{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Divisive Clustering With Coresets Using CUDA-Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial will explore a CUDA-Q implementation of recent research (ArXiv Paper: https://arxiv.org/pdf/2402.01529.pdf) performed by a team from the University of Edinburgh. This tutorial was jointly developed by NVIDIA and the authors so users can better understand their method and explore how CUDA-Q removed barriers to scaling. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code for this tutorial is based off the MIT licensed code found here: https://github.com/Boniface316/bigdata_vqa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clustering is a common unsupervised learning technique aimed at grouping data with similar characteristics. The unique properties of quantum computers could allow for enhanced pattern finding in clustering applications and enable more reliable data analysis. However, quantum computers today are severely limited by qubit count and noise.  Performing practical clustering applications would require far too many qubits.  The Edinburgh team developed a new method (extending the work of Harrow) to leverage coresets for clustering applications on quantum computers and use far fewer qubits.  This tutorial will walk through an example using this approach for divisive clustering and emphasize the utility of CUDA-Q for scaling quantum simulations.\n",
    "\n",
    "The goal of divisive clustering is to begin with all data points as one set, and iteratively bipartition the data until each point is its own cluster.  The branching behavior of this process can be used to understand similarities in the data points.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If you are running outside of a CUDA-Q container or CUDA-Q directory tree, you may need to uncomment these lines to fetch the files.\n",
    "# If you are running inside a CUDA-Q tree, then this step can be skipped.\n",
    "# !mkdir divisive_clustering_src\n",
    "# !wget -P divisive_clustering_src https://raw.githubusercontent.com/NVIDIA/cuda-quantum/main/docs/sphinx/applications/python/divisive_clustering_src/divisive_clustering.py\n",
    "# !wget -P divisive_clustering_src https://raw.githubusercontent.com/NVIDIA/cuda-quantum/main/docs/sphinx/applications/python/divisive_clustering_src/main_divisive_clustering.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install the relevant packages.\n",
    "!pip install mpi4py==3.1.6 networkx==2.8.8 pandas==2.2.2 scikit-learn==1.4.2 tqdm==4.66.2 -q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cudaq\n",
    "from cudaq import spin\n",
    "\n",
    "# Auxillary Imports\n",
    "import os\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "from typing import Tuple\n",
    "from divisive_clustering_src.divisive_clustering import Coreset, DivisiveClustering, Dendrogram, Voironi_Tessalation\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The settings below are global parameters for the quantum simulation and can be toggled by the user.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit_depth = 1\n",
    "max_iterations = 75\n",
    "max_shots = 1000\n",
    "np.random.seed(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Given a data set $X = (x_1, x_2, \\cdots, x_N)$, a coreset is weighted data set of much smaller size ($X', w$) that represents $X$ enough such that analysis of ($X', w$) can allow us to draw reasonable approximate conclusions about $X$. There are various approaches to build coresets. They can be found in Practical Coreset Construction for Machine Learning (https://arxiv.org/pdf/1703.06476.pdf) and New Streaming Algorithms for Coresets in Machine Learning (https://arxiv.org/pdf/1703.06476.pdf).\n",
    "\n",
    "\n",
    "Essentially, coreset construction boils down to finding the optimal coreset size and weights given some error tolerance.  Given the constraints of a quantum computer, in this work, a coreset size is selected $a$ $priori$, and the error is determined for each model.\n",
    "\n",
    "\n",
    "The following is an example $M=10$ coreset constructed from a 1000-point data set and loaded into a pandas data frame. See the image below where the coreset is represented by the black stars, the size of which corresponds to the weights.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using BFL2 method to generate coresets\n",
      "          X         Y     weights Name\n",
      "0  7.028364  1.669787  234.230716    A\n",
      "1  7.167441  0.354792  101.319288    B\n",
      "2  1.022889 -0.921443  125.158339    C\n",
