoFE13yGCiMg0kZGReP311+Hv789nc1OLwkApkLsFStLvdvpV+MR0hEugT72XvSUOtnAL9UOZTAGNsmbgZKmjPYIe6AeJrQ0e2LNa73ZhU2Jx/LXPa45z8Rq8okPg2TkI+Snn6q3Hs1MQlOWVKM7KBwD4xHTUXv5OOPqu3m3aDu+Bq78YNswOEbUspjzrm6ipYqAUSO1zvqnxsrf/Dp+Yjgh/eBhOLftK7zqhE4ZAYmuDK1sPaucFPtAPNs4ONc8Gz8zX2Sbq8fsRnDAIJ9/8D9TVSuT8fAyhE4cg/OG4egOlf2xXOPl7IXvH79obckKnDIWqogopz6+HRq07lmbMyqcQNmXYPR8ovb29kZiYqPcRo0RE1DwxUFKzkZH8G6IeG4kOT42G/GgqcvedqbPco3MQui98GHfkt3Dxs1+088OmDEXFrRKcf/9HvZebpY52GLjuObS9rxdyth/FtV0nUHA8DUEP9kfugbO4/N+64d85wBsxK5+CsrwSZ1ZtAQDYuDgicHRf5B44i+yfjuqtPyCuO0LGD4ZD61Yov37btBejGfP09MTUqVOFLoOIiMyIgZKaDVV5FX57dAWGb34ZwzYtRM6OY5AfSYVGpYJX11CEjB+MqqJS/PboClQoigAAbqF+aNM7Ehn/3Vtv38Vrv56Eqqoa4Q8PRc72mjC4/4l/Y/hXL2PAmmcQ9EAMZL/9AeWdCrj/70k5YqkEB59Zi9vp1wAAweMGQOpgh5wdv9dbf86OYwibPBShE4fg3Ls/mPfFaUaKi4tx/Phx9O7dG66u+gegJyKi5oWBkpqV4it52Dbsxf89y7sPAoZ1g41Tzc0xhRevYufYV+reJDOlZniNnJ+P1bvPqqIyyI+kwndQNBz9PHEn7ybKr9/GjtGLEDGj5lne3ZImQWJrgzsFhcj6/hDOv/8jSnIK/nacoVBXK3Ht1/ofc5l38CyqSu4gdFLsPR0o8/LysGjRInz55ZcMlERELQQDJTU71aXl+HPNt9rncIskYgz5aB7ax/dB6OShuPDhXwPJn3xzk84A5/rsnrJUZ56qshoXPtqBCx81PFTT9viXGlxHXaXE5vAZDa5HRETU3HAcSmr2NCo1Djy1Btf2nELvJY8iYsYIoUsiIiK6p7CFkloEdbUSv01fLnQZRERE9yS2UBKRVdnZ2SEiIgJ2dnZCl0JERGbCFkoisqqgoCBs2tRwv1YiImo+2EJJRERERCZhoCQiq0pPT0f//v2Rnp4udClERGQmDJREZFUajQbV1dXQaHQfT0lERM0T+1ASERHpIZFIkJCQYLb9rdq4BSVlZXBxcsL8pybpTJuDRCIxy36IDMVASUREpIdIJIJUar4/kxoAak3NV6lUqjNN1JzxkjcRERERmYQfiYjIqgIDA5GcnAx/f3+hSyEiIjNhoCQiq7K3t0dISIjQZRARkRnxkjcRWVV+fj6WLl2K/Px8oUshIiIzYaAkIqsqKirCtm3bUFRUJHQpRERkJgyURERERGQSBkoiIiIiMgkDJRERERGZhIGSiKxKLBajW7duEIv59kNE1FLwHZ2IrEqtVuOPP/6AWq0WuhQiIjITBkoiIiIiMgkDJRERERGZhIGSiIiIiEzCQElEVuXi4oKRI0fCxcVF6FKIiMhM+CxvIrIqf39/vPHGG0KXQUREZsQWSiKyqsrKSly7dg2VlZVCl0JERGbCQElEVpWVlYWEhARkZWUJXQoREZkJAyURERERmYR9KImIiEiHRqOBSqUSugyDSCQSiEQiocu4JzFQEhERkQ6VSoWtW7cKXYZBEhISIJUy2giBl7yJiIiIyCSM8URkVZGRkTh+/LjQZRARkRmxhZKIiIiITMJASURWlZOTg5kzZyInJ0foUoiIyEwYKInIqsrLy3H+/HmUl5cLXQoREZkJAyURERERmYSBkoiIiIhMwkBJRERERCZhoCQiq/L19cWSJUvg6+srdClERGQmHIeSiKzKzc0N8fHxQpdBRERmxBZKIrKqwsJCfPPNNygsLBS6FCKystLSUly/fh1yuRy3bt2CWq02aPv9+/cjPz/fQtWRKdhCSURWVVBQgFWrVqFz585wd3cXuhwisqDCwkKkpKTg0qVLyMzMxK1bt+osd3BwQGBgIIKDgxETE4OQkBCIRCK9+9q1axc+++wzuLu747XXXmO3mSaGLZRWoFAokJSUhNDQUNjb26Nt27ZITExEWVkZZs2aBZFIhHfffVfoMomIiMzi8uXLWLt2LebMmYPNmzfj5MmTOmESqBmXNi0tDTt27MArr7yCl19+Gfv379dpuawNk0BNSD1x4oRVzoMajy2UFnbmzBnEx8dDLpfDyckJHTp0QF5eHtatW4crV65of8G6du0qbKECcQ3xQ5d/TYBn5yA4tnGH2EaKslwFZL+dxvn3f0T59dtCl0hERI1UWVmJLVu2YOfOndBoNHWW1bZGuru7QywW486dO7h69SoUCoV2nczMTHzwwQfYt28fnnrqKfj5+dUJkwDw4IMPYsyYMVY7J2ocBkoLUigUGDNmDORyOebNm4fFixfDxcUFALBy5UosWLAAUqkUIpEI0dHRAlcrDCdfTzi2boWrO4+jLO8mNCoV3CPbIXxaHILG9se2uBdRcbNY6DKJiKgBMpkMq1evhlwu185zc3NDbGwsBg4cCF9fX4jFuhdGi4uLcerUKezevRuZmZkAgPT0dCxYsAC9e/fG4cOHtes++OCDmDRpUr2XxUk4DJQW9Pzzz0Mmk2HOnDlYvXp1nWVJSUnYvHkzzp49i6CgILi6ugpUpbDyD51D/qFzOvPlv6ch9qN5CJ0Ui/Pv/yhAZWQpjo6O6NOnDxwdHYUuhYjMJCsrC8uWLUNJSQkAwMbGBhMnTsTIkSNhY2Nz121dXV0RGxuL2NhYpKam4sMPP0RBQQGqq6sZJpsR9qG0kLS0NGzZsgVeXl5Yvny53nV69OgBAOjSpYt2XkpKCuLi4uDr6ws7OzsEBARg0qRJSEtLs0rdTUWZ7AYAwLaVk8CVkLm1a9cO69evR7t27YQuhYjMQC6XY/ny5dowGRgYiLfeegtjxoxpMEz+U8eOHbFixQpERETUmd+1a1eGySaOLZQWkpycDLVajalTp8LZ2VnvOg4ODgDqBsrCwkJ07twZTz31FFq3bg2ZTIbly5cjJiYG58+fR0BAgFXqtzaJnQ2kTvaQ2NmgVXhb9Hh5GgBA9tsfAldG5qZSqVBeXg4HBwdIJBKhyyEiE6jVarz77rsoLq7pmhQeHo6XXnrJpCsQBw4cQHp6ep1558+fR15eHvz9/U2qlyyHgdJC9u7dCwCIjY2tdx2ZTAagbqB84IEH8MADD9RZr1evXoiIiMDWrVuRmJhogWqFF/bwMPRd9rh2uuRqAQ4++w6uH7u3WmbvBRkZGZgxYwa+/PJLREZGCl0OEZlgx44duHz5MgDAx8cHCxYsMClM/vMGnKCgIGRlZUGpVGLDhg1444039PbDJOExUFpITk4OAKB9+/Z6lyuVSm3fkL8HSn08PT0BAFJpy/3vuvrLcRRdzoWNkz08OgWh7YhesPNwEbosIiKqx61bt/D1118DAEQiEZ5++mk4ORnfTUnf3dzjxo3DSy+9hPz8fFy+fBl79+5FXFycybWT+bXchCKwsrIyADVjbOmzZcsWKBQKuLi4ICgoSGe5SqWCWq1GTk4OFi5cCB8fH0ycONGoWnr27FnnrjtrstGIsRi9G1zvTv4t3MmvGULp6i8nkLPjGEbvfAtSBzucW//9XbcNnTgEvd98DMVZcmwfuQAAYO/pioHrn4NLex+oqqrx+8KPUPB7TWvnwPcS4TegE7J+PIzjr31+132LbaUY9G4iWkW2BTQaZP14BGff/gYA0HXeREQ+dh+un7yEvY+uAAC4BPlg4DvPwc7DBdUld3Ao8V3cvlTTEn3ft6/Do0N7nF3zLS58tEN7jPCwcFSLDHtaRFMyfvx4g9a/fv06AGDnzp04depUo7YZN26cwXU1NeMeewFOzq7Il+cjICBAZ7qlu9fPH2h+r4GtrW299wAAwL59+1BdXQ0AuO+++3T6PRpCX5is7TM5e/ZsLF68WLvesGHD6u1LGR4ejqqqKqPruNf5+Pjg5MmTRm3LQGkhPj4+KCwsxOnTpxETE1NnWX5+PubPnw8AiI6O1vuLMXjwYG0LZmhoKPbu3Qtvb2+japHL5cjNzTVqW1PZiiRAG8O3K0zLwa3zWYh85L4GAyUAyI+kYu9jK7XTPV6ehhunMrD74f+DZ5cQDP00Cd/2eQYapQopz76DrvMmwtat4csyQWP7w97bDT8MngupvS2mXPgMaR/vQFXxHQBA5ncpdUJpv5VP4dJ/duPy1/vRflRfDHhnDrbHvwQA2DX+dQxY+6zOMfLy81ClUTVYS1NV++GpsWo/ZJWXlzd6W6F+fs1JrVJpv+bm5upMt3T3+vkDze81sLOzq3eZUqnEnj17ANS0To4ePdro49wtTAJAREQEIiIikJ6ejmvXruHixYuIiorSu6+8vDxUVlYaXQsZj4HSQuLi4pCWloYVK1Zg+PDhCA8PBwCcOHEC06dP1w7kWt+A5p988glu376NrKwsrFq1CiNGjMDhw4eNujPWx8fH6PMwlY1GDBjZ+Caxt4Wte80NTfd9+zoK03Jw/NWaNx0bF0ckHF2P7wfP1btt4AMx+C7mOQDAzbNXcKfgFnxiOiA/RXeIortxDvDGrfNZgEYDr26hqCotR1WJ/lZne09XeHYJwa+T3wQA5Oz4HX2XzYJLoA9KsutvIfbz9WvWLZSGXuKqDZEODg6N3rYldMQX/+8GJLFEAn9/f53plu5eP3+g+b0Gtra29S67ePEiCgsLAdRcBfPy8jLqGA2FyVrDhw/X3qhz+PDhegOln58fWyhNYEpeYKC0kNpxJq9du4aOHTsiMjISFRUVuHz5MuLj4xEYGIhdu3bV23+y9tJBnz59MHLkSAQGBmLlypVGPaLR2OZrc6i+U4GvQqbVu9zBuxXKb9zWme/TryNaRbaF/MgFAMCvk97Ag/vXwC3MH0UZuQibMhSy3/5ApZ5Bz+3cnSGWSuvst/TaDTj5G97CKxKLAY0GQz9bgHYje+H8B9uAfzz9oZaTvxfKCwqhUf0VDktzFXDy97proLyUcQk2jvYG19ZUGPoINKVSiUcffRQuLi6N7he8du1aIyprWpa99xWKS8vg6+MLmUymM93S3evnDzS/10CpVGLr1q16l125ckX7fe0QeIZqbJisPYZIJIJGo9EOfq7PpUuXWvT9Bk0Zb5WykICAAKSkpGDUqFGwt7dHdnY2PDw8sHHjRuzYsQOXLl0C0PANOQDQqlUrhIaGau+ka0n6rngCo7YvQ/eFDyN8+nBEPX4/Bqx7DsOTX4GytAInl3wBANCo1Mj47z6ETowFRCJEPnof0j7dabU69z62AluiH4d7RFt0mWtYn0GqSyqVwt3dnW/6RM1YVlaW9vuQkBCDtzckTAI1VzR8fX0BAFevXoVSqTT4mGRZfEe3oKioKGzfvl1nfmlpKbKzsyEWi9GpU6cG93P9+nWkp6ejT58+lihTUFnfH0LIhCEISRgEe09XaDQalOUqcGnTbpzfsA1luX97xuvWgxi1fRmun0xH5a0S3Dx7Re8+KwtLoVap6rR+Orf1RlnuDZNqLb9x+3+hdoje5WW5Cji0cYdIIta2Ujr7e9U5B6oZLmvNmjWYO3duk7wRgYgalpeXB6DmA6Kfn59B2xoaJmsFBgYiLy8PSqUSBQUFTbKbwL2MgVIAqamp0Gg0CA8P1xmva9q0aQgNDUXXrl3RqlUrZGRkYM2aNZBKpZg7V39/weYs+6ejyP7paKPWvSO/haLLuYhZ8SROvvnlXdfN+ekoImaMwJl/fw3PLiFw9PGA/OgFvet6dQ1F90VT8evEJXqXt+4TBamTPZRlFWjTtwNup1/Tu17FzWLcOpeFkIRB2ptyyvJv3fVy972otLQUKSkpeOKJJ4QuhYiM5ObmBg8PD9ja2hr0gII9e/YYFSYBwN3dHe7u7gY/fYesg4FSAOfO1dwYou9yd9++ffHll1/inXfeQUVFBdq2bYvY2FgsWrSo3jEt7yVXth5Er8UzkL3t7iH05NL/YOC7z+Ohw+uhqlYiZc46aJT676R2busNVUX9nbhtHO0xdu+/oSyrQMnV6zg897161z2StBED1j6Lzs8/hOrSchx6of51iYiaq5dfftmo7QICAmBnZ4fKykqDn809ffp0TJ8+3ajjkuUxUArgboFyzpw5mDNnjrVLajbKZArcyb8FdfXd+89UKIqw+393WzekTUxHnHu3/qGJcvf90eB4lbWKr+Th5zHGvdESEbV0kZGRWLhwIVJTU/HQQw/x2dwtCG/KEcDdAiUZTllRBY+OgRj9y4pGrT/wvUQEJwzUDv9zbNHHuH78osHHrS6rQMDwnhj6+YJGrX/ft6+jTUwHVN/hGGlEdO+KjIxEQkICw2QLwxZKAdQ+55sMJz+aim3D59eZl73tCLK3HWn0PlKefafR657599f1Lkv9YBtSP9jW6H3tGv96o9dtyby9vZGYmGj0QP1ERNT0MFASkVV5enpi6tSpQpdBRERmxEveRGRVxcXF2LNnD4qLdQelJyKi5omBkoisKi8vD4sWLdKOY0dERM0fAyURERERmYSBkoiIiIhMwkBJRERERCZhoCQiq7Kzs0NERATs7OyELoWIiMyEwwYRkVUFBQVh06ZNQpdBRERmxBZKIiIiIjIJAyURWVV6ejr69++P9PR0oUshIiIzYaAkIqvSaDSorq6GRqMRuhQiIjITBkoiIiIiMglvyiEiIiIdEokECQkJZtvfqo1bUFJWBhcnJ8x/apLOtDlIJBKz7IcMx0BJREREOkQiEaRS88UEDQC1puarVCrVmabmjf+DRGRVgYGBSE5Ohr+/v9ClEBGRmTBQEpFV2dvbIyQkROgyiIjIjHhTDhFZVX5+PpYuXYr8/HyhSyEiIjNhoCQiqyoqKsK2bdtQVFQkdClERGQmDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIrMrDwwOPPPIIPDw8hC6FiIjMhIGSiKxKLBbDxsYGYjHffoiIWgq+oxORVSkUCnz88cdQKBRCl0JERGbCQElEREREJmGgJCIiIiKTMFASERERkUkYKInIqlxcXDBy5Ei4uLgIXQoREZmJVOgCiOje4u/vjzfeeEPoMoiIyIzYQklEVlVZWYlr166hsrJS6FKIiMhMGCiJyKqysrKQkJCArKwsoUshIiIz4SVvIiIiIj00Gg1UKpXQZTSaRCKBSCQS5NgMlERERER6qFQqbN26VegyGi0hIQFSqTDRjpe8iYiIiMgkDJREREREZBJe8iYiq4qMjMTx48eFLoOIiMyILZREREREZBIGSiKyqpycHMycORM5OTlCl0JERGbCQElEVlVeXo7z58+jvLxc6FKIiMhMGCiJiIiIyCQMlERERERkEgZKIiIiIjIJAyURWZWvry+WLFkCX19foUshIiIzYaAkIqtyc3NDfHw83NzchC6FiKhZUavVuHnzptBl6MWBzYnIqgoLC7Fnzx7ExcXB3d1d6HKIiCyquroamZmZyMzMRFZWFm7evAmlUgmpVAo3NzcEBwcjKCgIISEhsLe3r3c/arUa77//PlJTU/Hqq