└── how_to_solve_qubo.ipynb


/how_to_solve_qubo.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "id": "19cf4efc-ea31-4b90-b4f1-8217ce8cdd1d",
  6 |    "metadata": {},
  7 |    "source": [
  8 |     "\n",
  9 |     "\n",
 10 |     "# Events organization\n",
 11 |     "\n",
 12 |     "Events: $E_1$, $E_2$, $E_3$, $E_4$ and $E_5$\n",
 13 |     "\n",
 14 |     "People: $P_1$, $P_2$, $P_3$ and $P_4$.\n",
 15 |     "\n",
 16 |     "\n",
 17 |     "Preferences:\n",
 18 |     "- $P_1$ want to go to $E_1$ and $E_4$.\n",
 19 |     "- $P_2$ want to go to $E_2$ and $E_3$.\n",
 20 |     "- $P_3$ want to go to $E_4$ and $E_5$.\n",
 21 |     "- $P_4$ want to go to $E_3$ and $E_4$.\n",
 22 |     "\n",
 23 |     "Binary variables:\n",
 24 |     "\n",
 25 |     "- $x_i = 0$ if the i-th event is on Saturday\n",
 26 |     "- $x_i = 1$ if the i-th event is on Sunday\n",
 27 |     "\n",
 28 |     "Formulation:\n",
 29 |     "\n",
 30 |     "$f(x_1,x_2,x_3,x_4,x_5) = 4 + x_1 + x_2 + 2x_3 + 3x_4 + x_5 -2x_1x_4-2x_2x_3-2x_4x_5-2x_3x_4$\n",
 31 |     "\n",
 32 |     "Change of variable:\n",
 33 |     "\n",
 34 |     "$x_i = \\frac{1-z_i}{2}$\n",
 35 |     "\n",
 36 |     "- $z_i = 1$ if the i-th event is on Saturday\n",
 37 |     "- $z_i = -1$ if the i-th event is on Sunday\n",
 38 |     "\n",
 39 |     "New formulation:\n",
 40 |     "\n",
 41 |     "$f(z_1,z_2,z_3,z_4,z_5) = 6 - \\frac{1}{2}z_1z_4- \\frac{1}{2}z_2z_3- \\frac{1}{2}z_4z_5- \\frac{1}{2}z_3z_4$"
 42 |    ]
 43 |   },
 44 |   {
 45 |    "cell_type": "code",
 46 |    "execution_count": 3,
 47 |    "id": "6f9bf672-c7ca-4ef2-aad2-8325293254e5",
 48 |    "metadata": {},
 49 |    "outputs": [
 50 |     {
 51 |      "name": "stdout",
 52 |      "output_type": "stream",
 53 |      "text": [
 54 |       "  (-6.0) [I1]\n",
 55 |       "+ (0.5) [Z1 Z4]\n",
 56 |       "+ (0.5) [Z2 Z3]\n",
 57 |       "+ (0.5) [Z4 Z5]\n",
 58 |       "+ (0.5) [Z3 Z4]\n"
 59 |      ]
 60 |     }
 61 |    ],
 62 |    "source": [
 63 |     "import pennylane as qml\n",
 64 |     "from pennylane import numpy as np\n",
 65 |     "\n",
 66 |     "H = - 6 * qml.Identity(1) + \\\n",
 67 |     "    0.5 * qml.PauliZ(1) @ qml.PauliZ(4) + \\\n",
 68 |     "    0.5 * qml.PauliZ(2) @ qml.PauliZ(3) + \\\n",
 69 |     "    0.5 * qml.PauliZ(4) @ qml.PauliZ(5) + \\\n",
 70 |     "    0.5 * qml.PauliZ(3) @ qml.PauliZ(4) \n",
 71 |     "    \n",
 72 |     "print(H)"
 73 |    ]
 74 |   },
 75 |   {
 76 |    "cell_type": "code",
 77 |    "execution_count": 4,
 78 |    "id": "b89f50b5-5d5d-464c-bd05-c989a10e9761",
 79 |    "metadata": {},
 80 |    "outputs": [
 81 |     {
 82 |      "data": {
 83 |       "text/plain": [
 84 |        "tensor(-4., requires_grad=True)"
 85 |       ]
 86 |      },
 87 |      "execution_count": 4,
 88 |      "metadata": {},
 89 |      "output_type": "execute_result"
 90 |     }
 91 |    ],
 92 |    "source": [
 93 |     "dev = qml.device(\"default.qubit\", wires = H.wires)\n",
 94 |     "\n",
 95 |     "@qml.qnode(dev)\n",