      "3  2.706134 -2.636852   13.650774    D\n",
      "4  6.998497  0.455847  116.758239    E\n",
      "5  7.507918  0.630311  120.727176    F\n",
      "6 -2.102508  2.297727   53.294127    G\n",
      "7  5.722463  1.400433   77.415840    H\n",
      "8 -1.425868  2.341136   42.847985    I\n",
      "9  7.985373 -0.063209  240.116237    J\n"
     ]
    }
   ],
   "source": [
    "raw_data = Coreset.create_dataset(1000)\n",
    "coreset = Coreset(\n",
    "    raw_data=raw_data,\n",
    "    number_of_sampling_for_centroids=10,\n",
    "    coreset_size=10,\n",
    "    number_of_coresets_to_evaluate=4,\n",
    "    coreset_method=\"BFL2\",\n",
    ")\n",
    "\n",
    "coreset_vectors, coreset_weights = coreset.get_best_coresets()\n",
    "\n",
    "coreset_df = pd.DataFrame({\n",
    "    \"X\": coreset_vectors[:, 0],\n",
    "    \"Y\": coreset_vectors[:, 1],\n",
    "    \"weights\": coreset_weights\n",
    "})\n",
    "coreset_df[\"Name\"] = [chr(i + 65) for i in coreset_df.index]\n",
    "print(coreset_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(raw_data[:, 0], raw_data[:, 1], label=\"Raw Data\", c=\"#7eba00\")\n",
    "plt.scatter(\n",
    "    coreset_df[\"X\"],\n",
    "    coreset_df[\"Y\"],\n",
    "    s=coreset_df[\"weights\"],\n",
    "    label=\"Coreset\",\n",
    "    color=\"black\",\n",
    "    marker=\"*\",\n",
    ")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.title(\"Raw data and its best 10 coreset using BFL2\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to cluster data on a quantum computer, the task needs to be cast into the form of a binary optimization problem.  Each qubit represents a coreset point, and the quantum algorithm determines how to bipartition the coreset points at each iteration of the divisive clustering routine. \n",
    "\n",
    "The first step is to convert coreset points into a fully connected graph. The edge weight is calculated by:\n",
    "\n",
    "$e_{ij} = w_iw_jd_{ij}$ where $d_{ij}$ is the Euclidean distance between points $i$ and $j$. \n",
    "\n",
    "This process is handled by `Coreset.coreset_to_graph()`. The function returns a fully connected graph $G$ with edge weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The divisive clustering problem will be implemented on a quantum computer using a variational quantum algorithm (VQA) approach.  A VQA takes a Hamiltonian (encoded with the optimization problem) and a parameterized ansatz and evaluates expectation values (quantum computer) that inform updates to the ansatz parameters (classical computer).  The graph $G$ (Code in the \"src\" file) is used to construct the Hamiltonian, derived specifically for the divisive clustering problem, and motivated by a max-cut Hamiltonian.  The `spin.z(i)` method in CUDA-Q adds a Pauli Z operation that acts on qubit $i$ to the Hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_K2_Hamiltonian(G: nx.Graph) -> cudaq.SpinOperator:\n",
    "    \"\"\"Returns the K2 Hamiltonian for the given graph G\n",
    "\n",
    "    Args:\n",
    "        G (nx.Graph): Weighted graph\n",
    "    \"\"\"\n",
    "    H = 0\n",
    "\n",
    "    for i, j in G.edges():\n",
    "        weight = G[i][j][\"weight\"]\n",
    "        H += weight * (spin.z(i) * spin.z(j))\n",
    "\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below constructs a quantum kernel, defining the circuit which will serve as an ansatz.  The structure of the circuit is a hardware efficient ansatz consisting of layers of parameterized $R_Z$ and $R_Y$ gate acting on each qubit, followed by a linear cascade of CNOT gates, and two more rotation gates.\n",
    "\n",
    "The `@cudaq.kernel` decorator allows us to define a quantum circuit in the new kernel mode syntax which provides performance benefits to JIT compilation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_VQE_circuit(number_of_qubits: int, circuit_depth: int) -> cudaq.Kernel:\n",
    "    \"\"\"Returns the VQE circuit for the given number of qubits and circuit depth\n",
    "\n",
    "    Args:\n",
    "        number_of_qubits (int): Number of qubits\n",
    "        circuit_depth (int): Circuit depth\n",
    "\n",
    "    Returns:\n",
    "        cudaq.Kernel: VQE Circuit\n",
    "    \"\"\"\n",
    "\n",
    "    @cudaq.kernel\n",
    "    def kernel(thetas: list[float], number_of_qubits: int, circuit_depth: int):\n",
    "        \"\"\"VQE Circuit\n",
    "\n",
    "        Args:\n",
    "            thetas (list[float]): List of parameters\n",
    "            number_of_qubits (int): Number of qubits\n",
    "            circuit_depth (int): Circuit depth\n",
    "        \"\"\"\n",