6/Cz8/PimfRMAZKIrKqgoICrFq1Cp07d2agJKIWq6CgAHv27MH+/ftRUlJS73pHjhwBADg4OGDQoEEYPnw4AgIC6qxTGyYPHToEAFi+fDnefvtt2NjYWO4EDMRL3lagUCiQlJSE0NBQ2Nvbo23btkhMTERZWRlmzZoFkUiEd999V+gymwSJgy0Sfn8Pj+Z/iz7/N0vocoiIiAxSUVGBTz75BC+88AJ++umnu4bJvysvL8euXbvw4osvYt26ddrt/hkmJRIJHnnkkSYVJgG2UFrcmTNnEB8fD7lcDicnJ3To0AF5eXlYt24drly5glu3bgEAunbtKmyhTUS3+ZNh7+kqdBlEREQGS01NxQcffIAbN25o50mlUvTq1QsdOnRAcHAwfH19YWtrC6VSCblcjszMTKSnp+P3339HZWUlgJpWy9TUVMyaNQvHjx+vEybnzp2Lnj17CnJ+d8NAaUEKhQJjxoyBXC7HvHnzsHjxYri4uAAAVq5ciQULFkAqlUIkEiE6OlrgaoXn0TkIHZ4YhZNLN6H3648KXQ4REVGjHTp0CO+//z7UajUAwM7ODg888ADi4uL03oQolUoRGBiIwMBADB06FDNmzMD+/fvx3XffoaysDEVFRXj77be16zflMAnwkrdFPf/885DJZJgzZw5Wr16tDZMAkJSUhC5dukCpVCIwMBCurvd2q5xILEa/1bORu+8Mru44JnQ5ZEGOjo7o06cPHB0dhS6FiMgsjhw5gvfee08bJqOiorBixQokJCQ0ekQLJycnjBo1CqtXr0b37t3rLBOLxU06TAIMlBaTlpaGLVu2wMvLC8uXL9e7To8ePQAAXbp0qXc/8fHxEIlEeP311y1RZpPR4cnRcAv1x7FFHwtdCllYu3btsH79erRr107oUoiITJaTk4P33nsPGo0GABAXF4dXX30VPj4+Ru3Pzc0NDg4Odeap1eq73gHeFDBQWkhycjLUajWmTp0KZ2dnvevU/sDUFyi//vprnDlzxlIlNhnObVuj6/yJOPv2tyiV3Wh4A2rWVCoVSktLoVKphC6FiMgkSqUSGzZs0L6fxcbGYtasWRCLjYtXtTfgHD58GAAgEom0yzZu3IiKigrTi7YQBkoL2bt3L4CaH676yGQyAPoDZXFxMV544QWsXr3aMgU2ITErn0RpTgFSN/4kdClkBRkZGRg6dCgyMjKELoWIyCQ//fQTsrOzAQBt27bFzJkz64RAQ+i7m/tf//oXoqKiAAA3btzA5s2bzVK3JfCmHAvJyckBALRv317vcqVSqf0Eoi9QvvzyywgPD8fUqVMxbdo0k2rp2bMn5HK5Sfswlo1GjMXoXe/y4ISB8BsUjZ3jXoNGeW+2WIWHhaNapBa6DKONHz/eoPWvX78OANi5cydOnTrVqG3GjRtncF1NzbjHXoCTsyvy5fkICAjQmW7p7vXzB/gaNMfzt7W1rbfbWlVVFXbs2AGgpo/j7NmzjR7KR1+YrO0z2bZtWyxYsACVlZXYu3cvxo8fX+99F+Hh4aiqqjKqBgDw8fHByZMnjdqWgdJCysrKANSMK6XPli1boFAo4OLigqCgoDrLTp48iY8++qjRf2wbIpfLkZuba5Z9GcpWJAHa6F8mtpWi1+uPQvbbHyi/fhsugTX9TRx9PWq2dXWES6APKm8Vo6r4jrVKtrq8/DxUaZpvmK79WW+s2t+J8vLyRm8r1M+vOan/d0lMrVIhNzdXZ7qlu9fPH+Br0BzP387Ort5lR48eRWlpKQCgX79+CAkJMeoYdwuTQE3Ii4uLw44dO6BUKrFv3z6MHTtW777y8vK0Qw9ZGwOlhfj4+KCwsBCnT59GTExMnWX5+fmYP38+ACA6OrpO87hKpcJTTz2FOXPmoGPHjmarRSg2GjFQT+Ob1N4WDl5uaDu8B9oO76GzPGT8YISMH4wTS75E6gfbLFypcPx8/Zp1C6WTk5NB69eGSAcHh0Zv6+/vb3BdTY1YItF+9ff315lu6e718wf4GjTH87e1ta13WW3XNgAYMWKEUftvKEzWGj58uLY1dO/evfUGSj8/P5NbKI3FQGkhcXFxSEtLw4oVKzB8+HCEh4cDAE6cOIHp06dDoVAA0B3Q/N1330VBQYFZ7+o2tvnaHKrvVOCrEP2X7KvvVGLf47p9RO09XRGz4knI9v6BjM2/oTAtx9JlCupSxiXYODbtu/fu5sSJEwatf/HiRSQnJyM+Ph6RkZGN2mbt2rVGVNa0LHvvKxSXlsHXxxcymUxnuqW7188f4GvQHM9fqVRi69atOvOrq6tx+fJlAICvry/CwsIM3ndjwyRQE/SioqKQlpaGgoICFBYW6n107aVLlyCVChPtGCgtJCkpCZs3b8a1a9fQsWNHREZGoqKiApcvX0Z8fDwCAwOxa9euOv0nFQoFXn31VaxevRpKpRK3b9/WLquoqMDt27fh6upq9N1jTY1GqULOjt915jsHeAMASrLlepdT8xYaGopdu3bVGZeViKg5uXr1qvbO7rCwMINvxDEkTNYKDQ1FWloaACAzM1M79GBT0TKSSRMUEBCAlJQUjBo1Cvb29sjOzoaHhwc2btyIHTt24NKlSwDq3pAjk8lQUlKCp556Cu7u7tp/ALBixQq4u7vj6tWrgpwPkblIpVK4u7sL9imaiMhUtXd2A9C5D6IhxoRJAAgODtZ7/KaC7+gWFBUVhe3bt+vMLy0tRXZ2NsRiMTp16qSdHxoain379umsHxsbi0ceeQSPPvqooP0hraVUdgOf+xp25zA1HzKZDGvWrMHcuXOb7J2dRER3U3szDgB4eno2ejtjw+Q/j/P34zcVDJQCSE1NhUajQXh4eJ3Hzzk7O2PIkCF6twkMDKx3GVFzUlpaipSUFDzxxBNCl0JEZJT+/fsjNDQUVVVVBrVQ5uXlafudG/psbn9/fyxYsAA2Njbw8vIyqm5LYqAUwLlz5wDc/ZGLRERE1DR5eXkZFeoCAgKwcOFCrF69GrNnzzbo2dxOTk7o1q2bwce0FgZKARgaKGufD0pERETNW2RkJNatW1fnCmVLwJtyBMAWSiIiontXSwuTAFsoBfH3wVCJ7jXe3t5ITEyEt7e30KUQEZGZMFASkVV5enpi6tSpQpdBRERmxEveRGRVxcXF2LNnD4qLi4UuhYiIzISBkoisKi8vD4sWLUJeXp7QpRARkZkwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSiKyKjs7O0RERMDOzk7oUoiIyEw4bBARWVVQUBA2bdokdBlERGRGbKEkIiIiIpMwUBKRVaWnp6N///5IT08XuhQiIjITBkoisiqNRoPq6mpoNBqhSyEiIjNhH0qyKKmDHaZe+Y/QZTRpUgfenEJE1BRJJBIkJCSYZV+rNm5BSVkZXJycMP+pSfXOM4VEIjF5H8ZioCSLEolEsHG0F7oMIiIig4lEIkil5olKGgBqTc3X2n3qm9dc8ZI3EREREZmkecdhImp2AgMDkZycDH9/f6FLISIiM2GgJCKrsre3R0hIiNBlEBGRGfGSNxFZVX5+PpYuXYr8/HyhSyEiIjNhoCQiqyoqKsK2bdtQVFQkdClERGQmDJREREREZBIGSiIiIiIyCQMlEREREZmEd3kTkUl69epl0PoBAQFYvHgx4uLi4Ovra6GqiIjImhgoiciqfH198frrrwtdBhERmREveRMRERGRSRgoiYiIiMgkDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSgIAvP766xCJRDr/Ll++LHRpRFSPn3/+GV27doWdnR0CAwPx9ttvC12SVR08eBBjx45F+/btIRKJsHTpUqFLsqpVq1YhJiYG7u7uaNWqFQYMGIBffvlF6LKsZtOmTejRowfc3d3h4OCAqKgovP3229BoNEKXJoi9e/dCIpEgNDRUkONLBTkqNUmBgYE4evRonXne3t4CVUNEd3Py5EmMHTsWL774IpKTk3Hs2DHMnj0bjo6OmD17ttDlWUVpaSk6dOiAhx9+GC+88ILQ5Vjd3r17MXPmTPTq1QuOjo74+OOPMXr0aBw4cAD9+/cXujyLa926NV599VVERETAzs4OKSkpeOaZZyCRSJCYmCh0eVYll8vxyCOPYMSIEcjIyBCkBgZK0pJIJPDx8RG6DCJqhLfffhu9evXC8uXLAQBRUVFITU3FW2+9dc8Eyvvvvx/3338/AGDBggUCV2N9O3furDO9cuVK/PLLL/juu+/uiUB533331ZkODg7GDz/8gP37999TgVKtVmPatGl49tlnUVFRIVig5CVv0pLJZAgICEBAQADi4+Nx5MgRoUsionocPnwYI0eOrDNv5MiRyMnJgUwmE6gqEpJarUZxcTGcnJyELsXqNBoNjh8/jsOHDyM2NlbocqzqzTffhEgkEvxDFVsoCQDQu3dvfPbZZ+jQoQOKi4uxceNGDBw4EL/88guGDx8udHlEzcad8grI5Aqd+UqVSvv1UpZMZ/rv/Np4wtnR4a7Hyc/P17miUDudn5+PgIAAo8/BVFnX8lGtVNWZZ8j5Ozvaw6+Nl3WKtYCbhcW4ebtYZ74hr0FIOz9IJIa1+Sxbtgy3b9/Gk08+aWTl5lGtVCLrmlxnviHn7+XhBg83lwaPVVRUBH9/f1RVVUGtVmPx4sV4/vnnzXAWppHJb+BOeWWdefrOt77XwM5GivYBDV8x3LdvHz744AP88ccfEIlE5irfKAyUBADay0a1Bg4cCJlMhlWrVjFQEhnAztYWvx48AZn8ht7ld8or8OnXP9c73cbLHXMeGWfxOi0pr+AmfvpN/xWOhs5fBOCJKaMtXaJFSSRibP5xDyoqq/Qub+g16NEpHOFBhn0geP/997Fs2TJs27ZN0A8TACCVSHDibBrOpWfpXd7Q+Ts52uOFmeMbdSwXFxecOXMGd+7cwZEjR7Bw4UL4+flh1qxZpp2EiUrLyvH5t/pvkPrn+eqbNz5+cIOBUqFQYNq0afjss8+aRHc1XvKmesXExCA7O1voMoiaFYlEjImjYyGVSgzfVlyzrY204c/6vr6+kMvrtgIVFBRolwkppkdHhLb3N2rbAb2iEdzOz8wVWVcrV2eMHW5cH8ZWrs4YE9fPoG1Wr16N+fPnY9u2bYiLizPquOYkEonw4H0D4eJ091b2+jw0chBcnBwbta5YLEZoaCiio6Mxe/ZsJCUl4eWXXzbquOYUGdIOfbpGGbVth7D26NE5vMH1zp8/j7y8PIwePRpSqRRSqRRvvPEGrly5AqlUis2bNxt1fGMxUFK9Tp8+jbZt2wpdBlGz09qzFe4f0sfg7eIG9IB/Iy/19u/fH7t27aoz75dffkH79u0Fb6ESi0SYcP9g2NvZGrRdGy93jBjU00JVWVfXDqGIjgw2aBsRgImjYw163V577TUsWbIEP//8c5MIk7WcHOwxPn6wwdv17ByBjmGBRh9XrVajoqLC6O3N6f7YvvBs5WrQNs6ODnjovkGNunzdq1cvnDt3DmfOnNH+mz17Ntq2bYszZ85g1KhRxpZuFF7yJgDAv/71L4wePRqBgYEoLi7GRx99hN27d+PHH38UujSiZqlv945Iu5yDjOzcRq3f3r8NBvfp0uj9z507F/369cPLL7+M6dOn49ixY1i/fj3WrFljbMlm5ebqjAdHDMB/f9rbqPUlYjEmjRnaqNbZWqWlpdqxcquqqiCXy3HmzBk4OzsLNhZfLZFIhAdHDECWTI6S0juN2mZg72gEt2186/ILL7yAjRs3Ijk5GREREdoWawcHB7i5uRlVtzlF/K+V7tiZtEat7+7mgtHDYhq9/8WLF2PgwIEIDg5GdXU1Dh48iBUrVuCxxx4ztmSzsrO1wcTRsfjgq22NHhvzofhBcG5ky66TkxM6depUZ17r1q1ha2urM98a2EJJAGo68c+YMQNRUVEYMWIE0tPTsWfPHowZM0bo0oiaJbFIhPH3D4GDvV2D69raSDFxVCzE4sa/Jffq1Qs//PADtm/fji5duuC1117D//3f/zWpIYMMaaUbPrAn/Fp7GrT/kydPolu3bujWrRvy8/Px3nvvoVu3bnj88ceNKdfsHB3sMaGRrXQ+3h4YMbCXQft/5513UFFRgXHjxsHX11f7rykNmTMqti883RtupRMBmDhqiEGts8XFxZg9ezY6duyIvn374oMPPsDy5cub1AD/7f3bYEjfro1at1d0JDqEtrdsQRYk0tyrQ8oTEVnB2QuXkdxAK91DIwehd5dIK1VkXXfKK7D2029RfJdWusAAHzw5ZbRBgbo5+eHXQ/j9jwv1LpdIxJgzYxx8DQzUzcXV3AJsaKCVbnCfLog3optIc6BUqbBh04/ILdAd/aGWh5sLEh9LgJ2B3USakpb520sWc6e8ArJ8/XevEpGuLh1C0SUqpN7lUaHt0Cs6wooVWZejgz3G3z+k3uW2tjaYMGpIiw2TAHD/kD7w8qj/EvSIgT1bbJgEgHb+bRAb063e5T7eHhg+oGX0ndVHKpHU3Kgn0X+jnkgkwsTRsc06TAIMlGSglBPn8O6X32PH3t+FLoWo2Rg7YgBcnXUHm3ZysMdDIxvXAb85Cw8KQEz3jnqXjRkaY/CNC82Nra0NJo2KhVjP/3NggA8G9ooWoCrrGtavO/x9dG84k0jEmDxmqFGjIjQnbbzcMXJIb73LBvfpgsBGjDnZ1LWYQCkSibRvyj/99BMGDhwIV1dXeHl5Yfz48bhy5Yp23e3bt2Pw4MFo1aoVXF1dMXbs2Ls+qqiyshLvvPMO+vXrh1atWsHe3h4RERGYP38+FAr9TdjHjh3DggUL0KtXL/j4+MDOzg7+/v6YOHEiTpw4Ue+xfv75Z9x///1o3bo1bGxs4OnpiaioKMycOROHDx828tUxj7LyChw5dR4AWsQPP5G1ONrbYcL9un3pDBkepbmLH9IH3v9opYsKbY+eLbh19u/a+rVGbL+6rXS2tjaY2MJbZ2tJJGJMGqU7nNZ9A3vBx9tDoKqsq1+PTjrDafm29kTcgB4CVWReLe6n+L333sMDDzyAzMxMhIaG4s6dO9i6dSsGDx6MGzduYO3atRgzZgwyMjIQHBwMpVKJbdu2YdCgQbhxQ/dSbkFBAWJiYvDCCy/g2LFjaNWqFcLDw5GTk4PVq1ejR48eyMzM1Nlu6tSpWLlyJTIzM+Hl5YWOHTuisrIS33zzDfr164etW7fqbPP+++9j1KhR2LlzJ9RqNaKjo9GmTRvIZDJ89tln2LRpk0Ves8Y6dOIcKquq4dvaEx3Cmm/HYSIhhAUFoF+Pv1rpenQOR8fwQOEKsjJbGykmjv6rlc7J0R4J90Dr7N8NjemOAB9v7fQDw/rBo4W3zv5day93xA/+q59kUFtfDOjVWcCKrKvmRr2/htOSSMSYdJdL4c1NiwuUSUlJ+OKLL5Cbm4vTp09DJpOhV69eyM3NxcyZM7Fo0SJ88cUXyMvLw+nTp3Ht2jX06NEDcrkc//73v+vsS6PRYNKkSfjjjz8watQoXLlyBdnZ2fjzzz+hUCgwc+ZMXL16FdOmTdOp47XXXkNGRgZu3ryJ8+fP4/Tp07h+/Tq+++472Nvb4/HHH0dpaal2faVSiVdeeQVATbAsKCjAqVOncOHCBRQXF+PAgQO47777LPvi3cXfWyfj+ve4p/4IEJnLyMF94O3RCu5uLhgzzLDBq1uCtr6tMbRfdwA1rbONHR6lpagNEDZSSaMHr25page9t7sH+s7q8/dB70cO6t2iWmdbzF3etQHnueeew7p16+os++WXXxAfH1/v8p07d+L+++9HdHQ0zp49q53/888/Y9SoUejUqRNOnDgBe3v7OtupVCr07t0bp0+fxqFDh9C/f+OejPDqq69i6dKlSE5OxuTJkwEAcrkcvr6+cHd3x61btww7+Qas/+I7lJSWm7SPyqoqVFZVQywWN/iMYSKqn0qlggZoMa0ShtJoNKiuVsLW1kboUgRTVa2EVCKBWHxvfjBXq9VQqdSwsbk3h8LWaDSoqlbC1kba5BpnXJwd8NwjDxm1bYv739Q3/lj37t0btfyfl65rL0s/8sgjOmESACQSCR544AGcPn0a+/fv1wmUGRkZ+O9//4uzZ8/i5s2bqK6uBgBcv34dAHDmzBltoPT29oa9vT1u376N3bt3m/X52SWl5SguLTPLvtRqtdn2RUT3rooq/c+5pntHeWWl0CUIqrKF/Q60uEAZEqI7PIe3t/ddl7du3RoA6lyCBoA///wTAPDZZ5/hhx9+0Hu82mfn5ubWfRrGv//9b7z00ktQKpX11nrz5k3t9xKJBImJiVixYgVGjBiB7t27Iy4uDgMGDMDgwYPh6mp8PxsXZ9NaFNk6SURE1PKZkhdaXKB0ctIdmuPvTcoNLf+727dvAwAuXKh/QNpad+78NWjv4cOH8eKLL0IikWDp0qUYO3YsAgMD4eTkBJFIhE8//RSzZs3StljWWrZsGQICAvDee+/h9OnTOH36NFauXAk7Ozs8/PDDWL16NTw8DO9vYWzzNVDTd3LlB8kAgKlj4+6pmwiIiIiocVpcoDQnZ2dnAMC2bdsMegRh7d3Y8+bNw8svv6yz/O8tk38nFosxZ84czJkzBzKZDCkpKdi9eze+/vprfPbZZ7h27Rp2795t8HmY0ofy762TP+4+jB93Czt0EREREVkG+1BaSMeOHXHmzBmcP3/eoECZlZUFABgwYIDe5b//3vCg4AEBAZgyZQqmTJmCefPmoXPnztizZw+ysrIQFBTU6FoA8/ShZN9JIiIiqg8D5V2MHz8eX331FT788EM899xz2hbLhjg41PRBkMvlOssyMjKwfft2g+ro2LEj3NzccPv2beTl5RkcKI3tE8G+k0RERPcO9qG0kLFjx2Lw4ME4cOAARowYgQ8//BCdOnXSLler1Th27Bi++OILJCUlITg4GAAwcOBA/Pjjj1i+fDmGDh2qvREoNTUVCQkJesfdunDhAtasWYNZs2ahT58+2n6dKpUK69evx+3bt2Fvb4+OHfU/vuxujGm+Zt9JIiIiaqwWNw5lfadj7HKFQoGxY8fiyJEjAID27dvDx8cH5eXluHLlCsrKai4Dp6WlITIyEgBQUlKC7t274/Lly7CxsUFERATUajXS0tLg6+uLZ555Bq+88goeeeQRfP755wBqhhDq1q3msVwuLi4ICQmBRCJBdna2ts/l+++/j6efftqo18dQuw6ewL6jf8C3tSeef/ShJjdWFhERETUd99YQ9Ubw8vLCgQMH8Pnnn2P48OEoKyvDyZMnkZWVhdDQUCQmJuLAgQMID//riQcuLi44dOgQZs6cCXd3d6Snp6O0tBRPPfUUTp8+DX9/f53jhIeH4+OPP8akSZPg6+uLzMxMnD17Fvb29pgwYQJSUlKsFib5VBwiIiIyRItpoSTzuXm7GD/sSkHpnQq2ThIREVGDGCipXhWVVdqH2BMRERHVh4GSiIiIiEzCPpREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSRgoiYiIiMgkDJREREREZBIGSiIiIiIyCQMlEREREZmEgZKIiIiITMJASUREREQmYaAkIiIiIpMwUBIRERGRSf4f8nA8HfCKA+0AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from demo_src.map import map_ising_to_circuit\n", + "\n", + "circuit = map_ising_to_circuit(cost_hamiltonian, num_layers=1)\n", + "circuit.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "315c495a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "ParameterView([ParameterVectorElement(β[0]), ParameterVectorElement(γ[0])])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "circuit.parameters" + ] + }, + { + "cell_type": "markdown", + "id": "82f70daa-ff68-447a-8064-8b7df7a646cf", + "metadata": {}, + "source": [ + "## Step 2. Optimize problem for quantum execution" + ] + }, + { + "cell_type": "markdown", + "id": "c08be444-e3ed-4178-a10b-414069b1b411", + "metadata": {}, + "source": [ + "The circuit above contains a series of abstractions useful to think about quantum algorithms, but not possible to run in the hardware. To be able to run it in a quantum chip, the circuit needs to undergo a series of operations that make up the **transpilation** or **circuit optimization** step of the pattern.\n", + "\n", + "The Qiskit library offers a series of **transpilation passes** that cater to a wide range of circuit transformations. We don't only want to get a circuit, but we want to make sure that the circuit is **optimized** for our purpose. \n", + "\n", + "Transpilation may involve many steps, such as:\n", + "\n", + "
\n", + "
    \n", + "
  • Intial mapping of the qubits in the circuit (i.e. decision variables) to physical qubits on the device.
    • \n", + "
  • Unrolling of the instructions in the quantum circuit to the hardware native instructions that the backend understands.
    • \n", + "
  • Routing of any qubits in the circuit that interact to physical qubits that are adjacent with one another.
    • \n", + "
  • Error supression by adding single-qubit gates to supress noise with dynamical decoupling.\n", + "
\n", + "\n", + "
\n", + "\n", + "In this example, we have encapsulated a series of transpilation passes in the `optimize_circuit` function. The function takes a circuit and a backend (device) and returns an optimized circuit ready to run in the corresponding device:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "95cd3eed-0348-4373-b664-16a65d42f1e7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# IBM Quantum devices are named after cities\n", + "# For the purpose of the first part of this demo, we will\n", + "# use a simulated device from the \"fake_provider\"\n", + "from qiskit_ibm_runtime.fake_provider import FakeVigoV2\n", + "backend = FakeVigoV2()\n", + "\n", + "from demo_src.transpile import optimize_circuit\n", + "opt_circuit = optimize_circuit(circuit, backend)\n", + "opt_circuit.draw('mpl', fold=False)" + ] + }, + { + "cell_type": "markdown", + "id": "4e75cad7-f599-4937-b5fe-f4d01f53423c", + "metadata": {}, + "source": [ + "## Step 3. Execute using Qiskit Runtime primitives" + ] + }, + { + "cell_type": "markdown", + "id": "9b99ce67-f121-4244-b62a-536be38fea86", + "metadata": {}, + "source": [ + "In the general QAOA workflow, the optimal QAOA parameters are found in an iterative optimization loop, where we run a series of circuit evaluations and use a classical optimizer to find the optimal $\\beta_k$ and $\\gamma_k$ parameters. In this demo, we will not optimize these parameters, we will simply assume that someone has done this for us. Note that finding such parameters is a research field in itself.\n", + "\n", + "Once the optimal parameters are defined, we want to perform one final sampling with the resulting circuit to find our candidate solution.\n", + "\n", + "
\n", + "This means preparing a quantum state $\\psi$ in the computer and then measuring it. A measurement will collapse the state into a single computational basis state, for example 010101110000... which corresponds to a candidate solution $x$ to our initial optimization problem ($\\max f(x)$ or $\\min f(x)$ depending on the task).\n", + "
\n", + " \n", + "The execution is done through the **cloud** using the **Qiskit IBM Runtime service**." + ] + }, + { + "cell_type": "markdown", + "id": "00b2b0f1-9bad-4ad3-b93e-5cbf40395dbf", + "metadata": {}, + "source": [ + "### Define circuit with optimal parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "afa5747f-44dc-4e41-a875-7b6f896f13e2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "optimal_gamma = 5.11350346\n", + "optimal_beta = 5.52673212\n", + "\n", + "candidate_circuit = opt_circuit.assign_parameters([optimal_gamma, optimal_beta])\n", + "candidate_circuit.draw('mpl', fold=False)" + ] + }, + { + "cell_type": "markdown", + "id": "b867f1b0-7196-4d34-9b28-e3fb1de8221c", + "metadata": {}, + "source": [ + "### Define backend and execution primitive\n", + "\n", + "To interact with a IBM backends we use the **Qiskit Runtime Primitives**. There are two primitives: Sampler and Estimator, and the choice of primitive depends on the task that we want to run on the quantum computer. We are interested in drawing samples from the quantum computer, so we will use the **Sampler**. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "ff947109-cddc-4d3c-9119-2c729df73115", + "metadata": {}, + "outputs": [], + "source": [ + "# For the purpose of the first part of this demo, we will\n", + "# use a simulated device from the \"fake_provider\"\n", + "from qiskit_ibm_runtime.fake_provider import FakeVigoV2\n", + "from qiskit.primitives import BackendSampler\n", + "\n", + "backend = FakeVigoV2()\n", + "sampler = BackendSampler(backend=backend)" + ] + }, + { + "cell_type": "markdown", + "id": "ebe288e7-ce87-4b6d-949c-041db09c7c47", + "metadata": {}, + "source": [ + "### Run\n", + "\n", + "The primitives offer a series of execution modes to schedule workloads on quantum devices, this example involves a single job, but a realistic QAOA workflow would be run iteratively in a Session.