{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4cc4aa0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as pl\n",
    "from pennylane import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c896f750",
   "metadata": {},
   "source": [
    "# Exercise 1: Uniform superposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "471d2d94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial state: [1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      "After applying the Hadamard gates: [0.5+0.j 0.5+0.j 0.5+0.j 0.5+0.j]\n",
      "execution_results: [0.25 0.25 0.25 0.25]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_bits = 2\n",
    "dev = pl.device(\"default.qubit\", wires=n_bits)\n",
    "wires = list(range(n_bits))\n",
    "\n",
    "@pl.qnode(dev)\n",
    "def circuit():\n",
    "    pl.Snapshot(\"Initial state\")\n",
    "    for i in range(n_bits):\n",
    "        pl.Hadamard(wires=i)\n",
    "    pl.Snapshot(\"After applying the Hadamard gates\")\n",
    "    return pl.probs(wires=wires)  \n",
    "\n",
    "pl.drawer.use_style(\"black_white\")\n",
    "pl.draw_mpl(circuit)();\n",
    "results = pl.snapshots(circuit)()\n",
    "for k, result in results.items():\n",
    "    print(f\"{k}: {result}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ca7966f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h5Bp6nJYvXy4bN2404SYgIEAGDBhg+txobY02Yek1OsKqd+/eqS4PAADIoOGmRYsWZrRS3759U/VwndFY58fRgKJz5Dz//PNSv379eO9p3bq1CT9KQ42OjtKlH7Zt22aatXTiv3uHhwMAgIzLrXCjo4+05mTOnDlSsmRJU6MS16xZs5J9L+08rDMOJ0YnBbyXNoelpkkMAADYy61wo7UlutxCoUKFTG0KAACAX4ebJUuWyNq1a00/GQAAAL+fxE8nwitdurTnSwMAAOCLcNOwYUP53//+l9pnAwAApI9mqRMnTshnn31mOhTrWlD3dihOaiVwAACAdBdudPmDe1cFBwAAyNCrggMAAKT7VcF1EcyPPvrIk7cEAADwfrjRWYNffvllKVy4sAwcONATtwQAAPBuuDl58qS8++67UqZMGalbt65Z+HLevHkSExPj7i0BAAC8G250wcxly5aZtaXCwsJk0aJF8uabb5pz06ZNk2bNmklQUFDqSwUAAOCNDsXFihWTK1euyEsvvSRbtmxxLVjZtWtXd58PAADgu5obbXIKDQ2VsmXLmqADAADg1+Hm2LFjppZm6tSpJuR06NDBrDEFAADgl+GmQIEC0q9fP9mzZ4+sWrXKdCJu0qSJOTdq1ChzHAAAwC9HS9WsWVOmT59ulmL45JNPJCIiQipWrMiCmgAAwL/nucmVK5d06dJFNmzYILt375amTZt6pmQAAAC+nqG4QoUKMnHiRE/eEgAAwHfhBgAAwNcINwAAwCqEGwAAYBW3ws1jjz0mkyZNYh0pAABgR7jRNaTGjRsnRYoUkTZt2siKFSvMulMAAAB+GW50wr7Dhw/LkiVLJCAgwCyk+cgjj8jQoUMlOjra86UEAABI6z43gYGB0rhxY1mwYIEcP35cevXqZWpzSpcuLXXr1pWlS5e6e2sAAADvrAqekKioKJkxY4bMnz9fChUqJJ06dZLTp09L+/bt5dVXX5XJkyen9hEAAABpG25Onjwpn3/+uQk1Bw4cMH1wNNw0bNjQ1Oio3r17S7Vq1Qg3AAAg/YebokWLSqlSpaRz587yyiuvSMGCBe97T/ny5U24AQAASPd9bt5++2359ddfZeDAgfcFG11A02n16tWpLyEAAEBah5vBgwcnek6bqAAAAKyYoTgmJkZCQkI8eUsAAIC063PTtGnTBPdVbGys7Nu3T+rUqZOyEgAAAPgq3Ggn4oT2VZYsWaRJkybSoUMHz5UOAAAgLcONrielChQoIMOGDUvpswAAANJnnxuCDQAA8Puam0aNGpmvkZGRrv3E6HsAAADSdbipWLFigvsAAAB+GW50UcyE9gEAAKyd5wYAAMDv+twkB31uAACAX/W5AQAAsKrPDQAAQHpFnxsAAGAV5rkBAABWYZ4bAABgFea5AQAAGXfhzHtdunRJoqOjXauE586d21PlAgAA8F6H4qtXr0qPHj3M6uBVq1Y1m+736tVLrl275l5JAAAAfBVuNMSsWrVK5s+fL0ePHjWb7q9cuVJee+01T5QLAADAe81SixYtkqioKHnsscdcx4oUKSIlSpSQ2rVry8yZM90rDQAAgC9qbkJCQkyYuZce03MAAAB+FW6aN28uw4cPl9u3b7uO6f6IESPMOQAAgHTfLNWmTRvXvnYaXrFihSxcuFAqV64sDodDdu7cKadOnZLGjRunVVkBAAA8F250NFRc3bt3j/c6PDw8ubcCAADwfbiZMmVK2pUCAADAQ1g4EwAAWMXtGYrPnz8vP/74oxw+fFju3LkT79yAAQM8UTYAAADvhJtNmzZJkyZNJFeuXHLo0CF59NFH5c8//5Rbt25JhQoVCDcAAMC/mqW0ZqZ///5y8OBB8/rXX381