    "        qubits = cudaq.qvector(number_of_qubits)\n",
    "\n",
    "        theta_position = 0\n",
    "\n",
    "        for i in range(circuit_depth):\n",
    "            for j in range(number_of_qubits):\n",
    "                ry(thetas[theta_position], qubits[j])\n",
    "                rz(thetas[theta_position + 1], qubits[j])\n",
    "\n",
    "                theta_position += 2\n",
    "\n",
    "            for j in range(number_of_qubits - 1):\n",
    "                cx(qubits[j], qubits[j + 1])\n",
    "\n",
    "            for j in range(number_of_qubits):\n",
    "                ry(thetas[theta_position], qubits[j])\n",
    "                rz(thetas[theta_position + 1], qubits[j])\n",
    "\n",
    "                theta_position += 2\n",
    "\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the circuit using the `cudaq.draw()` method. Below, we are drawing the circuit for 5 qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     ╭────────────╮ ╭────────────╮      ╭────────────╮╭────────────╮»\n",
      "q0 : ┤ ry(0.8904) ├─┤ rz(0.7335) ├───●──┤ ry(0.4343) ├┤ rz(0.2236) ├»\n",
      "     ├────────────┤ ├────────────┤ ╭─┴─╮╰────────────╯├────────────┤»\n",
      "q1 : ┤ ry(0.7937) ├─┤ rz(0.9981) ├─┤ x ├──────●───────┤ ry(0.3945) ├»\n",
      "     ├───────────┬╯ ├────────────┤ ╰───╯    ╭─┴─╮     ╰────────────╯»\n",
      "q2 : ┤ ry(0.696) ├──┤ rz(0.3352) ├──────────┤ x ├───────────●───────»\n",
      "     ├───────────┴╮╭┴────────────┤          ╰───╯         ╭─┴─╮     »\n",
      "q3 : ┤ ry(0.6658) ├┤ rz(0.05277) ├────────────────────────┤ x ├─────»\n",
      "     ├───────────┬╯├─────────────┴╮                       ╰───╯     »\n",
      "q4 : ┤ ry(0.791) ├─┤ rz(0.003569) ├─────────────────────────────────»\n",
      "     ╰───────────╯ ╰──────────────╯                                 »\n",
      "\n",
      "################################################################################\n",
      "\n",
      "                                             \n",
      "─────────────────────────────────────────────\n",
      "╭────────────╮                               \n",
      "┤ rz(0.4119) ├───────────────────────────────\n",
      "├────────────┤╭────────────╮                 \n",
      "┤ ry(0.3205) ├┤ rz(0.3504) ├─────────────────\n",
      "╰────────────╯├────────────┤ ╭────────────╮  \n",
      "──────●───────┤ ry(0.3913) ├─┤ rz(0.7392) ├──\n",
      "    ╭─┴─╮     ├────────────┤╭┴────────────┴─╮\n",
      "────┤ x ├─────┤ ry(0.3171) ├┤ rz(0.0008056) ├\n",
      "    ╰───╯     ╰────────────╯╰───────────────╯\n",
      "\n"
     ]
    }
   ],
   "source": [
    "parameter_count = 4 * circuit_depth * 5\n",
    "parameters = np.random.rand(parameter_count)\n",
    "\n",
    "circuit = get_VQE_circuit(5, circuit_depth)\n",
    "print(cudaq.draw(circuit, parameters, 5, circuit_depth))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to select a classical optimizer. There are multiple [optimizers](https://nvidia.github.io/cuda-quantum/latest/api/languages/python_api.html#optimizers) built-in to CUDA-Q that can be selected. The code below returns the optimizer with the proper number of initial parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimizer(optimizer: cudaq.optimizers.optimizer, max_iterations,\n",
    "                  **kwargs) -> Tuple[cudaq.optimizers.optimizer, int]:\n",
    "    \"\"\"Returns the optimizer with the given parameters\n",
    "\n",
    "    Args:\n",
    "        optimizer (cudaq.optimizers.optimizer): Optimizer\n",
    "        max_iterations (int): Maximum number of iterations\n",
    "        **kwargs: Additional arguments\n",
    "\n",
    "    Returns:\n",
    "        tuple(cudaq.optimizers.optimizer, int): Optimizer and parameter count\n",
    "    \"\"\"\n",
    "    parameter_count = 4 * kwargs[\"circuit_depth\"] * kwargs[\"qubits\"]\n",
    "    initial_params = np.random.uniform(-np.pi / 8.0, np.pi / 8.0,\n",
    "                                       parameter_count)\n",
    "    optimizer.initial_parameters = initial_params\n",
    "\n",
    "    optimizer.max_iterations = max_iterations\n",
    "    return optimizer, parameter_count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Divisive Clustering Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `DivisiveClusteringVQA` class enables the procedure to iteratively bipartition the coreset points until each is its own cluster. If you wish to develop on top of this or see how the underlying code works, please see the `divisive_clustering.py` file in the src directory. \n",
    "\n",