\n", + "\n", + "\"execution-modes\"" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "2989e76e-4296-4dd8-b065-2b8fced064cf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{2: 0.0108, 30: 0.0136, 31: 0.0067, 15: 0.0174, 6: 0.0148, 29: 0.0083, 0: 0.0065, 13: 0.0402, 23: 0.0203, 10: 0.0475, 28: 0.014, 18: 0.0441, 24: 0.0084, 26: 0.0582, 1: 0.0159, 3: 0.0148, 25: 0.0116, 16: 0.019, 4: 0.0171, 12: 0.0319, 11: 0.0848, 17: 0.0274, 8: 0.0218, 19: 0.032, 14: 0.0266, 5: 0.0579, 21: 0.0451, 7: 0.0109, 20: 0.0925, 9: 0.0877, 27: 0.0126, 22: 0.0796}\n" + ] + } + ], + "source": [ + "final_distribution = sampler.run(candidate_circuit, shots=int(1e4)).result().quasi_dists[0]\n", + "print(final_distribution)" + ] + }, + { + "cell_type": "markdown", + "id": "dace5fed-5555-4f1c-9109-7f5a31832d04", + "metadata": {}, + "source": [ + "## Step 4. Post-process, return result in classical format\n", + "\n", + "The post-processing step interprets the sampling output to return a solution for our original problem, in this case, we are interested in the bitstring that will determine our optimal cut. The symmetries in the problem allow for 4 possible solutions. The sampling process will return one of them with a slightly higher probability, but you can see in the plotted distribution below that the four of the bitstrings are distictively more likely than the rest." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d4f7fc70-883f-4b6b-8e92-2fc4afbbea46", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Result bitstring: [0 0 1 0 1]\n" + ] + } + ], + "source": [ + "from demo_src.post import sample_most_likely\n", + "\n", + "best_result = sample_most_likely(final_distribution, len(demo_graph))\n", + "print(\"Result bitstring:\", best_result)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "650875e9-adbc-43bd-9505-556be2566278", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from demo_src.post import plot_distribution\n", + "\n", + "plot_distribution(final_distribution)" + ] + }, + { + "cell_type": "markdown", + "id": "207443f2-34d9-424a-a6d7-44707ef1488b", + "metadata": {}, + "source": [ + "### Visualize best cut" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "33135970-8bc4-4fb2-ab87-08726a432ce4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from demo_src.post import plot_result\n", + "\n", + "plot_result(demo_graph, best_result)" + ] + }, + { + "cell_type": "markdown", + "id": "2e2a89de-cef3-46ea-b201-cf931b65dfea", + "metadata": {}, + "source": [ + "---\n", + "\n", + "# Part 2: Let's scale it up and run!" + ] + }, + { + "cell_type": "markdown", + "id": "9a9a69e0-aa07-40aa-91ac-ef6740f2677f", + "metadata": {}, + "source": [ + "Let's try to solve Max-Cut on a 125-node weighted graph, with both positive (green) and negative (red) weights following the 4 steps laid out in part 1. This is a \"utility-scale\" problem that requires more than 100 qubits to run.\n", + "\n", + "
\n", + "\n", + "
\n", + "\n", + "We want to take this opportunity to run on two devices with different processor architectures: **Eagle** and **Heron**.\n", + "\n", + "\n", + "
\n", + "\n", + "
\n", + "\n", + "Each of you will be assigned a team (Eagle or Heron), and will run the workload on the assigned device. At the end, we will compare the performance of both teams in the QAOA setting.\n", + "\n", + "
\n", + "We have precomputed steps 1-3 for you, so you get to run step 4 on a real quantum device using the Qiskit IBM Runtime service.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "31bb3bc1-f19e-4553-9e93-a89e92ea5469", + "metadata": {}, + "source": [ + "## Step 1. Map the classical inputs to a quantum problem" + ] + }, + { + "cell_type": "markdown", + "id": "e9cf2c59-1f55-432c-9243-d1f94d50d0ad", + "metadata": {}, + "source": [ + "### Graph → QUBO\n", + "\n", + "The cell below shows you what the quadratic program for this problem looks like. There are 125 variables, which will map to 125 qubits." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "01e39c4e-5c44-44c7-9844-f7a59596998b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\ This file has been generated by DOcplex\n", + "\\ ENCODING=ISO-8859-1\n", + "\\Problem name: CPLEX\n", + "\n", + "Minimize\n", + " obj: [ - 8 x0^2 + 8 x0*x1 + 8 x0*x13 - 8 x1^2 + 8 x1*x2 - 8 x2*x3 + 8 x3*x4\n", + " - 4 x4^2 - 8 x4*x5 + 8 x4*x14 + 8 x5*x6 - 8 x6^2 + 8 x6*x7 - 8 x7^2\n", + " + 8 x7*x8 - 12 x8^2 + 8 x8*x9 + 8 x8*x15 - 8 x9*x10 + 8 x10^2 - 8 x10*x11\n", + " + 8 x11*x12 - 8 x12*x16 - 8 x13*x17 - 8 x14*x21 - 8 x15*x25 + 8 x16^2\n", + " - 8 x16*x29 + 8 x17*x18 - 8 x18^2 + 8 x18*x19 + 4 x19^2 - 8 x19*x20\n", + " - 8 x19*x32 + 8 x20*x21 - 4 x21^2 + 8 x21*x22 - 8 x22^2 + 8 x22*x23\n", + " - 12 x23^2 + 8 x23*x24 + 8 x23*x33 - 8 x24^2 + 8 x24*x25 + 4 x25^2\n", + " - 8 x25*x26 + 8 x26*x27 - 4 x27^2 + 8 x27*x28 - 8 x27*x34 - 8 x28*x29\n", + " + 12 x29^2 - 8 x29*x30 + 8 x30^2 - 8 x30*x31 + 8 x31^2 - 8 x31*x35\n", + " + 8 x32*x38 - 8 x33*x42 + 8 x34^2 - 8 x34*x46 + 8 x35^2 - 8 x35*x50\n", + " - 8 x36^2 + 8 x36*x37 + 8 x36*x51 - 8 x37*x38 - 4 x38^2 + 8 x38*x39\n", + " - 8 x39*x40 + 12 x40^2 - 8 x40*x41 - 8 x40*x52 + 8 x41^2 - 8 x41*x42\n", + " + 12 x42^2 - 8 x42*x43 + 8 x43*x44 - 4 x44^2 + 8 x44*x45 - 8 x44*x53\n", + " - 8 x45*x46 + 12 x46^2 - 8 x46*x47 + 8 x47*x48 + 4 x48^2 - 8 x48*x49\n", + " - 8 x48*x54 + 8 x49^2 - 8 x49*x50 + 8 x50^2 - 8 x51^2 + 8 x51*x55\n", + " + 8 x52*x59 + 8 x53^2 - 8 x53*x63 + 8 x54*x67 - 8 x55^2 + 8 x55*x56\n", + " - 8 x56^2 + 8 x56*x57 - 4 x57^2 - 8 x57*x58 + 8 x57*x70 + 8 x58^2\n", + " - 8 x58*x59 - 4 x59^2 + 8 x59*x60 - 8 x60^2 + 8 x60*x61 - 4 x61^2\n", + " - 8 x61*x62 + 8 x61*x71 + 8 x62^2 - 8 x62*x63 + 4 x63^2 + 8 x63*x64\n", + " - 8 x64^2 + 8 x64*x65 + 4 x65^2 - 8 x65*x66 - 8 x65*x72 + 8 x66*x67\n", + " - 12 x67^2 + 8 x67*x68 - 8 x68^2 + 8 x68*x69 - 8 x69^2 + 8 x69*x73\n", + " - 8 x70^2 + 8 x70*x76 - 8 x71^2 + 8 x71*x80 + 8 x72*x84 - 8 x73*x88\n", + " - 8 x74*x75 + 8 x74*x89 + 8 x75*x76 - 12 x76^2 + 8 x76*x77 - 8 x77*x78\n", + " + 4 x78^2 + 8 x78*x79 - 8 x78*x90 - 8 x79^2 + 8 x79*x80 - 4 x80^2\n", + " - 8 x80*x81 + 8 x81^2 - 8 x81*x82 - 4 x82^2 + 8 x82*x83 + 8 x82*x91\n", + " - 8 x83^2 + 8 x83*x84 - 12 x84^2 + 8 x84*x85 - 8 x85^2 + 8 x85*x86\n", + " - 4 x86^2 + 8 x86*x87 - 8 x86*x92 - 8 x87^2 + 8 x87*x88 - 8 x89*x93\n", + " + 8 x90^2 - 8 x90*x97 - 8 x91*x101 + 8 x92^2 - 8 x92*x105 + 8 x93^2\n", + " - 8 x93*x94 + 8 x94*x95 - 12 x95^2 + 8 x95*x96 + 8 x95*x108 - 8 x96*x97\n", + " + 4 x97^2 + 8 x97*x98 - 8 x98*x99 + 12 x99^2 - 8 x99*x100 - 8 x99*x109\n", + " + 8 x100*x101 - 4 x101^2 + 8 x101*x102 - 8 x102^2 + 8 x102*x103 + 4 x103^2\n", + " - 8 x103*x104 - 8 x103*x110 + 8 x104*x105 + 4 x105^2 - 8 x105*x106\n", + " + 8 x106^2 - 8 x106*x107 + 8 x107^2 - 8 x107*x111 - 8 x108*x112\n", + " + 8 x109*x116 + 8 x110^2 - 8 x110*x120 + 8 x111*x124 + 8 x112^2\n", + " - 8 x112*x113 + 8 x113*x114 - 8 x114*x115 + 8 x115^2 - 8 x115*x116\n", + " - 4 x116^2 + 8 x116*x117 - 8 x117^2 + 8 x117*x118 - 8 x118*x119\n", + " + 8 x119*x120 + 4 x120^2 - 8 x120*x121 + 8 x121^2 - 8 x121*x122 + 8 x122^2\n", + " - 8 x122*x123 + 8 x123*x124 - 8 x124^2 ]/2 + 4\n", + "Subject To\n", + "\n", + "Bounds\n", + " 0 <= x0 <= 1\n", + " 0 <= x1 <= 1\n", + " 0 <= x2 <= 1\n", + " 0 <= x3 <= 1\n", + " 0 <= x4 <= 1\n", + " 0 <= x5 <= 1\n", + " 0 <= x6 <= 1\n", + " 0 <= x7 <= 1\n", + " 0 <= x8 <= 1\n", + " 0 <= x9 <= 1\n", + " 0 <= x10 <= 1\n", + " 0 <= x11 <= 1\n", + " 0 <= x12 <= 1\n", + " 0 <= x13 <= 1\n", + " 0 <= x14 <= 1\n", + " 0 <= x15 <= 1\n", + " 0 <= x16 <= 1\n", + " 0 <= x17 <= 1\n", + " 0 <= x18 <= 1\n", + " 0 <= x19 <= 1\n", + " 0 <= x20 <= 1\n", + " 