 96 |     "def circuit(params):\n",
 97 |     "    \n",
 98 |     "    for param, wire in zip(params, H.wires):\n",
 99 |     "        qml.RY(param, wires = wire)\n",
100 |     "        \n",
101 |     "    return qml.expval(H)\n",
102 |     "\n",
103 |     "circuit([0,0,0,0,0])"
104 |    ]
105 |   },
106 |   {
107 |    "cell_type": "code",
108 |    "execution_count": 5,
109 |    "id": "085873a7-09bb-43f4-9b1b-d7ecb7490802",
110 |    "metadata": {},
111 |    "outputs": [
112 |     {
113 |      "data": {
114 |       "text/plain": [
115 |        "tensor(-8., requires_grad=True)"
116 |       ]
117 |      },
118 |      "execution_count": 5,
119 |      "metadata": {},
120 |      "output_type": "execute_result"
121 |     }
122 |    ],
123 |    "source": [
124 |     "params = np.random.rand(len(H.wires))\n",
125 |     "opt = qml.AdagradOptimizer(stepsize = 0.5)\n",
126 |     "epochs = 200\n",
127 |     "\n",
128 |     "for epoch in range(epochs):\n",
129 |     "    params = opt.step(circuit, params)\n",
130 |     "    \n",
131 |     "circuit(params)"
132 |    ]
133 |   },
134 |   {
135 |    "cell_type": "code",
136 |    "execution_count": 6,
137 |    "id": "0b500e66-56bd-4098-a382-9e6d30bab8af",
138 |    "metadata": {},
139 |    "outputs": [
140 |     {
141 |      "data": {
142 |       "text/plain": [
143 |        "tensor([0, 1, 0, 1, 0], requires_grad=True)"
144 |       ]
145 |      },
146 |      "execution_count": 6,
147 |      "metadata": {},
148 |      "output_type": "execute_result"
149 |     }
150 |    ],
151 |    "source": [
152 |     "dev = qml.device(\"default.qubit\", wires = H.wires, shots = 1)\n",
153 |     "\n",
154 |     "@qml.qnode(dev)\n",
155 |     "def circuit(params):\n",
156 |     "    \n",
157 |     "    for param, wire in zip(params, H.wires):\n",
158 |     "        qml.RY(param, wires = wire)\n",
159 |     "        \n",
160 |     "    return qml.sample()\n",
161 |     "\n",
162 |     "circuit(params)"
163 |    ]
164 |   },
165 |   {
166 |    "cell_type": "code",
167 |    "execution_count": null,
168 |    "id": "90631edd-cd02-48df-a2c1-6eb40d3cc395",
169 |    "metadata": {},
170 |    "outputs": [],
171 |    "source": []
172 |   }
173 |  ],
174 |  "metadata": {
175 |   "kernelspec": {
176 |    "display_name": "Python 3.8.13",
177 |    "language": "python",
178 |    "name": "python3"
179 |   },
180 |   "language_info": {
181 |    "codemirror_mode": {
182 |     "name": "ipython",
183 |     "version": 3
184 |    },
185 |    "file_extension": ".py",
186 |    "mimetype": "text/x-python",
187 |    "name": "python",
188 |    "nbconvert_exporter": "python",
189 |    "pygments_lexer": "ipython3",
190 |    "version": "3.8.13"
191 |   },
192 |   "vscode": {
193 |    "interpreter": {
194 |     "hash": "bf04860b618df62924ac577937eb78853ed0fe0f51833c65adb948f2cfa38ea7"
195 |    }
196 |   }
197 |  },
198 |  "nbformat": 4,
199 |  "nbformat_minor": 5
200 | }
201 | 


--------------------------------------------------------------------------------