    "`run_divisive_clustering`, takes the current iteration's coreset points that will be bipartitioned as inputs, extracts the appropriate weights, and builds a graph $G$. The graph is then an input into the `get_counts_from_simulation` function. \n",
    "\n",
    "\n",
    "`get_counts_from_simulation` handles preparation and execution of the quantum simulation. First, it takes $G$ and from it builds a spin Hamiltonian. Second, it defines a cost function, which in this case is a lambda function that returns the expectation value of our parameterized quantum circuit and the Hamiltonian. This value is obtained using the CUDA-Q `observe` command, accelerated by GPUs.  After the expectation value is minimized, the quantum circuit corresponding to the optimal parameters is sampled using the CUDA-Q `sample` function. The bitstrings and their associated counts are returned by `get_counts_from_simulation`.\n",
    "\n",
    "A subset of these counts is evaluated to compute their exact cost. The best bitstring is returned and later used to assign the coreset points to one of two clusters.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DivisiveClusteringVQA(DivisiveClustering):\n",
    "\n",
    "    def __init__(\n",
    "        self,\n",
    "        **kwargs,\n",
    "    ):\n",
    "        super().__init__(**kwargs)\n",
    "\n",
    "    def run_divisive_clustering(\n",
    "        self,\n",
    "        coreset_vectors_df_for_iteration: pd.DataFrame,\n",
    "    ):\n",
    "        \"\"\"Runs the Divisive Clustering algorithm\n",
    "\n",
    "        Args:\n",
    "            coreset_vectors_df_for_iteration (pd.DataFrame): Coreset vectors for the iteration\n",
    "\n",
    "        Returns:\n",
    "            str: Best bitstring\n",
    "\n",
    "        \"\"\"\n",
    "        coreset_vectors_for_iteration_np, coreset_weights_for_iteration_np = (\n",
    "            self._get_iteration_coreset_vectors_and_weights(\n",
    "                coreset_vectors_df_for_iteration))\n",
    "\n",
    "        G = Coreset.coreset_to_graph(\n",
    "            coreset_vectors_for_iteration_np,\n",
    "            coreset_weights_for_iteration_np,\n",
    "            metric=self.coreset_to_graph_metric,\n",
    "        )\n",
    "\n",
    "        counts = self.get_counts_from_simulation(\n",
    "            G,\n",
    "            self.circuit_depth,\n",
    "            self.max_iterations,\n",
    "            self.max_shots,\n",
    "        )\n",
    "\n",
    "        return self._get_best_bitstring(counts, G)\n",
    "\n",
    "    def get_counts_from_simulation(self, G: nx.graph, circuit_depth: int,\n",
    "                                   max_iterations: int,\n",
    "                                   max_shots: int) -> cudaq.SampleResult:\n",
    "        \"\"\"\n",
    "        Runs the VQA simulation\n",
    "\n",
    "        Args:\n",
    "            G (nx.graph): Graph\n",
    "            circuit_depth (int): Circuit depth\n",
    "            max_iterations (int): Maximum number of iterations\n",
    "            max_shots (int): Maximum number of shots\n",
    "\n",
    "        Returns:\n",
    "            cudaq.SampleResult: Measurement from the experiment\n",
    "        \"\"\"\n",
    "\n",
    "        qubits = len(G.nodes)\n",
    "        Hamiltonian = self.create_Hamiltonian(G)\n",
    "        optimizer, parameter_count = self.optimizer_function(\n",
    "            self.optimizer,\n",
    "            max_iterations,\n",
    "            qubits=qubits,\n",
    "            circuit_depth=circuit_depth)\n",
    "\n",
    "        kernel = self.create_circuit(qubits, circuit_depth)\n",
    "\n",
    "        def objective_function(\n",
    "            parameter_vector: list[float],\n",
    "            hamiltonian: cudaq.SpinOperator = Hamiltonian,\n",
    "            kernel: cudaq.Kernel = kernel,\n",
    "        ) -> float:\n",
    "            \"\"\"\n",
    "\n",
    "            Objective function that returns the cost of the simulation\n",
    "\n",
    "            Args:\n",
    "                parameter_vector (List[float]):\n",
    "                hamiltonian (cudaq.SpinOperator): Circuit parameter values as a vector\n",
    "                kernel (cudaq.Kernel) : Circuit configuration\n",
    "\n",
    "            Returns:\n",
    "                float: Expectation value of the circuit\n",
    "\n",
    "            \"\"\"\n",
    "\n",
    "            get_result = lambda parameter_vector: cudaq.observe(\n",
    "                kernel, hamiltonian, parameter_vector, qubits, circuit_depth\n",
    "            ).expectation()\n",
    "\n",