0 <= x21 <= 1\n", + " 0 <= x22 <= 1\n", + " 0 <= x23 <= 1\n", + " 0 <= x24 <= 1\n", + " 0 <= x25 <= 1\n", + " 0 <= x26 <= 1\n", + " 0 <= x27 <= 1\n", + " 0 <= x28 <= 1\n", + " 0 <= x29 <= 1\n", + " 0 <= x30 <= 1\n", + " 0 <= x31 <= 1\n", + " 0 <= x32 <= 1\n", + " 0 <= x33 <= 1\n", + " 0 <= x34 <= 1\n", + " 0 <= x35 <= 1\n", + " 0 <= x36 <= 1\n", + " 0 <= x37 <= 1\n", + " 0 <= x38 <= 1\n", + " 0 <= x39 <= 1\n", + " 0 <= x40 <= 1\n", + " 0 <= x41 <= 1\n", + " 0 <= x42 <= 1\n", + " 0 <= x43 <= 1\n", + " 0 <= x44 <= 1\n", + " 0 <= x45 <= 1\n", + " 0 <= x46 <= 1\n", + " 0 <= x47 <= 1\n", + " 0 <= x48 <= 1\n", + " 0 <= x49 <= 1\n", + " 0 <= x50 <= 1\n", + " 0 <= x51 <= 1\n", + " 0 <= x52 <= 1\n", + " 0 <= x53 <= 1\n", + " 0 <= x54 <= 1\n", + " 0 <= x55 <= 1\n", + " 0 <= x56 <= 1\n", + " 0 <= x57 <= 1\n", + " 0 <= x58 <= 1\n", + " 0 <= x59 <= 1\n", + " 0 <= x60 <= 1\n", + " 0 <= x61 <= 1\n", + " 0 <= x62 <= 1\n", + " 0 <= x63 <= 1\n", + " 0 <= x64 <= 1\n", + " 0 <= x65 <= 1\n", + " 0 <= x66 <= 1\n", + " 0 <= x67 <= 1\n", + " 0 <= x68 <= 1\n", + " 0 <= x69 <= 1\n", + " 0 <= x70 <= 1\n", + " 0 <= x71 <= 1\n", + " 0 <= x72 <= 1\n", + " 0 <= x73 <= 1\n", + " 0 <= x74 <= 1\n", + " 0 <= x75 <= 1\n", + " 0 <= x76 <= 1\n", + " 0 <= x77 <= 1\n", + " 0 <= x78 <= 1\n", + " 0 <= x79 <= 1\n", + " 0 <= x80 <= 1\n", + " 0 <= x81 <= 1\n", + " 0 <= x82 <= 1\n", + " 0 <= x83 <= 1\n", + " 0 <= x84 <= 1\n", + " 0 <= x85 <= 1\n", + " 0 <= x86 <= 1\n", + " 0 <= x87 <= 1\n", + " 0 <= x88 <= 1\n", + " 0 <= x89 <= 1\n", + " 0 <= x90 <= 1\n", + " 0 <= x91 <= 1\n", + " 0 <= x92 <= 1\n", + " 0 <= x93 <= 1\n", + " 0 <= x94 <= 1\n", + " 0 <= x95 <= 1\n", + " 0 <= x96 <= 1\n", + " 0 <= x97 <= 1\n", + " 0 <= x98 <= 1\n", + " 0 <= x99 <= 1\n", + " 0 <= x100 <= 1\n", + " 0 <= x101 <= 1\n", + " 0 <= x102 <= 1\n", + " 0 <= x103 <= 1\n", + " 0 <= x104 <= 1\n", + " 0 <= x105 <= 1\n", + " 0 <= x106 <= 1\n", + " 0 <= x107 <= 1\n", + " 0 <= x108 <= 1\n", + " 0 <= x109 <= 1\n", + " 0 <= x110 <= 1\n", + " 0 <= x111 <= 1\n", + " 0 <= x112 <= 1\n", + " 0 <= x113 <= 1\n", + " 0 <= x114 <= 1\n", + " 0 <= x115 <= 1\n", + " 0 <= x116 <= 1\n", + " 0 <= x117 <= 1\n", + " 0 <= x118 <= 1\n", + " 0 <= x119 <= 1\n", + " 0 <= x120 <= 1\n", + " 0 <= x121 <= 1\n", + " 0 <= x122 <= 1\n", + " 0 <= x123 <= 1\n", + " 0 <= x124 <= 1\n", + "\n", + "Binaries\n", + " x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21\n", + " x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 x34 x35 x36 x37 x38 x39 x40 x41\n", + " x42 x43 x44 x45 x46 x47 x48 x49 x50 x51 x52 x53 x54 x55 x56 x57 x58 x59 x60 x61\n", + " x62 x63 x64 x65 x66 x67 x68 x69 x70 x71 x72 x73 x74 x75 x76 x77 x78 x79 x80 x81\n", + " x82 x83 x84 x85 x86 x87 x88 x89 x90 x91 x92 x93 x94 x95 x96 x97 x98 x99 x100\n", + " x101 x102 x103 x104 x105 x106 x107 x108 x109 x110 x111 x112 x113 x114 x115 x116\n", + " x117 x118 x119 x120 x121 x122 x123 x124\n", + "End\n", + "\n" + ] + } + ], + "source": [ + "with open(\"data/125node_example.lp\", \"r\") as file:\n", + " problem = file.read()\n", + "print(problem)" + ] + }, + { + "cell_type": "markdown", + "id": "af34ecad-5132-4ea3-88f5-1bdacc1e9f07", + "metadata": {}, + "source": [ + "### QUBO → Hamiltonian\n", + "\n", + "Below we show the first 10 Pauli terms in the cost-function Hamiltonian. They look similar, except for the positions of the `Z` and the coefficients. These encode the weight of the edges in the graph for which we want to find the maximum cut." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "d1715aab-b84e-46d0-98d7-22f7cf68befd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZ, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZI, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII, -1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIII, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIII, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIII, -1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIII, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIII, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIII, 1.0\n", + "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIII, 1.0\n" + ] + } + ], + "source": [ + "with open(\"data/125node_example_ising.txt\") as input_file:\n", + " for _ in range(10):\n", + " print(str(next(input_file)).replace(\"\\n\", \"\"))" + ] + }, + { + "cell_type": "markdown", + "id": "ba1796e6", + "metadata": {}, + "source": [ + "### Hamiltonian → Quantum Circuit\n", + "\n", + "\n", + "
\n", + " To scale the circuit building step to utility-scale problems, we take advantage of high-level transpilation strategies for remapping and optimizing our QAOA layers during step 1.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "cf31d488-d672-4c91-8a80-867273502396", + "metadata": {}, + "source": [ + "## Step 2. Optimize problem for quantum execution\n", + "\n", + "
\n", + " To scale the circuit optimization step to utility-scale problems, we take advantage of the high performance transpilation strategies introduced in Qiskit 1.0. Other tools include the new transpiler service with AI Transpiler passes.\n", + "
\n", + "\n", + "\n", + "We have prepared the optimized circuits for you. These are stored in binary files that we can import with `qpy`, Qiskit's circuit serializer.\n", + "\n", + "\n", + "
\n", + "Call to Action: Fill out the cell below with your team number (1 or 2). This will determine the device you will execute on.\n", + "
\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "aced78d5", + "metadata": {}, + "outputs": [], + "source": [ + "team = 1 # Fill in your team here, either 1 or 2" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "4247e41e-b27b-400b-9212-c30bc7aecc1e", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import qpy # QPY is the circuit serializer in Qiskit.\n", + "\n", + "# Load the circuits\n", + "if team == 1:\n", + " backend_type = \"eagle\"\n", + "elif team == 2:\n", + " backend_type == \"heron\"\n", + "else:\n", + " raise ValueError(\"team should be 1 or 2.\")\n", + "\n", + "# Depth zero-circuit\n", + "with open(f\"data/125node_{backend_type}_depth_zero.qpy\", \"rb\") as fd:\n", + " depth_zero_circuit = qpy.load(fd)[0]\n", + "\n", + "# Depth one-circuit\n", + "with open(f\"data/125node_{backend_type}_depth_one.qpy\", \"rb\") as fd:\n", + " depth_one_circuit = qpy.load(fd)[0]" + ] + }, + { + "cell_type": "markdown", + "id": "077936f8-6dbe-457d-aceb-8662cd1be924", + "metadata": {}, + "source": [ + "You can print the circuit by uncommenting the line below. However, note that the output for utility-scale experiments is typically large." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "94e58ec2-856b-4d83-a976-bb5ad4aafc29", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "depth_one_circuit.draw('mpl', fold=False)" + ] + }, + { + "cell_type": "markdown", + "id": "8a8e65f0-9089-4237-b833-6f99da859ce2", + "metadata": {}, + "source": [ + "## Step 3. Execute using Qiskit Runtime Primitives\n", + "\n", + "To run QAOA we need to know the optimal parameters $\\gamma_k$ and $\\beta_k$ to put in the variational circuit. Once again, we will not optimize these parameters here. We will simply assume that someone has done this for us. The optimal parameters to use are\n", + "\n", + "* Depth-zero QAOA: `None`\n", + "* Depth-one optimal (gamma, beta): `(0.3792, 0.3792)`" + ] + }, + { + "cell_type": "markdown", + "id": "18ef47d2", + "metadata": {}, + "source": [ + "
\n", + "Call to Action: Uncomment and fill out the cell below with your IQP token (credentials) to authenticate your account.\n", + "