sxQ3bNhQmjVr5tZyDnr93bt3U1RzdPny5RQ/CwAA2M2tcLNjxw7p2bPn/7tBYKDcvHlTHnroIdPp+PPPP0/2fTTM6HIN+fLlM7MdFypUSObOnZvkNdOnT5dy5cqZhTpDQ0PNUPT169e7820AAAALuRVutMYkT548Zr9gwYKm343KmzevnDt3Ltn3GTt2rFmTavv27ea6UaNGSfv27WX37t2JhqENGzbIkiVL5OzZs+aaOnXqmNoifQ0AAJDq0VJPP/20DBw4UCIjI6V3796mJiW5PvroI+nSpYupiVHdunUz8+V8/PHHCb4/U6ZMMm3aNNPHR2XJkkWGDh1qmqg2b97MpwkAANwLN++991682peLFy9Ky5YtTY3L1KlTk3UPnc34yJEjUrNmzXjHa9WqJVu2bEl2WbS/j0porSsAAJDxuDVaKu5Q76JFi5oh4SkVExNjvubPn/++mZCT24fmypUr0qdPH9ORuVKlSom+T/sE6eZ06dKlFJcXAABkgGYpDQlbt241W0oDg3ZEVnEX31Q6nFybnx7kxo0b0qJFC4mNjZXZs2cn+d7Ro0eb1cqdW1hYWIrKCgAALA83OnS7R48eppalatWqZtP9Xr16mUU1k0NrfNTJkyfjHdfXznOJ0VoYDTY6fHzVqlX3rXt1r8GDB5umM+emzWEAAMBOboUbDTEaKnSkkwYM3XR/5cqVZmh3cgQHB5tQ9O2338artdF71K1b13XszJkz8cKIM9joHDvaHKbDxx8kW7Zskjt37ngbAACwk1t9bhYtWiRRUVFmbhon7dBbokQJqV27tsycOTNZ9xk+fLi0atVKqlSpYjoWT5gwQbJmzWpqheLWumzcuNF0Vtah4K1btzbNYFoGrUGKjo52DUkntAAAALdqbrTfSkKjk/SYnksunZ9mwYIFsnTpUunUqZM5tnbt2nidjDW0FCtWzOxrvx4dHaW1Ph07dpRGjRq5trg1QAAAIONyq+amefPmptZl4sSJZq4ZZ8fgESNGmHMpoU1MuiXmnXfece3rJIHOmhoAAIBUhZs2bdq49rXT8IoVK2ThwoVm0j6HwyE7d+40c9c0btw4ubcEAADwXbi5d0RS9+7d473WmYUBAAD8JtzoopgAAADWry0FAABgRbjRUU1NmzaVkiVLmiYp3ddjAAAAfhdu5syZI88884wEBQVJz549zcR9uq/H9BwAAIBfDQV/6623zOrfnTt3jnd82rRp5tyLL77oqfIBAACkfc3NH3/8Ic8999x9x/WYngMAAPCrcFO4cGGz/MK91q9fL6GhoZ4oFwAAgPeapXr37m2anvr27SvVq1c3xzZt2iSTJk2SYcOGuVcSAAAAX4WbgQMHmjWkxo4da/rYKB0x9d5770m3bt08US4AAADvhZstW7aYEKPbjRs3zDEdLQUAAOCX4aZGjRpy9+5ds0+oAQAAft+huFixYoyKAgAA9oSb4cOHS5cuXWT37t1y584dz5cKAADAm81SGmy0WapSpUoSEBAggYHxMxKBBwAA+FW4iYiI8HxJAAAAfBFuIiMjZdmyZeJwOKR58+bSqFEjT5QDAADA+31uvvjiC2ncuLEJON9++63ZnzVrlmdKAgAA4O1wM378eBk3bpwZKaXbu+++a14DAAD4Zbj5/fffpXv37q7XPXv2lOjo6LQoFwAAQNqHm2vXrkmuXLlcr4ODg+Xq1avuPRkAACA9dChOqBnq3mMDBgxIXakAAAC8EW7y588vY8aMeeAxwg0AAPCLcBMTE5N2JQEAAPDV8gsAAADpFeEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFjF5+Fmy5Yt0rlzZ2natKkMHjxYzp49+8Brdu3aJb1795b69evLjh07vFJOAADgH3wabqKioqRWrVoSHBwsHTp0cL2+evVqote89dZb0q5dO8mfP7/88MMPcv78ea+WGQAApG8+DTdDhgyRJk2ayKRJk6Rt27YSEREhx44dk2nTpiV6TY8ePUzNTdeuXb1aVgAA4B98Fm6uX78uP/30k7Ro0cJ1TGtw6tWrJ999912i1xUsWNBLJQQAAP4os68efOTIEYmNjZWiRYvGO66vf/zxR48+6+bNm2ZzunTpkkfvDwAA0g+f1dzcunXLfM2ePXu84zly5HCd85TRo0dLSEiIawsLC/Po/QEAQPrhs3CTN29e8/XcuXPxjutoKec5T9FRWBcvXnRtWmsEAADs5LNwU6RIEXnooYdk69at8Y7r6ypVqnj0WdmyZZPcuXPH2wAAgJ18OlrqlVdekenTp8vp06fN6+XLl8v27dvNcacJEyYwMgoAAKT/DsVq5MiRsmfPHildurSULFlS9u3bJ2PHjjVz3Tjt3btXNm7c6HqtI6n0Pc4Owv379zfNWC+//LLZAABAxubTcKOdh7W2Zv/+/XLq1CkpV66cFChQIN57NLxoPxmnSpUqyaBBg+67V3h4uFfKDAAA0jefhhunMmXKmC0hGnjiKly4sNkAAADS5dpSAAAAnkS4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3AAAAKsQbgAAgFUINwAAwCqEGwAAYBXCDQAAsArhBgAAWIVwAwAArEK4AQAAViHcAAAAqxBuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWyezrAsTGxsqmTZvk1KlTUrFiRSlVqlSaXAMAADIGn9bcXLx4UWrVqiVt2rSRDz/8UCpXriyDBg3y+DUAACDj8GnNzdChQ+XcuXOyd+9eCQkJkXXr1kmdOnWkQYMGUq9ePY9dAwAAMg6f1dw4HA6ZPXu2dO7c2YQUVbt2balevbrMmjXLY9cAAICMxWc1N0ePHpULFy6YPjNxVapUSbZv3+6xa9TNmzfNFrdpS126dCmV30UCz7ri8VsimdLg44yHz9bOz5bP1Xf4nbXXpTT6nXX+v62VHeky3DgDRr58+eIdz58/vwkwnrpGjR49WkaOHHnf8bCwMLfKjvTpI18XAGmGz9ZOfK72+iiN73/58mVXC066CjfZsmUzX69ciV/Voa+DgoI8do0aPHiw9OvXL95oK+23o6EoICAgVd+HTTQRa+A7cuSI5M6d29fFgYfwudqLz9ZefLYJ0xobDTahoaGSFJ+Fm2LFiknmzJnl8OHD8Y4fOnRIwsPDPXaNMxQ5g5FTnjx5UlV+m2mwIdzYh8/VXny29uKzvV9SNTY+71CsYUNHNy1YsMB1LCYmRlatWiVNmjRxHdu8ebNERkam6BoAAJBxBTge1CsnDWknYB3t1LJlS6lZs6ZMmzbNNBNFRUW5alq6dOkiGzdulN27dyf7GrhfDaqJWPs2UXNjDz5Xe/HZ2ovP1o8n8atSpYps3bpVChcubGYcbteunaxduzZeSNFh3o0bN07RNXCP/gyHDx/Oz9IyfK724rO1F5+tH9fcAAAAeBoLZwIAAKsQbgAAgFUINwAAwCqEGwAAYBXCTQalszpPmDDBjESrUKGClC5dWmrUqCE9evQwo9Bg7/BS/dzhn7766iszQvTxxx+XUqVKSeXKleW5554zCwrfvXvX18VDGtEpT3RtRSQfo6UyoJMnT5q5gk6fPi3169eXIkWKSPbs2eXs2bPy888/mzmF/vvf/0qfPn18XVR4mP4D+cQTT/APpR9q3769zJkzx/zuli1b1syyrnNS/fHHH7JmzRp5+umnZfny5ZIpUyZfFxUepr+zkyZNMl+RPD5bfgG+M2bMGClRooTs2LFDcubMed/5JUuWmL8OX3nlFSbz8yO68v2GDRuSfM+ZM2e8Vh54zurVq+W7774zv7MVK1a87/zBgwflmWeekYULF0rbtm350fsRnbfNudJ1Yh50Hvcj3GRAu3btkr59+yYYbFSLFi3kkUcekf3798tf//pXr5cP7tHgon+9P4jW1MH/fmebNm2aYLBRxYsXN6FG30e48S+9evWiK0AaINxkQA8//LD5C7958+YJnj9x4oRZjFTfB//x0EMPScGCBc1f+LrifWJNkhpe4V/0d1H/wtfauYRmY4+NjTVNyny2/ufRRx+VVq1amdryxCT2bzUSR7jJgF577TXzF7621esvjf4lHxQUZPrc/PLLL6bzmnY0DgsL83VRkQL6n572y/j+++9lwIAB/OwsorU2Q4YMMevpaXOx/oeofW60uUJ/j7VDcXR0tMydO9fXRUUK6SCOf/7zn/Lmm28m+p6sWbPyc00pXX4BGc/q1asdtWvXdgQGBuryG67t4YcfdgwaNMhx/fp1XxcRbjhw4IBj/PjxiZ6/evWqY/78+fxs/dDx48cdHTp0cOTMmTPe72xQUJCjdevWjujoaF8XEW4aMmSI48KFC4mej4iIcJw+fZqfbwowWiqDu3btmhw5ckRu374t+fLlk9DQUF8XCUASdMj34cOHzXQOOXLkMP3jMmemEh6Ii3ADAACsQtzPoPSvvo8//tj0z9C/Am/dumVqbnRysE6dOpkJ/eCf9u3bZz5b7WCqI6h03hPtV/W3v/1NevbsaToewz5RUVHm97phw4a+Lgo8TPtBNmrUSIoWLcrPNpmYoTgD0hEzVapUkREjRpjJ+3R+jJYtW5phpuvXrzcTRb3//vu+LibcsHjxYjNr7bJly8ys09phXP+zK1CggPlMdTZqDT+wM9zoSDnYhxmKU46amwyISfzs5HA4pHfv3jJu3Dh5/fXX7zt/584defXVV82oG53GH/5D+8XpqKik6PnE5q5C+sUkfmmDcJMBMYmfnWJiYszQYA04CdFOp/3795fWrVt7vWxInXnz5snAgQMf+D79fOFfmMQvbRBuMiAm8bNTSEiIGUmj4VWbphKikzcyOaP/0XlttM+UzmeTmKlTp8r169e9Wi6kHpP4pQ3CTQbEJH520om+tMOw9qHq3Lmz1KpVy/S10eYo7Welncc/++yzJP+DRPr07LPPmqZGnYm4WLFiiYZbwo3/YRK/tMFQ8AxKVxEeNmyY6YSo/2A66V/1Olpq+PDhZtZi+Bf9LMePHy8ffvihWUIjLh0J9+9//9t0Hof/0UUxdaTbU089leD5PXv2mHDDenD+Z+jQoWaGYg2oCfnmm2+kevXqjHRMAcJNBsckfvY6ffq0GQoeGBhohoLnzp3b10UCAK8g3AAAAKswzw0AALAK4QYAAFiFcAMAAKxCuAEAAFYh3ACwmi4KO3fuXLlw4UKyr7l69aq5Rhei9PazAaQe4QZAqp06dUpWrlxpFm7U/bhu3Lhh/oO/ePFiiu7p7nX30iUpXnzxRTl48GCyr9Eh9HqNTn7o7WcDSD3CDYBU0YkBS5QoIW+//bZMnjxZqlWrJu3btzdzKCmttdD/4HXxx5Rw9zoAYPkFAG5bvXq1CTXr1q0zyz04Z0nWhR5v3rwp2bNnl6VLl5rjkZGRsnv3bjPLar169WT+/PnmvZkyZZJHHnnEzKCcJUsW1wrniV3nrBHRdbJUlSpVUrxeVlLPvtf+/fvlt99+k+LFi0ulSpXuO5/asgDwPMINALdp6NBlOp588knXMZ0RWWtclAaIFStWmP0ffvjBTC9ftmxZE1I0vOhCn7r21c6dO0240CATFhZmwk1i1y1atEi6du1qgkaOHDlMsBg1apRZMy25knp2XLqe0++//y7h4eEmwOlzJ02a5DrvibIASAMOAHDTpk2bHAEBAY4ePXo4du3a5YiNjb3vPSdOnHDoPzV6PjF37951tG7d2tGxY8ckrztw4IAjZ86cjtWrV7uObd682REUFOTYt29fgvc+c+aMuc+2bduS/ew///zTXFO/fn3HrVu3XN9rYGCgY+3atckuy4OeDSBtUHMDwG26mN+cOXNk5MiRMmXKFAkODjYLO2qNR4MGDR54/d69e+XAgQNmVJI2O61duzbJ9+uz8ufPbzr8LliwwNTwqHz58slPP/1kaneSKznPfuONN1zNVfq91q1b1zRp1alTx6NlAeBZhBsAqdK2bVuzHTt2TDZu3CgzZ86Uhg0byrJly6Rp06YJXqOrVzdr1ky2bdtmOiBrs5N2HNbFPpOio450eLWukB2Xho0CBQokq7wpebb2s4lLO047V1v3RFkApA3CDQCP0JXHW7duLa1atZKKFSvKl19+mWi4+eKLL0xfFg0KuXLlMsc++OADGTFiRJLP0JXN8+bNa4aIuyslzz5//vx9r53BxRNlAZA2GAoOwG3Hjx83tRdxaSdiPZYnTx7z2hkgdN4aJ50/RsOQ85yzc25cCV3XqFEj2bdvn6xZsybeey9fvmy25EjOs52WLFni2tf5drRzs3NUmCfKAiBtBGjHmzS6NwDLffXVV9K/f39p0aKFlCtXTm7fvm36pGzfvl2ioqKkfPny5n3a/0RHFLVs2dIMldYajxo1aphRRVrLo/fR9+vQ7JiYGNf9771OR0t1797d1Ar16dNHSpYsaYZp6/U6gaA2G91L76d9arQZSodqb9269YHP1iYnvVfBggXNyC8txyeffGJCm17v7IfzoLLc+2wA3kHNDQC3aejQYKBzxWzevNkMDdegEx0d7Qo2KiIiwgynXr58uels+5e//MV81aHY69evlyZNmsjixYtNk1Zc916npk6davq5aEdgfbaGHh2CnVCwUdmyZTN9gjRQqeQ8O2fOnOYa7WQcGhoqP//8s/zjH/8w18WdD+dBZbn32QC8g5obAABgFWpuAACAVQg3AADAKoQbAABgFcINAACwCuEGAABYhXADAACsQrgBAABWIdwAAACrEG4AAIBVCDcAAMAqhBsAAGAVwg0AABCb/B9+iMcN7NSpcAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = np.real(results[\"After