added template for exercise 03

template-exercise-03.ipynb

@@ -0,0 +1,220 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "fb789dfb",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "# Template to Exercise 3\n",
+    "\n",
+    "Author: Tobias Stollenwerk, Institute for Quantum Computing Analytics (PGI-12), FZ Jülich\n",
+    "\n",
+    "**Please use this template for exercise 3**\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "b0602cae",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import qiskit\n",
+    "# numerics\n",
+    "import numpy as np\n",
+    "# functional programmin tools\n",
+    "import itertools\n",
+    "import functools\n",
+    "import operator\n",
+    "# plotting\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn\n",
+    "# data analysis\n",
+    "import pandas as pd\n",
+    "# qiskit \n",
+    "from qiskit import QuantumCircuit, transpile\n",
+    "from qiskit_aer import QasmSimulator, AerSimulator\n",
+    "from qiskit.quantum_info import Pauli\n",
+    "from qiskit.visualization import array_to_latex, plot_histogram\n",
+    "from qiskit.quantum_info import Kraus, SuperOp, SparsePauliOp, Operator, DensityMatrix, Statevector\n",
+    "from qiskit_aer.noise import NoiseModel, QuantumError, ReadoutError, depolarizing_error\n",
+    "from qiskit.circuit import ParameterVector\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "a65a8836",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 454.517x284.278 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "circuit = QuantumCircuit(2, 2)\n",
+    "circuit.h(0)\n",
+    "circuit.cx(0, 1)\n",
+    "circuit.measure(0, 0)\n",
+    "circuit.measure(1, 1);\n",
+    "# display the circuit\n",
+    "display(circuit.draw('mpl'))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "6947dacd-c4ef-4640-a005-ccacace9ade0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p = 0.1\n",
+    "\n",
+    "error_1 = depolarizing_error(p, 1)\n",
+    "error_2 = error_1.tensor(error_1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "959f011f-9c47-4b36-929c-82430417ee0e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ... build noise model "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Hints for exercise 3.2 - quantum optimization\n",
+    "\n",
+    "Consider the MaxCut case\n",
+    "\n",
+    "$$\n",
+    "H_f = \\sum_{u, v \\in E} Z_u Z_v\n",
+    "$$\n",
+    "\n",
+    "for the edge set $E = \\{(1, 2), (2, 3), (2, 4), (3, 4)\\}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "E = [(1, 2), (2, 3), (2, 4), (3, 4)]\n",
+    "V = [1, 2, 3, 4]\n",
+    "\n",
+    "pauli_strings = []\n",
+    "for u, v in E:\n",
+    "    pauli_strings.append(\"\".join([\"I\" if i not in (u, v) else \"Z\" for i in V ]))\n",
+    "H = SparsePauliOp(pauli_strings)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "dict_keys([(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (0, 0, 1, 1), (0, 1, 0, 0), (0, 1, 0, 1), (0, 1, 1, 0), (0, 1, 1, 1), (1, 0, 0, 0), (1, 0, 0, 1), (1, 0, 1, 0), (1, 0, 1, 1), (1, 1, 0, 0), (1, 1, 0, 1), (1, 1, 1, 0), (1, 1, 1, 1)])\n"
+     ]
+    }
+   ],
+   "source": [
+    "basis_states = {}\n",
+    "ket = {0: Statevector([1, 0]), 1: Statevector([0, 1])}\n",
+    "for i, bitstring in enumerate(itertools.product([0, 1], repeat=4)):\n",
+    "    state = ket[bitstring[0]]\n",
+    "    for k in range(len(bitstring) - 1):\n",
+    "        state = state.tensor(ket[bitstring[k + 1]])\n",
+    "    basis_states[bitstring] = state\n",
+    "print(basis_states.keys())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<(0, 0, 0, 0)|H|(0, 0, 0, 0)> = (4+0j)\n",
+      "<(0, 0, 0, 1)|H|(0, 0, 0, 1)> = 0j\n",
+      "<(0, 0, 1, 0)|H|(0, 0, 1, 0)> = 0j\n",
+      "<(0, 0, 1, 1)|H|(0, 0, 1, 1)> = 0j\n",
+      "<(0, 1, 0, 0)|H|(0, 1, 0, 0)> = (-2+0j)\n",
+      "<(0, 1, 0, 1)|H|(0, 1, 0, 1)> = (-2+0j)\n",
+      "<(0, 1, 1, 0)|H|(0, 1, 1, 0)> = (-2+0j)\n",
+      "<(0, 1, 1, 1)|H|(0, 1, 1, 1)> = (2+0j)\n",
+      "<(1, 0, 0, 0)|H|(1, 0, 0, 0)> = (2+0j)\n",
+      "<(1, 0, 0, 1)|H|(1, 0, 0, 1)> = (-2+0j)\n",
+      "<(1, 0, 1, 0)|H|(1, 0, 1, 0)> = (-2+0j)\n",
+      "<(1, 0, 1, 1)|H|(1, 0, 1, 1)> = (-2+0j)\n",
+      "<(1, 1, 0, 0)|H|(1, 1, 0, 0)> = 0j\n",
+      "<(1, 1, 0, 1)|H|(1, 1, 0, 1)> = 0j\n",
+      "<(1, 1, 1, 0)|H|(1, 1, 1, 0)> = 0j\n",
+      "<(1, 1, 1, 1)|H|(1, 1, 1, 1)> = (4+0j)\n"
+     ]
+    }
+   ],
+   "source": [
+    "for bitstring, state in basis_states.items():\n",
+    "    f = state.expectation_value(H)\n",
+    "    print(\"<{}|H|{}> = {}\".format(bitstring, bitstring, f))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "celltoolbar": "Slideshow",
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}