\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6f2f684", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "# QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"\", overwrite=True, set_as_default=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "eee717c7-6aed-47f2-9e20-04e7886cf72b", + "metadata": {}, + "outputs": [], + "source": [ + "service = QiskitRuntimeService(channel='ibm_quantum')\n", + "\n", + "if team == 1:\n", + " backend = service.get_backend('ibm_sherbrooke')\n", + "elif team == 2:\n", + " backend = service.get_backend('ibm_torino')" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "39cd3a9d-e63a-45a9-afe6-237ca1fbda22", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import Sampler, Options\n", + "\n", + "# Since we have already done the transpilation we can skip it.\n", + "options = Options()\n", + "options.transpilation.skip_transpilation = True\n", + "\n", + "sampler = Sampler(backend=backend, options=options)" + ] + }, + { + "cell_type": "markdown", + "id": "24b10973-5d7c-4536-842c-b87049b6fc7f", + "metadata": {}, + "source": [ + "### Bind the parameters for the depth-one ansatz\n", + "\n", + "As mentioned above, the depth-one QAOA circuit has two parameters $\\gamma$ and $\\beta$ that need to be bound before we can run the circuits." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "e6a4f88c-c2a4-48c1-ad14-3e5ed58031e3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "ParameterView([Parameter(β1), Parameter(γ1)])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "depth_one_circuit.parameters" + ] + }, + { + "cell_type": "markdown", + "id": "bb0702af-0581-4aa5-89fa-a3afcb0c20d2", + "metadata": {}, + "source": [ + "We create a circuit with bound parameter values below." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "12f9dc1f-bfcb-44e7-8304-c249e4f1fa53", + "metadata": {}, + "outputs": [], + "source": [ + "depth_one_bound_circuit = depth_one_circuit.assign_parameters([0.3927, 0.3927], inplace=False)" + ] + }, + { + "cell_type": "markdown", + "id": "45ee588b", + "metadata": {}, + "source": [ + "
\n", + "Call to Action: Uncomment the cells below to run the sampling on one of the selected devices.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "5e11ce39-a046-4f65-a8e6-bc9ca123eb9a", + "metadata": {}, + "source": [ + "### Sample candidate solution from backend" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "db601a74-afb7-47ac-b6ad-cfb8e77f9594", + "metadata": {}, + "outputs": [], + "source": [ + "# sampler_job = sampler.run([depth_one_bound_circuit, depth_zero_circuit])" + ] + }, + { + "cell_type": "markdown", + "id": "4ac5aab1-e82a-4321-8130-ff7b30e71af0", + "metadata": {}, + "source": [ + "Each call to the sampler returns a JobId that we can use to retrive the results when they are ready." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "89dcca9f-3b53-4973-97bd-fae1da61738f", + "metadata": {}, + "outputs": [], + "source": [ + "# sampler_job.job_id()" + ] + }, + { + "cell_type": "markdown", + "id": "364f0f06-4a28-455b-b893-3883576e5a7c", + "metadata": {}, + "source": [ + "In addition, we can check the status of our jobs to see if they are finished." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "1f01dc43-d91c-4b9c-a542-aeab3eda8ec4", + "metadata": {}, + "outputs": [], + "source": [ + "# sampler_job.status()" + ] + }, + { + "cell_type": "markdown", + "id": "0b853887-d2eb-499a-b1b8-c55d6c144313", + "metadata": {}, + "source": [ + "Now, we will locally save the samples that the backend returned so that we can share them and later analyze them." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "fd479ac2-1bde-4f6f-83a0-bf96094b1d25", + "metadata": {}, + "outputs": [], + "source": [ + "# from demo_src.run import save_result\n", + "\n", + "# save_result(sampler_job.result(), backend_type, path=\"sampler_data\")" + ] + }, + { + "cell_type": "markdown", + "id": "50ad3918-5cc4-488a-b323-6743ebfc7400", + "metadata": {}, + "source": [ + "## Step 4. Post-process, return result in classical format\n", + "\n", + "Now, we need to compute the objective value of each sample that we measured on the quantum computer. The best one will be the solution returned by the quantum computer." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "6fa05a0d-782e-499d-9b96-e8657b6d52fd", + "metadata": {}, + "outputs": [], + "source": [ + "from demo_src.post import load_data, samples_to_objective_values, load_qp, plot_cdf\n", + "\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "a4b43732-da13-4732-813f-db1b9534f17a", + "metadata": {}, + "outputs": [], + "source": [ + "qp, max_cut, min_cut = load_qp()" + ] + }, + { + "cell_type": "markdown", + "id": "00883eef-7a32-414d-b99c-751c25165e55", + "metadata": {}, + "source": [ + "The following cell will load all the data that we have gathered. Note that we give it `qp`, the quadratic program of the MaxCut optimization problem, so that `load_data` can directly convert the samples to the value of the objective function." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "8a264ca3-1657-4788-a3bd-7e878c70a7de", + "metadata": {}, + "outputs": [], + "source": [ + "depth_one_heron, depth_zero_heron, depth_one_eagle, depth_zero_eagle = load_data(qp)" + ] + }, + { + "cell_type": "markdown", + "id": "351dee24-6eb9-4589-8a16-b0c50deb231d", + "metadata": {}, + "source": [ + "Now, in the last cell we will display the cumulative distribution function of the sampled solutions for depth-zero QAOA (blue line) and depth-one QAOA (orange line). \n", + "\n", + "
\n", + "The dashed orange line displays the best sampled solution from the quantum computer. The black dashed line is the optimal solution. We can see that there is still a gap between the best sampled solution and the optimal solution. To get better solutions we would need to use deeper QAOA circuits. But be careful, this might result in more noise.\n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "822487d7-da2a-44e2-9524-9285b50d4a77", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "if team == 1:\n", + " depth_zero = depth_zero_eagle\n", + " depth_one = depth_one_eagle\n", + " \n", + "elif team ==2:\n", + " depth_zero = depth_zero_heron\n", + " depth_one = depth_one_heron \n", + " \n", + "fig, ax = plt.subplots(1, 1)\n", + "\n", + "plot_cdf(depth_zero, depth_one, max_cut, min_cut, ax, \"Approximation ratio:\")" + ] + }, + { + "cell_type": "markdown", + "id": "9b553b70", + "metadata": {}, + "source": [ + "
\n", + "Call to Action: Uncomment the cells below to see a side-by-side comparison of the Eagle and Heron results.\n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e7b9ae91", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fig, ax = plt.subplots(1, 2, figsize=(15, 6))\n", + "# plot_cdf(depth_zero_eagle, depth_one_eagle, max_cut, min_cut, ax[0], \"Approximation ratio Eagle:\")\n", + "# plot_cdf(depth_zero_heron, depth_one_heron, max_cut, min_cut, ax[1], \"Approximation ratio Heron:\")" + ] + }, + { + "cell_type": "markdown", + "id": "69ebc85b-6a29-4671-8d16-1ac97f089607", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "In this tutorial we present the Qiskit patterns and how to solve an optimization problem with a quantum computer. We demonstrate this at utility-scale, i.e., using on the order of 100 qubits. Currently, quantum computers do not outperform classical computers for combinatorial optimization. They are currently too noisy. However, the hardware is getting better and better and new algorithms for quantum computers are always being developped. This is also where the era of utility will be important. Indeed, much of the research working on quantum heuristics for combinatorial optimization are tested with classical simulations which only allow for a small number of qubits, typically aroud 20 qubits. Now, with larger qubit counts and devices with less noise we will be able to start benchmarking these quantum heuristics at large problem sizes on actual quantum hardware." + ] + }, + { + "cell_type": "markdown", + "id": "9b6bd37f-973a-48f2-b0df-b5d9172d09b9", + "metadata": {}, + "source": [ + "-----\n", + "\n", + "## Appendix A: Reformulation in spin variables\n", + "\n", + "Here, we rewrite the QUBO $x^TQx$ in terms of spin-variables $x_i=(1-z_i)/2$.