applying the Hadamard gates\"])\n",
    "bit_strings = [f\"{x:0{n_bits}b}\" for x in range(len(y))]\n",
    "plt.bar(bit_strings, y, color = \"#70CEFF\")\n",
    "plt.xticks(rotation=\"vertical\")\n",
    "plt.xlabel(\"State label\")\n",
    "plt.ylabel(\"Probability Amplitude\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83f70d12",
   "metadata": {},
   "source": [
    "# Exercise 2: Oracle as a reflection\n",
    "\n",
    "Recall that for one marked key $w$, Grover's phase oracle is\n",
    "\n",
    "$$O_w=I-2|w\\rangle\\langle w|.$$\n",
    "\n",
    "This is a **reflection**: it changes the sign of the marked state's amplitude and leaves the other computational-basis amplitudes unchanged.\n",
    "\n",
    "We will construct it as a quantum circuit in **two steps**:\n",
    "\n",
    "1. **Check the key.** Construct the reversible oracle $U_f|x\\rangle|b\\rangle=|x\\rangle|b\\oplus f(x)\\rangle$, where $f(x)=1$ precisely when $x=w$. To check a key such as `01`, apply $X$ to the wires where the key contains a `0`, use a multi-controlled $X$ on the extra qubit, and undo the initial $X$ gates.\n",
    "2. **Turn the check into a phase flip.** Prepare the extra qubit in $|-\\rangle=(|0\\rangle-|1\\rangle)/\\sqrt2$. Since $X|-\\rangle=-|-\\rangle$, the same checker now acts as $O_w$ on the data qubits:\n",
    "\n",
    "$$U_f(|x\\rangle|-\\rangle)=(-1)^{f(x)}|x\\rangle|-\\rangle.$$\n",
    "\n",
    "For this exercise, mark just **one key**, `01`. You can use `pl.ctrl(pl.PauliX, control=wires)(wires=flag_wire)` for the multi-controlled $X$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "72a17641",
   "metadata": {},
   "outputs": [],
   "source": [
    "keys = [[0,1]]  # one marked key\n",
    "flag_wire = n_bits\n",
    "dev = pl.device(\"default.qubit\", wires=n_bits + 1)\n",
    "\n",
    "def oracle(keys):\n",
    "    # build the reversible checker for keys[0]\n",
    "    for wire, bit in zip(wires, keys[0]):\n",
    "        if bit == 0:\n",
    "            pl.PauliX(wires=wire)\n",
    "    pl.ctrl(pl.PauliX, control=wires)(wires=flag_wire)\n",
    "    for wire, bit in zip(wires, keys[0]):\n",
    "        if bit == 0:\n",
    "            pl.PauliX(wires=wire)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7087e9d",
   "metadata": {},
   "source": [
    "Now apply the oracle to a uniform superposition. Prepare the extra qubit in $|-\\rangle$ using $X$ followed by $H$, and use the snapshots to observe the **reflection**: the amplitude of $|01\\rangle$ becomes negative, but its measurement probability does not change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "00c44e80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@pl.qnode(dev)\n",
    "def circuit(keys):\n",