    "            cost = get_result(parameter_vector)\n",
    "\n",
    "            return cost\n",
    "\n",
    "        energy, optimal_parameters = optimizer.optimize(\n",
    "            dimensions=parameter_count, function=objective_function)\n",
    "\n",
    "        counts = cudaq.sample(kernel,\n",
    "                              optimal_parameters,\n",
    "                              qubits,\n",
    "                              circuit_depth,\n",
    "                              shots_count=max_shots)\n",
    "\n",
    "        return counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An instance of the `DivisiveClusteringVQA` class is mostly constructed from variables previously discussed like the functions for building the Hamiltonians and quantum circuits. Parameters related to the quantum simulation can also be specified here such as `circuit_depth` and `max_shots`.  The ` threshold_for_max_cut` parameter specifies what percent of the sample results from the quantum computer are checked for the best bitstring value.\n",
    "\n",
    "The other options specify advanced features like if the data is normalized and how the graph weights are computed.\n",
    "\n",
    "\n",
    "Finally, the `get_divisive_sequence` method performs the iterations and produces the clustering data which we will analyze below. Note that this postprocessing code is not exposed in this tutorial but can be found in the source code. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "optimizer = cudaq.optimizers.COBYLA()\n",
    "\n",
    "divisive_clustering = DivisiveClusteringVQA(\n",
    "    circuit_depth=circuit_depth,\n",
    "    max_iterations=max_iterations,\n",
    "    max_shots=max_shots,\n",
    "    threshold_for_max_cut=0.75,\n",
    "    create_Hamiltonian=get_K2_Hamiltonian,\n",
    "    optimizer=optimizer,\n",
    "    optimizer_function=get_optimizer,\n",
    "    create_circuit=get_VQE_circuit,\n",
    "    normalize_vectors=True,\n",
    "    sort_by_descending=True,\n",
    "    coreset_to_graph_metric=\"dist\",\n",
    ")\n",
    "\n",
    "hierarchial_clustering_sequence = divisive_clustering.get_divisive_sequence(\n",
    "    coreset_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data can be nicely visualized with a Dendrogram which maps where the bipartitionings occurred. Early splits generally mark divisions between the least similar data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dendo = Dendrogram(coreset_df, hierarchial_clustering_sequence)\n",
    "dendo.plot_dendrogram(plot_title=\"Dendrogram of Coreset using VQE\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each branch point in the dendrogram aboves corresponds to one of the plots below. Notice the first iterations are the most complicated, and the final iterations become trivial bipartitioning of two points. Occasionally, especially in the first iteration, the partitioning might be puzzling at first glance. The data might seem to naturally cluster into two groups. However, there are cases where a stray point seems to belong in the wrong cluster.  There are two explanations for this.  1) The quantum sampling is approximate and stochastic. It is possible that too few shots were taken to sample the ground state of the problem. 2) It is important to remember that we are clustering coresets and not data points. There can be cases where it is optimal to pay a penalty by excluding a point based on proximity if the weights are small enough that the penalty has less impact. Usually, if a point looks unusually clustered and you go look at the original coresets plotted above, that point will have a small weight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1200 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Dendrogram.plot_hierarchial_split(hierarchial_clustering_sequence, coreset_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hierarchical clustering can be converted to flat clustering by drawing a line perpendicular to the branches. Any data point that intersects the line is considered to be in the same cluster. The function below performs this task at threshold height of 1.5. If you want to use the number of clusters instead of height, you can use `dendo.get_clusters_using_k()` method. You pass the number of desired clusters as an argument. The figure below shows the clusters that are formed at threshold height of 1.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "threshold_height = 1\n",
    "clusters = dendo.get_clusters_using_height(threshold_height)\n",
    "colors = [\"red\", \"blue\", \"green\", \"black\", \"purple\", \"orange\", \"yellow\"]\n",