\n", + "\\begin{align}\n", + "x^TQx=\\sum_{ij}Q_{ij}x_ix_j=\\frac{1}{4}\\sum_{ij}Q_{ij}(1-z_i)(1-z_j)=\\frac{1}{4}\\sum_{ij}Q_{ij}z_iz_j-\\frac{1}{4}\\sum_{ij}(Q_{ij}+Q_{ji})z_i + \\frac{n^2}{4}.\n", + "\\end{align}\n", + "If we write $b_i=-\\sum_{j}(Q_{ij}+Q_{ji})$ and remove the prefactor and the constant $n^2$ term we arrive at the two equivalent formulations of the same optimization problem\n", + "\\begin{align}\n", + "\\max_{x\\in\\{0,1\\}^n} x^TQx\\Longleftrightarrow \\max_{z\\in\\{-1,1\\}^n}z^TQz + b^Tz\n", + "\\end{align}\n", + "\n", + "Here, $b$ depends on $Q$. Note that to obtain $z^TQz + b^Tz$ we dropped an irrelevant factor of 1/4 and a constant offset of $n^2$ which do not play a role in the optimization. " + ] + }, + { + "cell_type": "markdown", + "id": "d1e0a59c-ba1a-4310-8eb7-cd969e013daa", + "metadata": {}, + "source": [ + "## Appendix B: Quantum notation\n", + "\n", + "The $Z$ matrices are imbedded in the quantum computer's computational space, i.e., a Hilbert space of size $2^n\\times 2^n$. Therefore, you should understand terms such as $Z_iZ_j$ as the tensor product $Z_i\\otimes Z_j$ imbedded in the $2^n\\times 2^n$ Hilbert space. For example, in a problem with five decision variables the term $Z_1Z_3$ is understood to mean $I\\otimes Z_3\\otimes I\\otimes Z_1\\otimes I$ where $I$ is the $2\\times 2$ identity matrix." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "ibm_tech_clean", + "language": "python", + "name": "ibm_tech_clean" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/demos/qiskit_patterns/data/125node_eagle_depth_one.qpy b/demos/qiskit_patterns/data/125node_eagle_depth_one.qpy new file mode 100644 index 0000000000000000000000000000000000000000..7f0fbe731a2dfc177cc6b41d6912631711ca1e36 GIT binary patch literal 198906 zcmeHw$*&d1v*yKcF_QOH8O%I`G3GKE17-$;8O-E+443i8U>n=`S*>36qSb%G 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name: CPLEX + +Minimize + obj: [ - 8 x0^2 + 8 x0*x1 + 8 x0*x13 - 8 x1^2 + 8 x1*x2 - 8 x2*x3 + 8 x3*x4 + - 4 x4^2 - 8 x4*x5 + 8 x4*x14 + 8 x5*x6 - 8 x6^2 + 8 x6*x7 - 8 x7^2 + + 8 x7*x8 - 12 x8^2 + 8 x8*x9 + 8 x8*x15 - 8 x9*x10 + 8 x10^2 - 8 x10*x11 + + 8 x11*x12 - 8 x12*x16 - 8 x13*x17 - 8 x14*x21 - 8 x15*x25 + 8 x16^2 + - 8 x16*x29 + 8 x17*x18 - 8 x18^2 + 8 x18*x19 + 4 x19^2 - 8 x19*x20 + - 8 x19*x32 + 8 x20*x21 - 4 x21^2 + 8 x21*x22 - 8 x22^2 + 8 x22*x23 + - 12 x23^2 + 8 x23*x24 + 8 x23*x33 - 8 x24^2 + 8 x24*x25 + 4 x25^2 + - 8 x25*x26 + 8 x26*x27 - 4 x27^2 + 8 x27*x28 - 8 x27*x34 - 8 x28*x29 + + 12 x29^2 - 8 x29*x30 + 8 x30^2 - 8 x30*x31 + 8 x31^2 - 8 x31*x35 + + 8 x32*x38 - 8 x33*x42 + 8 x34^2 - 8 x34*x46 + 8 x35^2 - 8 x35*x50 + - 8 x36^2 + 8 x36*x37 + 8 x36*x51 - 8 x37*x38 - 4 x38^2 + 8 x38*x39 + - 8 x39*x40 + 12 x40^2 - 8 x40*x41 - 8 x40*x52 + 8 x41^2 - 8 x41*x42 + + 12 x42^2 - 8 x42*x43 + 8 x43*x44 - 4 x44^2 + 8 x44*x45 - 8 x44*x53 + - 8 x45*x46 + 12 x46^2 - 8 x46*x47 + 8 x47*x48 + 4 x48^2 - 8 x48*x49 + - 8 x48*x54 + 8 x49^2 - 8 x49*x50 + 8 x50^2 - 8 x51^2 + 8 x51*x55 + + 8 x52*x59 + 8 x53^2 - 8 x53*x63 + 8 x54*x67 - 8 x55^2 + 8 x55*x56 + - 8 x56^2 + 8 x56*x57 - 4 x57^2 - 8 x57*x58 + 8 x57*x70 + 8 x58^2 + - 8 x58*x59 - 4 x59^2 + 8 x59*x60 - 8 x60^2 + 8 x60*x61 - 4 x61^2 + - 8 x61*x62 + 8 x61*x71 + 8 x62^2 - 8 x62*x63 + 4 x63^2 + 8 x63*x64 + - 8 x64^2 + 8 x64*x65 + 4 x65^2 - 8 x65*x66 - 8 x65*x72 + 8 x66*x67 + - 12 x67^2 + 8 x67*x68 - 8 x68^2 + 8 x68*x69 - 8 x69^2 + 8 x69*x73 + - 8 x70^2 + 8 x70*x76 - 8 x71^2 + 8 x71*x80 + 8 x72*x84 - 8 x73*x88 + - 8 x74*x75 + 8 x74*x89 + 8 x75*x76 - 12 x76^2 + 8 x76*x77 - 8 x77*x78 + + 4 x78^2 + 8 x78*x79 - 8 x78*x90 - 8 x79^2 + 8 x79*x80 - 4 x80^2 + - 8 x80*x81 + 8 x81^2 - 8 x81*x82 - 4 x82^2 + 8 x82*x83 + 8 x82*x91 + - 8 x83^2 + 8 x83*x84 - 12 x84^2 + 8 x84*x85 - 8 x85^2 + 8 x85*x86 + - 4 x86^2 + 8 x86*x87 - 8 x86*x92 - 8 x87^2 + 8 x87*x88 - 8 x89*x93 + + 8 x90^2 - 8 x90*x97 - 8 x91*x101 + 8 x92^2 - 8 x92*x105 + 8 x93^2 + - 8 x93*x94 + 8 x94*x95 - 12 x95^2 + 8 x95*x96 + 8 x95*x108 - 8 x96*x97 + + 4 x97^2 + 8 x97*x98 - 8 x98*x99 + 12 x99^2 - 8 x99*x100 - 8 x99*x109 + + 8 x100*x101 - 4 x101^2 + 8 x101*x102 - 8 x102^2 + 8 x102*x103 + 4 x103^2 + - 8 x103*x104 - 8 x103*x110 + 8 x104*x105 + 4 x105^2 - 8 x105*x106 + + 8 x106^2 - 8 x106*x107 + 8 x107^2 - 8 x107*x111 - 8 x108*x112 + + 8 x109*x116 + 8 x110^2 - 8 x110*x120 + 8 x111*x124 + 8 x112^2 + - 8 x112*x113 + 8 x113*x114 - 8 x114*x115 + 8 x115^2 - 8 x115*x116 + - 4 x116^2 + 8 x116*x117 - 8 x117^2 + 8 x117*x118 - 8 x118*x119 + + 8 x119*x120 + 4 x120^2 - 8 x120*x121 + 8 x121^2 - 8 x121*x122 + 8 x122^2 + - 8 x122*x123 + 8 x123*x124 - 8 x124^2 ]/2 + 4 +Subject To + +Bounds + 0 <= x0 <= 1 + 0 <= x1 <= 1 + 0 <= x2 <= 1 + 0 <= x3 <= 1 + 0 <= x4 <= 1 + 0 <= x5 <= 1 + 0 <= x6 <= 1 + 0 <= x7 <= 1 + 0 <= x8 <= 1 + 0 <= x9 <= 1 + 0 <= x10 <= 1 + 0 <= x11 <= 1 + 0 <= x12 <= 1 + 0 <= x13 <= 1 + 0 <= x14 <= 1 + 0 <= x15 <= 1 + 0 <= x16 <= 1 + 0 <= x17 <= 1 + 0 <= x18 <= 1 + 0 <= x19 <= 1 + 0 <= x20 <= 1 + 0 <= x21 <= 1 + 0 <= x22 <= 1 + 0 <= x23 <= 1 + 0 <= x24 <= 1 + 0 <= x25 <= 1 + 0 <= x26 <= 1 + 0 <= x27 <= 1 + 0 <= x28 <= 1 + 0 <= x29 <= 1 + 0 <= x30 <= 1 + 0 <= x31 <= 1 + 0 <= x32 <= 1 + 0 <= x33 <= 1 + 0 <= x34 <= 1 + 0 <= x35 <= 1 + 0 <= x36 <= 1 + 0 <= x37 <= 1 + 0 <= x38 <= 1 + 0 <= x39 <= 1 + 0 <= x40 <= 1 + 0 <= x41 <= 1 + 0 <= x42 <= 1 + 0 <= x43 <= 1 + 0 <= x44 <= 1 + 0 <= x45 <= 1 + 0 <= x46 <= 1 + 0 <= x47 <= 1 + 0 <= x48 <= 1 + 0 <= x49 <= 1 + 0 <= x50 <= 1 + 0 <= x51 <= 1 + 0 <= x52 <= 1 + 0 <= x53 <= 1 + 0 <= x54 <= 1 + 0 <= x55 <= 1 + 0 <= x56 <= 1 + 0 <= x57 <= 1 + 0 <= x58 <= 1 + 0 <= x59 <= 1 + 0 <= x60 <= 1 + 0 <= x61 <= 1 + 0 <= x62 <= 1 + 0 <= x63 <= 1 + 0 <= x64 <= 1 + 0 <= x65 <= 1 + 0 <= x66 <= 1 + 0 <= x67 <= 1 + 0 <= x68 <= 1 + 0 <= x69 <= 1 + 0 <= x70 <= 1 + 0 <= x71 <= 1 + 0 <= x72 <= 1 + 0 <= x73 <= 1 + 0 <= x74 <= 1 + 0 <= x75 <= 1 + 0 <= x76 <= 1 + 0 <= x77 <= 1 + 0 <= x78 <= 1 + 0 <= x79 <= 1 + 0 <= x80 <= 1 + 0 <= x81 <= 1 + 0 <= x82 <= 1 + 0 <= x83 <= 1 + 0 <= x84 <= 1 + 0 <= x85 <= 1 + 0 <= x86 <= 1 + 0 <= x87 <= 1 + 0 <= x88 <= 1 + 0 <= x89 <= 1 + 0 <= x90 <= 1 + 0 <= x91 <= 1 + 0 <= x92 <= 1 + 0 <= x93 <= 1 + 0 <= x94 <= 1 + 0 <= x95 <= 1 + 0 <= x96 <= 1 + 0 <= x97 <= 1 + 0 <= x98 <= 1 + 0 <= x99 <= 1 + 0 <= x100 <= 1 + 0 <= x101 <= 1 + 0 <= x102 <= 1 + 0 <= x103 <= 1 + 0 <= x104 <= 1 + 0 <= x105 <= 1 + 0 <= x106 <= 1 + 0 <= x107 <= 1 + 0 <= x108 <= 1 + 0 <= x109 <= 1 + 0 <= x110 <= 1 + 0 <= x111 <= 1 + 0 <= x112 <= 1 + 0 <= x113 <= 1 + 0 <= x114 <= 1 + 0 <= x115 <= 1 + 0 <= x116 <= 1 + 0 <= x117 <= 1 + 0 <= x118 <= 1 + 0 <= x119 <= 1 + 0 <= x120 <= 1 + 0 <= x121 <= 1 + 0 <= x122 <= 1 + 0 <= x123 <= 1 + 0 <= x124 <= 1 + +Binaries + x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 + x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 x34 x35 x36 x37 x38 x39 x40 x41 + x42 x43 x44 x45 x46 x47 x48 x49 x50 x51 x52 x53 x54 x55 x56 x57 x58 x59 x60 x61 + x62 x63 x64 x65 x66 x67 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+def draw_graph(G): + colors = ['tab:grey' for node in G.nodes()] + pos = nx.spring_layout(G) + default_axes = plt.axes(frameon=True) + nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, ax=default_axes, pos=pos) + edge_labels = nx.get_edge_attributes(G, "weight") + nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels) \ No newline at end