optimization + ai notebooks updated (#457)

* optimization + ai

* optimization + ai

* variational rerun

Author: liupibm

community/aqua/artificial_intelligence/qsvm_kernel_directly.ipynb

@@ -0,0 +1,262 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## _*Using Qiskit Aqua for clique problems*_\n",
+    "\n",
+    "This Qiskit Aqua Optimization notebook demonstrates how to use the VQE quantum algorithm to compute the clique of a given graph. \n",
+    "\n",
+    "The problem is defined as follows. A clique in a graph $G$ is a complete subgraph of $G$. That is, it is a subset $K$ of the vertices such that every two vertices in $K$ are the two endpoints of an edge in $G$. A maximal clique is a clique to which no more vertices can be added. A maximum clique is a clique that includes the largest possible number of vertices. \n",
+    "\n",
+    "We will go through three examples to show (1) how to run the optimization in the non-programming way, (2) how to run the optimization in the programming way, (3) how to run the optimization with the VQE.\n",
+    "We will omit the details for the support of CPLEX, which are explained in other notebooks such as maxcut.\n",
+    "\n",
+    "Note that the solution may not be unique."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "###  The problem and a brute-force method."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "from qiskit import Aer\n",
+    "\n",
+    "from qiskit_aqua import run_algorithm\n",
+    "from qiskit_aqua.input import EnergyInput\n",
+    "from qiskit_aqua.translators.ising import clique\n",
+    "from qiskit_aqua.algorithms import ExactEigensolver"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "first, let us have a look at the graph, which is in the adjacent matrix form."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.  4.  5.  3. -5.]\n",
+      " [ 4.  0.  7.  0.  6.]\n",
+      " [ 5.  7.  0. -4.  0.]\n",
+      " [ 3.  0. -4.  0.  8.]\n",
+      " [-5.  6.  0.  8.  0.]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "K = 3  # K means the size of the clique\n",
+    "np.random.seed(100)\n",
+    "num_nodes = 5\n",
+    "w = clique.random_graph(num_nodes, edge_prob=0.8, weight_range=10)\n",
+    "print(w) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us try a brute-force method. Basically, we exhaustively try all the binary assignments. In each binary assignment, the entry of a vertex is either 0 (meaning the vertex is not in the clique) or 1 (meaning the vertex is in the clique). We print the binary assignment that satisfies the definition of the clique (Note the size is specified as K)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "solution is  [1, 0, 0, 1, 1]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def brute_force():\n",
+    "    # brute-force way: try every possible assignment!\n",
+    "    def bitfield(n, L):\n",
+    "        result = np.binary_repr(n, L)\n",
+    "        return [int(digit) for digit in result]\n",
+    "\n",
+    "    L = num_nodes  # length of the bitstring that represents the assignment\n",
+    "    max = 2**L\n",
+    "    has_sol = False\n",
+    "    for i in range(max):\n",
+    "        cur = bitfield(i, L)\n",
+    "        cur_v = clique.satisfy_or_not(np.array(cur), w, K)\n",
+    "        if cur_v:\n",
+    "            has_sol = True\n",
+    "            break\n",
+    "    return has_sol, cur\n",
+    "\n",
+    "has_sol, sol = brute_force()\n",
+    "if has_sol:\n",
+    "    print(\"solution is \", sol)\n",
+    "else:\n",
+    "    print(\"no solution found for K=\", K)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Part I: run the optimization in the non-programming way"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "solution is [1. 0. 1. 1. 0.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "qubit_op, offset = clique.get_clique_qubitops(w, K)\n",
+    "algo_input = EnergyInput(qubit_op)\n",
+    "params = {\n",
+    "    'problem': {'name': 'ising'},\n",
+    "    'algorithm': {'name': 'ExactEigensolver'}\n",
+    "}\n",
+    "result = run_algorithm(params, algo_input)\n",
+    "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n",
+    "ising_sol = clique.get_graph_solution(x)\n",
+    "if clique.satisfy_or_not(ising_sol, w, K):\n",
+    "    print(\"solution is\", ising_sol)\n",
+    "else:\n",
+    "    print(\"no solution found for K=\", K)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Part II: run the optimization in the programming way"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "solution is [1. 0. 1. 1. 0.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "algo = ExactEigensolver(algo_input.qubit_op, k=1, aux_operators=[])\n",
+    "result = algo.run()\n",
+    "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n",
+    "ising_sol = clique.get_graph_solution(x)\n",
+    "if clique.satisfy_or_not(ising_sol, w, K):\n",
+    "    print(\"solution is\", ising_sol)\n",
+    "else:\n",
+    "    print(\"no solution found for K=\", K)     "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Part III: run the optimization with the VQE"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "solution is [1. 0. 1. 1. 0.]\n"
+     ]
+    }
+   ],
+   "source": [
+    "algorithm_cfg = {\n",
+    "    'name': 'VQE',\n",
+    "    'operator_mode': 'matrix'\n",
+    "}\n",
+    "\n",
+    "optimizer_cfg = {\n",
+    "    'name': 'COBYLA'\n",
+    "}\n",
+    "\n",
+    "var_form_cfg = {\n",
+    "    'name': 'RY',\n",
+    "    'depth': 5,\n",
+    "    'entanglement': 'linear'\n",
+    "}\n",
+    "\n",
+    "params = {\n",
+    "    'problem': {'name': 'ising', 'random_seed': 10598},\n",
+    "    'algorithm': algorithm_cfg,\n",
+    "    'optimizer': optimizer_cfg,\n",
+    "    'variational_form': var_form_cfg\n",
+    "}\n",
+    "backend = Aer.get_backend('statevector_simulator')\n",
+    "result = run_algorithm(params, algo_input, backend=backend)\n",
+    "x = clique.sample_most_likely(len(w), result['eigvecs'][0])\n",
+    "ising_sol = clique.get_graph_solution(x)\n",
+    "\n",
+    "if clique.satisfy_or_not(ising_sol, w, K):\n",
+    "    print(\"solution is\", ising_sol)\n",
+    "else:\n",
+    "    print(\"no solution found for K=\", K)"
+   ]
+  }
+ ],
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+  "kernelspec": {
+   "display_name": "mykernel",
+   "language": "python",
+   "name": "mykernel"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
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+}