    "dendo.plot_dendrogram(\n",
    "    plot_title=\"Dendrogram of Coreset using VQE\",\n",
    "    colors=colors,\n",
    "    clusters=clusters,\n",
    "    color_threshold=threshold_height,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can visualize the flat clusters using `dendo.plot_clusters()` method. The function takes the clusters and colors as arguments. The clusters are represented by different colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dendo.plot_clusters(clusters,\n",
    "                    colors,\n",
    "                    plot_title=\"Clusters of Coreset using VQE\",\n",
    "                    show_annotation=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function below uses the `dendo.get_voronoi_tessalation()` method to convert the clusters into regions. `coreset_df`, `clusters` and `colors` need to be passed as the arguments to create the regions. This function creates a region for each coreset point separately and then colors them according to the clusters with colors passed as arguments. Another option is to create regions using the centroids of the clusters. You need to pass `tesslation_by_cluster=True` to the function to perform this task.\n",
    "\n",
    "Once the region creation is complete, you can use `plot_voironi()` method to plot the regions. The function takes the clusters and colors as arguments. \n",
    "\n",
    "Remembering that these regions were based on coresets, they can overlay the original data set and be used to cluster the data based on the coreset analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vt = Voironi_Tessalation(coreset_df,\n",
    "                         clusters,\n",
    "                         colors,\n",
    "                         tesslation_by_cluster=False)\n",
    "vt.plot_voironi(plot_title=\"Voironi Tessalation of Coreset using VQE\",\n",
    "                show_annotation=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QAOA Implementation\n",
    "\n",
    "CUDA-Q is designed to be a flexible tool for developers so they can test different implementations of the same code. For example, one can perform the same analysis, instead using a QAOA approach. Only the kernel needs to be changed as is done below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                             »\n",
      "q0 : ──●──────────────────●──────────────────────────────────────────────────»\n",
      "     ╭─┴─╮╭────────────╮╭─┴─╮                                                »\n",
      "q1 : ┤ x ├┤ rz(0.3527) ├┤ x ├──●──────────────────●──────────────────────────»\n",
      "     ╰───╯╰────────────╯╰───╯╭─┴─╮╭────────────╮╭─┴─╮                        »\n",
      "q2 : ────────────────────────┤ x ├┤ rz(0.3527) ├┤ x ├──●──────────────────●──»\n",
      "                             ╰───╯╰────────────╯╰───╯╭─┴─╮╭────────────╮╭─┴─╮»\n",
      "q3 : ────────────────────────────────────────────────┤ x ├┤ rz(0.3527) ├┤ x ├»\n",
      "                                                     ╰───╯╰────────────╯╰───╯»\n",
      "q4 : ────────────────────────────────────────────────────────────────────────»\n",
      "                                                                             »\n",
      "\n",
      "################################################################################\n",
      "\n",
      "                        ╭───╮╭────────────╮╭───╮╭───────────╮\n",
      "────────────────────────┤ x ├┤ rz(0.3527) ├┤ x ├┤ rx(1.111) ├\n",
      "                        ╰─┬─╯╰────────────╯╰─┬─╯├───────────┤\n",
      "──────────────────────────┼──────────────────┼──┤ rx(1.111) ├\n",
      "                          │                  │  ├───────────┤\n",
      "──────────────────────────┼──────────────────┼──┤ rx(1.111) ├\n",
      "                          │                  │  ├───────────┤\n",
      "──●──────────────────●────┼──────────────────┼──┤ rx(1.111) ├\n",
      "╭─┴─╮╭────────────╮╭─┴─╮  │                  │  ├───────────┤\n",
      "┤ x ├┤ rz(0.3527) ├┤ x ├──●──────────────────●──┤ rx(1.111) ├\n",
      "╰───╯╰────────────╯╰───╯                        ╰───────────╯\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def get_QAOA_circuit(number_of_qubits, circuit_depth) -> cudaq.Kernel:\n",
    "    \"\"\"Returns the QAOA circuit for the given number of qubits and circuit depth\n",
    "\n",
    "\n",
    "    Args:\n",
    "        number_of_qubits (int): Number of qubits\n",
    "        circuit_depth (int): Circuit depth\n",
    "\n",
    "    Returns:\n",
    "        cudaq.Kernel: QAOA Circuit\n",
    "    \"\"\"\n",
    "\n",