of file diff --git a/demos/qiskit_patterns/demo_src/map.py b/demos/qiskit_patterns/demo_src/map.py new file mode 100644 index 0000000..ab94853 --- /dev/null +++ b/demos/qiskit_patterns/demo_src/map.py @@ -0,0 +1,16 @@ +from qiskit_optimization.applications import Maxcut +from qiskit.circuit.library import QAOAAnsatz + +def map_graph_to_qubo(graph): + max_cut = Maxcut(graph) + qp = max_cut.to_quadratic_program() + return qp + +def map_qubo_to_ising(qubo): + qubitOp, offset = qubo.to_ising() + return qubitOp, offset + +def map_ising_to_circuit(hamiltonian, num_layers): + ansatz = QAOAAnsatz(cost_operator=hamiltonian, reps=num_layers) + ansatz.measure_all() + return ansatz diff --git a/demos/qiskit_patterns/demo_src/post.py b/demos/qiskit_patterns/demo_src/post.py new file mode 100644 index 0000000..107842c --- /dev/null +++ b/demos/qiskit_patterns/demo_src/post.py @@ -0,0 +1,149 @@ +from collections import defaultdict +import json +import matplotlib +import matplotlib.pyplot as plt +import networkx as nx +import numpy as np +import os + +from qiskit_optimization.applications import Maxcut + + +# auxiliary functions to sample most likely bitstring +def to_bitstring(integer, num_bits): + result = np.binary_repr(integer, width=num_bits) + return [int(digit) for digit in result] + + +def sample_most_likely(state_vector, num_bits): + keys = list(state_vector.keys()) + values = list(state_vector.values()) + most_likely = keys[np.argmax(np.abs(values))] + most_likely_bitstring = to_bitstring(most_likely, num_bits) + most_likely_bitstring.reverse() + return np.asarray(most_likely_bitstring) + +# auxiliary function to plot graphs +def plot_result(G, x): + colors = ['tab:grey' if i == 0 else 'tab:purple' for i in x] + pos, default_axes = nx.spring_layout(G), plt.axes(frameon=True) + nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, pos=pos) + + +def plot_distribution(final_distribution): + matplotlib.rcParams.update({'font.size': 10}) + final_bits = final_distribution.binary_probabilities() + values = np.abs(list(final_bits.values())) + top_4_values = sorted(values, reverse = True)[:4] + positions = [] + for value in top_4_values: + positions.append(np.where(values == value)[0]) + fig = plt.figure(figsize = (11,6)) + ax=fig.add_subplot(1,1,1) + plt.xticks(rotation=45) + plt.title("Result Distribution") + plt.xlabel("Bitstrings (reversed)") + plt.ylabel("Probability") + ax.bar(list(final_bits.keys()), list(final_bits.values()), color='tab:grey') + for p in positions: + ax.get_children()[int(p)].set_color('tab:purple') + plt.show() + + +# auxiliary function to convert bit-strings to objective values +def samples_to_objective_values(samples, qp): + """Convert the samples to values of the objective function.""" + objective_values = defaultdict(float) + for bit_str, prob in samples.items(): + + # Qiskit use little endian hence the [::-1] + candidate_sol = [int(bit) for bit in bit_str[::-1]] + fval = qp.objective.evaluate(candidate_sol) + objective_values[fval] += prob + + return objective_values + + +# auxiliary function to load saved samples +def load_data(qp): + depth_one_heron, depth_zero_heron, depth_one_eagle, depth_zero_eagle = {}, {}, {}, {} + for file in os.listdir("sampler_data/"): + with open(f"sampler_data/{file}", "r") as fin: + data = json.load(fin) + + if file.startswith("heron"): + depth_one_heron.update(data["depth-one"]) + depth_zero_heron.update(data["depth-zero"]) + else: + depth_one_eagle.update(data["depth-one"]) + depth_zero_eagle.update(data["depth-zero"]) + + depth_zero_heron = samples_to_objective_values(depth_zero_heron, qp) + depth_one_heron = samples_to_objective_values(depth_one_heron, qp) + depth_zero_eagle = samples_to_objective_values(depth_zero_eagle, qp) + depth_one_eagle = samples_to_objective_values(depth_one_eagle, qp) + + return depth_one_heron, depth_zero_heron, depth_one_eagle, depth_zero_eagle + + +# auxiliary function to load the QP from the saved Paulis +def load_qp(): + + # First, load the Paulis that encode the MaxCut problem. + with open("data/125node_example_ising.txt", "r") as fin: + paulis, lines = [], fin.read() + for edge in lines.split("\n"): + try: + pauli, coefficient = edge.split(", ") + paulis.append((pauli, float(coefficient))) + except ValueError: + pass + + # Next, convert the Paulis to a weighted graph. + wedges = [] + for pauli_str, coefficient in paulis: + wedges.append([idx for idx, char in enumerate(pauli_str[::-1]) if char == "Z"] + [{"weight": coefficient}]) + + weighted_graph = nx.DiGraph(wedges) + + # Create the Quadratic program to return form the weighted graph. + mc = Maxcut(weighted_graph) + qp = mc.to_quadratic_program() + + # Finding the min and max requires CPLEX. If this is not installed we use + # hard coded values for the sake of the demo. + try: + from qiskit_optimization.algorithms import CplexOptimizer + from qiskit_optimization.problems.quadratic_objective import ObjSense + + # Mximization gives the max cut + sol = CplexOptimizer().solve(qp) + + # Minimization gives the min cut + qp2 = mc.to_quadratic_program() + qp2.objective._sense = ObjSense.MINIMIZE + sol2 = CplexOptimizer().solve(qp2) + + max_cut, min_cut = sol.fval, sol2.fval + except: + max_cut, min_cut = 67, -63 + + return qp, max_cut, min_cut + + +# auxiliary function to help plot cumulative distribution functions +def _plot_cdf(objective_values: dict, ax, label): + x_vals = sorted(objective_values.keys()) + y_vals = np.cumsum([objective_values[x] for x in x_vals]) + ax.plot(x_vals, y_vals, label=label) + +def plot_cdf(depth_zero, depth_one, max_cut, min_cut, ax, title): + _plot_cdf(depth_zero, ax, "Depth-zero") + _plot_cdf(depth_one, ax, "Depth-one") + ax.vlines(max_cut, 0, 1, "k", linestyle="--") + ax.vlines(max(list(depth_one.keys())), 0, 1, "C1", linestyle="--") + approx = 100 * (max(list(depth_one.keys())) - min_cut) / (max_cut - min_cut) + ax.set_title(title + f" {approx}%") + ax.set_xlabel("Objective function value") + ax.set_ylabel("Cumulative distribution function") + ax.legend(loc=2); \ No newline at end of file diff --git a/demos/qiskit_patterns/demo_src/run.py b/demos/qiskit_patterns/demo_src/run.py new file mode 100644 index 0000000..3a9d963 --- /dev/null +++ b/demos/qiskit_patterns/demo_src/run.py @@ -0,0 +1,13 @@ +from uuid import uuid4 +import json + + +# auxiliary function to save result data +def save_result(result, backend_type, path="sampler_data"): + results_to_save = { + "depth-one": result.quasi_dists[0].binary_probabilities(), + "depth-zero": result.quasi_dists[1].binary_probabilities(), + } + + with open(f"{path}/{backend_type}_{str(uuid4())[0:8]}.json", "w") as fout: + json.dump(results_to_save, fout) diff --git a/demos/qiskit_patterns/demo_src/transpile.py b/demos/qiskit_patterns/demo_src/transpile.py new file mode 100644 index 0000000..824dd8d --- /dev/null +++ b/demos/qiskit_patterns/demo_src/transpile.py @@ -0,0 +1,4 @@ +from qiskit import transpile + +def optimize_circuit(circuit, backend): + return transpile(circuit, backend=backend) \ No newline at end of file diff --git a/demos/qiskit_patterns/imgs/circuit.png b/demos/qiskit_patterns/imgs/circuit.png new file mode 100644 index 0000000000000000000000000000000000000000..b40755713e6c2c022978616eeedf8edc3efbe14b GIT binary patch literal 693003 zcmeF32UJtrx~LUJQB*(_P?~~>AVs8il%^n{bm<#JdJUl$vn_PkAVnZF0g=!|q*u2T z>Ae$zv;YAjoe+||uEwy7Kw6SI-_h zcI^Da2MU_Uj$QkB?AV#-6sL&4d6ZA>M*MLcq^W%WSV1S#0`VWOEcG8gS5rI2O?*vp zjQse;V<+}6A^vyl_|;?Nf4x3-OyxM^|9-7`{MLV7Lw4*~pv|$9|9Oo8@#p?amHq$y z@1G~qj{p6RX=H!9`r5~|6MuVs=K22T7%1i3i9gObKX?i{cI%bo*9fCJ0^GR zp~5|F&*Mwoko_xPq~UVtxn7+;aq1ky9kcou$AK4s5CBU6C;%t`C;%t`C;%t`C;%t` 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