    "    for i in range(n_bits):\n",
    "        pl.Hadamard(wires=i)\n",
    "    pl.PauliX(wires=flag_wire)\n",
    "    pl.Hadamard(wires=flag_wire)\n",
    "    pl.Snapshot(\"Before oracle\")\n",
    "    oracle(keys)\n",
    "    pl.Snapshot(\"After oracle\")\n",
    "    return pl.state()\n",
    "\n",
    "results = pl.snapshots(circuit)(keys)\n",
    "\n",
    "# The flag stays in |->. Display the data amplitudes using its |0> component.\n",
    "y1 = np.sqrt(2) * np.real(results[\"Before oracle\"][::2])\n",
    "y2 = np.sqrt(2) * np.real(results[\"After oracle\"][::2])\n",
    "bit_strings = [f\"{x:0{n_bits}b}\" for x in range(len(y1))]\n",
    "pos = np.arange(len(y1))\n",
    "plt.bar(pos - 0.2, y1, width=0.4, color=\"#70CEFF\", label=\"Before oracle\")\n",
    "plt.bar(pos + 0.2, y2, width=0.4, color=\"#C756B2\", label=\"After oracle\")\n",
    "plt.xticks(pos, bit_strings)\n",
    "plt.axhline(0, color=\"black\", linewidth=0.8)\n",
    "plt.xlabel(\"State label\")\n",
    "plt.ylabel(\"Probability amplitude\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "assert np.allclose(y1, [0.5]*4)\n",
    "assert np.allclose(y2, [0.5,-0.5,0.5,0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b008098",
   "metadata": {},
   "source": [
    "# Exercise 3: Diffusion operator\n",
    "\n",
    "The second reflection in Grover's algorithm is the **diffusion operator**:\n",
    "\n",
    "$$D=2|s\\rangle\\langle s|-I,\\qquad |s\\rangle=H^{\\otimes n}|0^n\\rangle.$$\n",
    "\n",
    "Unlike the oracle's reflection, this one reflects the amplitudes **about their mean**. Together, the two reflections amplify the marked state's amplitude.\n",
    "\n",
    "To implement diffusion, apply $H$ to each data qubit, then $X$ to each data qubit, then a multi-controlled $Z$, and finally undo the $X$ and $H$ gates in reverse order. Use\n",
    "\n",
    "```python\n",
    "pl.ctrl(pl.PauliZ, control=wires[:-1])(wires=wires[-1])\n",
    "```\n",
    "\n",
    "This implementation gives $-D$ rather than $D$, which differs only by an overall global phase. The extra flag qubit is **not** part of diffusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "29a6952a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusion_operator(wires):\n",
    "    for wire in wires:\n",
    "        pl.Hadamard(wires=wire)\n",
    "    for wire in wires:\n",
    "        pl.PauliX(wires=wire)\n",
    "    pl.ctrl(pl.PauliZ, control=wires[:-1])(wires=wires[-1])\n",
    "    for wire in wires:\n",
    "        pl.PauliX(wires=wire)\n",
    "    for wire in wires:\n",
    "        pl.Hadamard(wires=wire)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a050822b",
   "metadata": {},
   "source": [
    "# Exercise 4: One Grover iteration\n",
    "\n",
    "A Grover iteration consists of the oracle reflection followed by the diffusion reflection. With two data qubits and one marked key, **one iteration** is enough to reach the marked state with probability $1$.\n",
    "\n",
    "Run the circuit and compare the amplitudes before the oracle, after the oracle, and after diffusion. In particular, check that **the oracle alone does not change the measurement probabilities**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fceb5e77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform superposition: [ 0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j\n",