    "    @cudaq.kernel\n",
    "    def kernel(thetas: list[float], number_of_qubits: int, circuit_depth: int):\n",
    "        qubits = cudaq.qvector(number_of_qubits)\n",
    "\n",
    "        layers = circuit_depth\n",
    "\n",
    "        for layer in range(layers):\n",
    "            for qubit in range(number_of_qubits):\n",
    "                cx(qubits[qubit], qubits[(qubit + 1) % number_of_qubits])\n",
    "                rz(2.0 * thetas[layer], qubits[(qubit + 1) % number_of_qubits])\n",
    "                cx(qubits[qubit], qubits[(qubit + 1) % number_of_qubits])\n",
    "\n",
    "            rx(2.0 * thetas[layer + layers], qubits)\n",
    "\n",
    "    return kernel\n",
    "\n",
    "\n",
    "circuit = get_QAOA_circuit(5, circuit_depth)\n",
    "\n",
    "print(cudaq.draw(circuit, np.random.rand(2 * circuit_depth), 5, circuit_depth))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimizer(optimizer: cudaq.optimizers.optimizer, max_iterations,\n",
    "                  **kwargs) -> Tuple[cudaq.optimizers.optimizer, int]:\n",
    "    \"\"\"\n",
    "    Returns the optimizer with the given parameters\n",
    "\n",
    "    Args:\n",
    "        optimizer (cudaq.optimizers.optimizer): Optimizer\n",
    "        max_iterations (int): Maximum number of iterations\n",
    "        **kwargs: Additional arguments\n",
    "\n",
    "    Returns:\n",
    "        tuple(cudaq.optimizers.optimizer, int): Optimizer and parameter count\n",
    "    \"\"\"\n",
    "\n",
    "    parameter_count = 2 * kwargs[\"circuit_depth\"]\n",
    "    optimizer.initial_parameters = np.random.uniform(-np.pi / 8.0, np.pi / 8.0,\n",
    "                                                     parameter_count)\n",
    "    optimizer.max_iterations = max_iterations\n",
    "    return optimizer, parameter_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 484/484 [00:00<00:00, 12163.89it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 12/12 [00:00<00:00, 52703.30it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 48/48 [00:00<00:00, 31987.07it/s]\n",
      "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4/4 [00:00<00:00, 36393.09it/s]\n",
      "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4/4 [00:00<00:00, 37957.50it/s]\n",
      "100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 4/4 [00:00<00:00, 42473.96it/s]\n"
     ]
    }
   ],
   "source": [
    "optimizer = cudaq.optimizers.COBYLA()\n",
    "\n",
    "divisive_clustering = DivisiveClusteringVQA(\n",
    "    circuit_depth=circuit_depth,\n",
    "    max_iterations=max_iterations,\n",
    "    max_shots=max_shots,\n",
    "    threshold_for_max_cut=0.75,\n",
    "    create_Hamiltonian=get_K2_Hamiltonian,\n",
    "    optimizer=optimizer,\n",
    "    optimizer_function=get_optimizer,\n",
    "    create_circuit=get_QAOA_circuit,\n",
    "    normalize_vectors=True,\n",
    "    sort_by_descending=True,\n",
    "    coreset_to_graph_metric=\"dist\",\n",
    ")\n",
    "\n",
    "hierarchial_clustering_sequence = divisive_clustering.get_divisive_sequence(\n",
    "    coreset_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling simulations with CUDA-Q\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The University of Edinburgh team quickly encountered scaling challenges when they were developing this method. By developing with CUDA-Q they were able to port their code to an HPC environment once GPUs became available. GPUs massively accelerated their development and testing and allowed them to produce the 25 qubit experiments presented in their publication. If you have a GPU available, run the following code examples and see how the times compare on your device. Each call executes the divisive clustering procedure using the QAOA method, 100000 simulated shots for each VQE loop, and maximum 75 VQE iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, try a slightly larger N=18 problem using the CPU (`qpp-cpu`) backend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uncomment the following line if you want to explicitly execute this step on your system.\n",
    "# !python3 divisive_clustering_src/main_divisive_clustering.py --target qpp-cpu --M 18"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try the N=18 example on the GPU backend (`nvidia`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using BFL2 method to generate coresets\n",
      "100%|███████████████████████████████████████| 751/751 [00:00<00:00, 3460.26it/s]\n",
      "100%|████████████████████████████████████████| 16/16 [00:00<00:00, 42771.74it/s]\n",
      "100%|█████████████████████████████████████| 4064/4064 [00:00<00:00, 6862.37it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 56871.92it/s]\n",
      "100%|████████████████████████████████████████| 16/16 [00:00<00:00, 44979.13it/s]\n",
      "100%|██████████████████████████████████████| 128/128 [00:00<00:00, 19366.94it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 53773.13it/s]\n",
      "100%|██████████████████████████████████████████| 8/8 [00:00<00:00, 54648.91it/s]\n",
      "100%|██████████████████████████████████████████| 8/8 [00:00<00:00, 51941.85it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 56111.09it/s]\n",
      "Total time for the execution: 461.866833317\n",
      "Total time spent on CUDA-Q: 10.452308367999706\n"
     ]
    }
   ],
   "source": [
    "!python3 divisive_clustering_src/main_divisive_clustering.py --target nvidia --M 18"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scaling up to N=25, the task becomes even more onerous on a CPU. Depending on your device, the simulation may not even run. Try it and feel free to interrupt after your patience has worn out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# target = 'qpp-cpu'\n",
    "# Uncomment the following line if you want to explicitly execute this step on your system.\n",
    "# !python3 divisive_clustering_src/main_divisive_clustering.py --target qpp-cpu --M 25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "N=25 can still easily be completed by a single GPU."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using BFL2 method to generate coresets\n",
      "100%|█████████████████████████████████████| 7352/7352 [00:03<00:00, 2063.82it/s]\n",
      "100%|███████████████████████████████████| 16492/16492 [00:03<00:00, 4739.44it/s]\n",
      "100%|██████████████████████████████████████| 256/256 [00:00<00:00, 15185.58it/s]\n",
      "100%|████████████████████████████████████████| 64/64 [00:00<00:00, 23728.05it/s]\n",
      "100%|██████████████████████████████████████| 256/256 [00:00<00:00, 15437.97it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 50840.05it/s]\n",
      "100%|████████████████████████████████████████| 32/32 [00:00<00:00, 33562.82it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 54120.05it/s]\n",
      "100%|██████████████████████████████████████████| 8/8 [00:00<00:00, 54560.05it/s]\n",
      "100%|██████████████████████████████████████████| 8/8 [00:00<00:00, 55924.05it/s]\n",
      "100%|████████████████████████████████████████| 16/16 [00:00<00:00, 42717.29it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 55007.27it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 53601.33it/s]\n",
      "100%|██████████████████████████████████████████| 4/4 [00:00<00:00, 47127.01it/s]\n",
      "Total time for the execution: 67.61674502899999\n",
      "Total time spent on CUDA-Q: 21.439895901\n"
     ]
    }
   ],
   "source": [
    "# target = 'nvidia'\n",
    "!python3 divisive_clustering_src/main_divisive_clustering.py --target nvidia --M 25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to push the simulation to an $N=34$ coreset, a single GPU (assuming A100) will run out of memory.  Run the code below to see for yourself. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using BFL2 method to generate coresets\n",
      "RuntimeError: NLOpt runtime error: nlopt failure\n"
     ]
    }
   ],
   "source": [
    "# target = 'nvidia'\n",
    "!python3 divisive_clustering_src/main_divisive_clustering.py --target nvidia --M 34"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute a problem with 34 qubits, we need to pool the memory of multiple GPUs.  If you have multiple GPUs available, try the code below to run the same computation on 4 GPUs. You do not need to wait for the code to finish, just note how it does not fail immediately due to memory issues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using BFL2 method to generate coresets\n",
      "Using BFL2 method to generate coresets\n",
      "Using BFL2 method to generate coresets\n",
      "Using BFL2 method to generate coresets\n",
      "^C\n"
     ]
    }
   ],
   "source": [
    "# target = 'nvidia-mgpu'\n",
    "gpu_count = !nvidia-smi -L | wc -l\n",
    "try:\n",
    "    gpu_count = int(gpu_count[0])\n",
    "except:\n",
    "    gpu_count = 0\n",
    "if gpu_count >= 4:\n",
    "    !mpirun -np 4 python3 divisive_clustering_src/main_divisive_clustering.py --target nvidia-mgpu --M 34\n",
    "else:\n",
    "    print(\n",
    "        f'Not enough GPUs found on this system ({gpu_count}) to run this step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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