      "  0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j]\n",
      "State marked by oracle: [ 0.35355339+0.j -0.35355339+0.j -0.35355339+0.j  0.35355339+0.j\n",
      "  0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j]\n",
      "Amplitude after diffusion: [ 9.52420783e-18+0.j -9.52420783e-18+0.j -7.07106781e-01+0.j\n",
      "  7.07106781e-01+0.j -6.49514367e-34+0.j  6.49514367e-34+0.j\n",
      " -1.66988925e-17+0.j  1.66988925e-17+0.j]\n",
      "execution_results: [1.81421069e-34 1.00000000e+00 8.43737825e-67 5.57706021e-34]\n"
     ]
    },
    {
     "data": {
      "image/png": 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1e++9J7ly5fJ+qQAAAHw5DG3fvl2ioqIkX7583i8RAACArzeTFS1aVK5du+b90gAAAPhDGBo1apT069dPDh06JLdv35Y7d+64bAAAAAEdhh577DHZuXOnlC9fXjJnziyZMmVy2QAAAAK6z1Dfvn3l8ccflxdffJEO1AAAwHph6OjRo7J+/XrJkyeP90sEAADg681kJUuWlMuXL0t60ZFsu3btMmuOeOLu3bty8OBBE+Lo0wQAAB44DGnzWO/evWX37t1y9epVl1XqU3Ol+r/++ks6duwojzzyiPTs2VMKFSokH330UbLXvPXWW2b0m17XvHlzKVGihHz33XepVkYAAGCBZrLBgweb22rVqqXpSvXjxo2THTt2yO+//25mv16yZIm0b99eatWqJbVr13ZbI3Tjxg05cOCAo0kvMjJSunTpYp5DwxQAALA2v1q1fs6cOfLSSy+ZIKTatWsnFStWNMfdhaGMGTPKm2++6XJMr9dQ9csvv0irVq3SrOwAAMA3+c2q9dHR0XLu3DmpXr26y3GtFdLmOk/plACqVKlSSZ5z8+ZNs9l52jcJAABYJAx5i3Zo1oCTnBo1apjFXy9dumT28+bN6/K47tsfu5eLFy/KwIEDpXPnzqbfUVImTJhgao8AAEDgS1EY0j5B8+fPl4ULF5oV7BOO0Nq3b59Hz6PXr1ixItlzFixYYDpA2ydz1E7UzrRPkE78eC8xMTHSsmVL009o5syZ95xhe+jQoS41Q+Hh4fd8DQAAYJEwNGnSJJk8ebL0799fli9fbmpStGOzdmh++eWXPX6e0aNHm80TGkYyZMggp0+fdjmu+8WLF0/2Wg0zOpJM+xCtXLlScuTIkez5ISEhZgMAAIEvRUPrZ8yYYWp1dGSWGjlypCxatEimTJkiJ06ckNSQLVs2qVOnjixbtsxxTBeL/eGHH6RZs2aOY8eOHXPpQ2QPQmr16tUSFhaWKuUDAAD+KciWgnHwwcHBpnlKm66yZs0q58+fN7Ut2hRVrFgxM/dQatiwYYMJPsOGDTPLgegcQxq+9uzZI6GhoeacF154QbZt22aa6nQR2YYNG5qANHv2bJcgVKZMGSlYsKBHr6uBSq/V95czZ85UeW8IPEM879fvc7q8s1z8WcSCNuldBAA+wNPf7xQ1k+n8PfY+PNpEpSO0GjdubPoPpeZCrQ0aNJB169bJv/71L9MsV6lSJZk3b54jCNlDzq1bt8z969evS1BQkDmmTXnOtDardevWqVZWAABgkdFkffr0MZMYNmnSRDZu3CgdOnSQ1FS3bl2zJWXEiBGO+5oGN2/enKrlAQAAFgxDFy5ccAkfOkJLJ2J87bXX7qsDNQAAgF+GoXz58rnsP//882YDAACwxGgyAACAQEEYAgAAlkYYAgAAlpaiMKQrvgMAAFg2DOnK8VWqVJGpU6d6vEgqAABAwIShI0eOyJNPPikTJ06UIkWKmHmGVq1aJfHx8d4vIQAAgK+FIfuMzjrj9LfffmtWrW/Tpo2UKFFCXn/9dTl+/Lj3SwoAAOBrHah1FfinnnrKLInxzjvvyLlz5+TNN9+U0qVLS/v27SUqKsp7JQUAAPC1MKQLor744otSuHBhmTx5srz66qumVkiP6yKp7dq1815JAQAAfGUG6kmTJplV4I8ePSqtWrWS+fPnm1utKVIPP/ywLFy40GUBVQAAgIAJQ9OmTTMLtPbu3dvUCrmTNWtWmTVr1oOWDwAAwPeaySpXriyjR492G4Q6derkuN+rV68HKx0AAIAvhqFFixa5Pa5D6xcvXvygZQIAAPDNZrKLFy+6vW8PQlu2bJFChQp5r3QAAAC+FIby58/v9r6ddqB+7733vFMyAAAAXwtDu3fvNrdVq1Z13LfLlCmTFCtWTMLCwrxbQgAAAF8JQ7oemdLJFDX4AAAAWCYMnT171txqn6Dg4GDHvjv0GwIAAAEXhuzD6G02W5JzC9npOQAAAAEVhvbu3ev2PgAAgCXCUMWKFd3eBwAAsFSfIU/QZwgAAARsnyFP0GcIAAAEdJ8hAAAAS/cZAgAAsPQ8Q/fqP0SfIQAA4C+YZwgAAFga8wwBAABLY54hAABgafe1UKuzq1evyvz58+XgwYNmv0KFCtKjRw8JDQ31ZvkAAABSVYaUXLRjxw4pWbKkREZGmjCk29ixY82xXbt2eb+UAAAAvlQzNGDAAOnUqZNMmTJFQkJCzLGbN2/K4MGDzWOpGYj0dVavXi3nzp2TSpUqSe3atT2+9vfff5fvv/9eqlSpIvXq1Uu1MgIAgAAPQ1oTtGbNGkcQUnr/jTfekOLFi0tqOX/+vDRs2NDcr1y5srz22mvSoUMHmTlzpkchqmPHjnL06FHp168fYQgAAKQ8DJUuXVpOnz4tefPmdTkeHR0tpUqVktQycuRIyZQpk2zbtk2yZs0qe/bskerVq0vbtm2lTZs2yV47dOhQqVOnTqqVDQAABHifobi4OMc2aNAg6dy5syxbtkzOnDljQpDe12NDhgxJlYLGx8fLN998I7169TJBSGlzlwacBQsWJHvt4sWLZe3atTJp0qRUKRsAALBAzVCOHDkSHdMamYT69u0rffr0EW+LiooyI9jKly/vclz3k+ujpNe99NJLsmLFCsmWLZtHr6VNarrZxcbGPkDJAQBAQIShrVu3ev3Ff/zxR8fQ/KT07NlTwsLCTBBSuXLlcnk8d+7cSYaVu3fvSvfu3U1tVbVq1Twu14QJE2TcuHEenw8AACwQhiIiIrz+4trEdujQoWTPuX37trm1N43ZQ5GdBqGkanw+//xz2bt3rzzzzDPy8ccfm2MXL16UX3/91ey/8sorEhQUlOi6UaNGmT5Gzq8RHh6egncIAAACdtJFb9BJGnXzhI5Sy5w5s5w4ccLl+PHjx6VMmTJurylRooR5/iNHjjiOafPX5cuXTQiz2Wxuw5COjHMeKQcAAAJXisKQhgidfXrhwoVy6tQpuXPnjsvj+/btE2/TUWRPPvmkfPHFF2ZovIaY//73v7J+/XqZMWOG47x169bJ2bNnpVu3blK/fn2zOdu8ebMZnq9zJAEAAKRoBmodlaVz/Gg/HG1y0tqXsmXLyoEDBxzzAKWGiRMnmmav1q1by/jx46Vx48ZmNNmzzz7r0jT21ltvpVoZAABAYElRzZDWxGitkM7irB2Ndf4fNXXqVFm1apWklkceecTUOs2bN8/MQD169GgThIKD//9taEDSZUGS0rVr1ySb1QAAgPUE2bTN6z5p+Lhx44ZputKOzToztA69j4mJkWLFiiXq5OzvtAO1jmjT95czZ870Lg78xJDd4re6vLNc/FnEguQnYQVgDbEe/n6nqJlMh6xrELJ3bN65c6e5r/2H7McBAAAsMZpMJ1js0qWLNGnSRDZu3GjWCgMAAAjoMHThwgXH/REjRkihQoXMpIzaqfrll1/2ZvkAAAB8Lwzly5fPZf/55583GwAAgGWaybSTtM41ZF9Oo0KFCmaIfWhoqDfLBwAAkKpS1IF6x44dZvh6ZGSkCUO6jR071hxLbtFUAACAgAhDAwYMkE6dOpnRY2vWrDGb3u/YsaN5DAAAIKCbybQmSAOQ8/pdev+NN94wQ+0BAAACumaodOnScvr06UTHo6OjpVSpUt4oFwAAgG+Fobi4OMc2aNAg6dy5syxbtkzOnDljQpDe12NDhgxJ3RIDAACkRzOZLreRUNu2bRMd69u3r5mIEQAAIKDCkE6qCAAAYNkwFBERkbolAQAA8Le1yXS1+sOHD4sufF+uXDkpUKCA90oGAADgq6PJrl+/bvoGFS5cWOrXry8NGjQw9/WYPgYAABDQYWjYsGGyefNmWbp0qVm09eLFi+b+pk2bZPjw4d4vJQAAQCoJsmkbVwoWav3xxx+lcuXKLsf37NkjzZo1c1nVPhDExsZKWFiYxMTESM6cOdO7OECq29ZluV9/yhEL2qR3EQD40e93imqGdK6h8PDwRMf1mC7gCgAA4C9SFIaqV68ub7/9tsTHxzuO6f233npLatSo4c3yAQAA+N5ossmTJ0vz5s1l0aJFjvCjq9VfunRJVq1a5e0yAgAA+FbNUO3ateXYsWNmpumMGTNKcHCwuX/06FHzGAAAQEDXDP3tb3+Tjz/+WMaMGeP9EgEAAPh6zdCsWbPk5s2b3i8NAACAP4Shxx9/3AytBwAAsGQzWb169aRbt27Sr18/qVChgmTOnNnl8R49enirfAAAAL4XhmbMmCFZs2aV+fPnu32cMAQAAAI6DJ05c8bcBgUFebs8AAAAvttn6MqVK6Z5LEeOHGbT+zrFNQAAgCXC0D/+8Q/ZuHGjjBgxwmwbNmwwxwAAACzRTLZ8+XIz67R9YsWmTZtK165dzZxDAAAAAV8zFB0d7bL2WK1ateT06dOpUS4AAADfC0N37941y2/Y6X09BgAAYJnRZBUrVrznsX379j1YqQAAAHwxDA0bNizRsZYtW0paOnnypMyZM0fOnTsnlSpVkr59+0qWLFmSvcZms5n+TmvXrpVs2bLJc889J+XKlUuzMgMAgAAJQ5MmTZL0pDVOdevWlebNm0tERIRMmzZN5s2bJ5s2bZJMmTK5veb27dvSsWNH2bNnj7z00ksmDPXs2VNmz55twhQAALC2FE26mF50OL922l64cKFjpuuHHnpI5s6da2qI3Jk8ebKZAmD//v1SrFgxc2zAgAFy7dq1NC07AAAIoIVa08OtW7dkzZo10qVLF8exggULSuPGjU0TWFKmT59uaoLsQUiFhIRInjx5Ur3MAADA9/lNzdCpU6dMk1eJEiVcjuu+NpO5o7NjnzhxwsyLNHPmTPn555+lSJEiZubs0qVLJ/laN2/eNJtdbGysF98JAADwJekahjSgbN68Odlz3n33XSlQoIDcuHHD7GfPnt3lcV0WxP5YQlevXjW3kZGRJhDVq1dPtm/fLo8++qisXLlSGjVq5Pa6CRMmyLhx41L4rgAAgD9J1zCkI7qCg5MvQtasWc1tzpw5HeujObt06ZKEhYW5vdZ+/JFHHpEvvvjC3H/55ZdNSBo7dmySYWjUqFEydOhQl5qh8PDw+3pvAADAP6RrGNKaGt08oWFEw412hH7yySddRpi5m/vIXmukHawTPq41Q59//nmSr6V9inQDAACBz286UGfIkMF0ntYh8XFxceaYNnnp1r17d8d5OgfRmDFjHPvaeXrVqlWOPkDa70ibyGrWrJkO7wIAAPgavwlD9r48OsGizg/09NNPS7NmzWTgwIHSokULxzlbtmyRJUuWuDR5aZ+j8uXLS+fOnc2tBiMdcg8AABBk0+mZ/cidO3dk48aNjhmoEzaB/fTTT3LhwgVp27at45i+xW3btskff/whxYsXN52pnddYuxftM6RNdDo6zd53CQhk27okPV2FP4hY0Ca9iwDAB3j6++03Q+vttMO1zi2UlDp16iQ6FhQUJI8//rjZAAAA/LaZDAAAwNsIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNIIQwAAwNL8LgytXLlSnnrqKalRo4b07t1bTp48mez5t27dkilTpkjz5s2lZs2a0rFjR1m1alWalRcAAPi2DP4WhNq0aSNPPPGEvP/++3LlyhWpV6+euU3KkCFDZOLEidKvXz/55JNPpEqVKtKqVStZvXp1mpYdAAD4Jr8KQ2PHjpWuXbvKyJEjpUGDBvLVV1/JtWvXZNq0aUles2LFCnnxxRflmWeeMTVDr7/+ujz66KMmWAEAAPhNGIqLi5OdO3eaWh27kJAQadq0qaxbty7J6+rWrSubNm2SGzdumP3Dhw/LiRMnTI0SAACA34Sh06dPi81mk8KFC7sc1/2oqKgkr5s1a5YULFjQbKVLl5bq1aubPkQdOnRI8pqbN29KbGysywYAAAJTcHq++JgxY2TJkiXJnvP9999LeHi43Llzx+xnzpzZ5XGtHbp9+3aS10+YMEE2btwo06dPl1KlSpm+QkOHDpXy5ctLnTp1krxm3LhxKXpPAADAvwTZtLolHWt7Ll++nOw5ZcuWNQHo7NmzphZo2bJlphO1XZ8+feTgwYOydevWRNdqjU6ePHlM7dDzzz/vON6uXTvTbJbUqDKtGdLN+Xk0kMXExEjOnDlT+G4B/7Gty3LxZxEL/v+/EQCsKzY2VsLCwu75+52uNUNFixY1mycKFSokRYoUke3bt7uEIQ1BTZo0cXuNBp67d+9Kvnz5XI7nz59f9u3bl+RraW2TbgAAIPD5TZ8h1b9/f5k5c6YcP37c7M+dO1eOHDkiL7zwgsuIs/bt25v72k+oQoUK8tFHH5lRZ+rQoUOyaNEiady4cTq9CwAA4EvStWbofo0ePdpMsliuXDlT23P9+nWZPXu2mTvIuent6NGjjv2vv/7aNKVpMCpQoIB5vHv37maIPQAAQLr2GUop7Wd08eJFKV68eKLmrOjoaBOSdOSYM52Y8c8//5RixYrddxOYp22OQKCgzxCAQOAXfYZSKnfu3GZzR/sVuZMrVy6zAQAA+H0Y8kXx8fFmHTTgQWTKlEkyZszIhwgAaYgw5AUagnRWaw1EwIPSGkwdPRkUFMSHCQBpgDD0gLTL1ZkzZ8z/zetcRBky+NUAPfjY35L2dzt//rzZTzjbOgAgdRCGHpDOjK0/YNpXKVu2bN75VmBZWbNmNbcaiHT0I01mAJD6qMZ4QDqpo7tlQoCUsofq5JaZAQB4D2HIS+jfAf6WAMA/EYaQrKtXr8qkSZOkX79+MmXKlID/tHQhX11AGABgHYQhi9OJKHv16iUffvih28d79+4tS5culdq1a0ulSpVk5cqV8s9//lMC1YEDB2TJkiXpXQwAQBqiA3UqGbJb0tQHVVN23bx588xabQsXLjTBJ+EMnevXr5cZM2ZIhw4dzL7WEi1btkzGjx/vjWIDAJDuCEMWN2vWLImMjJSPP/5YvvzyS7MYrtI13P7xj3+YpU8++eQTE4AiIiJkwYIFcurUKVObpJ5//nlp1KiRWQj3s88+k3379plRULpYrvOaccuXL5c9e/aY4/PnzzejpXRdOXfOnTtnyqXr0OnyKRrSdNqCez3X9u3b5d///rc5J3v27GaRXr024Sg/LauGwF9//dU8v65dl9ww9nu9NwCAf6OZzMK2bdtmFrXVQPPCCy/IzJkzHY9pmGjYsKGZN0mbx/R+2bJlpVSpUhIaGmr2ddMpBS5cuCBVq1aVVatWyaOPPmpGQWlA0tomOw0ekydPlo4dO0qePHmkfv36bssUFRUljz32mGzcuFEqVqwoP//8s9k/fPjwPZ9Lg4q9XLqYr75+zZo1XWYG16ClZf3000/Ne/nrr7+kefPmpm+UO568NwCAf6NmyMK09kUDRd68eU3tyNixY+W3334z4UNnQdbanwEDBkiTJk2kdevW5ppffvlFDh065KgZUlqbpEFh8eLFjmNlypSRIUOGyDPPPOM4FhcXJ7t27TIhJClahocfflhWrFhhgtjf//53adq0qYwePVq+/fbbZJ9Lr9PNTsv+yCOPmODy7LPPmmP6PDoNggZBXfpCDR48OMnFe7UztSfvDQDgvwhDFqVNP9rkpc1fSpd/aNOmjakdmjp16n0913/+8x8pXry4qV3SWZR1u3Tpkmlqu3jxouTLl8+cp8EluSCkNmzYIK+88orLTN5du3aVkSNHupyX1HNpU9l3331nZgXXCTG1VkjDm933339vwo89CCkNgw/63gAA/oswZFEahOx9YXRTZ8+eNWHkvffeS7KmJKkRaS1atJB69eq5HG/Xrp1kyZLFsa+1TfeizVIJw4kGDg0gGm6Cg4OTfC7tLzRixAgTXKpVq2b6CmlNlnMTmPaB0uY0b783AID/IgxZlNYA9ezZ0/SvsdP72kylo8u6devm8eSS2gnZ3qz2oLQWRjtOO9NFcIsWLeoIQkmZNm2ajBs3zjRh2enot4RlPXbsmMfl8eZ7AwD4JjpQW5DOpbN161YzWkx/5J03HULv3JE6Ie2wrLU0zp577jnTIVmf106bp7755pv7Lpv2w5kzZ47jNWJjY2X69OnSqVOne16rQU1rfux0vqD9+/e7nNOjRw8zVcAff/zhOLZ582ZTS+aON98bAMA3UTNk0Y7TOuxcOwInpM0/OgGj1sY4d0a2a9asmQwaNMh0atZaEx2JNmrUKPn999+lRo0aZmSX9sfZu3evGdbuSYhxNnz4cFm3bp0ZSfb444/Lzp07TX8mTyZ61H5FGui0Y7WuGaejzhK+Ry2rBiTtJK5l1bClIUonk3THm+8NAOCbgmzaIxTJ0h/MsLAwiYmJSTQpoQ7NtgcHf+lDop2mtV9O3bp1Ez2mIULn7qlTp44JEjofjw4l1+Dj3K/np59+kitXrpi5h3TEltLQoEPhdei9hgfnvjk6Sk2HzT/11FP3LJ/+SWrNlX2eIe2v49yhOrnnOn78uAlDOjXAE088YcJUjhw5pFatWi7n6ZxBummznL4H+/NrDZBON9C2bVuX85N7b97mC39T27osF38WsaBNehcBgI//fjsjDD3gh+kLP1wILL7wN0UYAmClMESfIQAAYGmEIQAAYGmEIQAAYGmEIQAAYGmEIQAAYGmEIQAAYGmEIQAAYGmEIQAAYGmEIdyTztT87bffyqZNm9Ll09JZpf/zn/849o8cOZJo+Yz4+HizxtjXX38thw8fNsd0hmw976uvvnJZuT6l3L0uAMD/EYYs7vbt2yYsbNu2ze3jb7zxhjRu3Fi+/PJLs0SGBo1Vq1alaRnXrl1r1kOzW7FihVnDzFmLFi2kX79+JrTpchr//e9/zXIi7777rlmw1RthyN3rAgD8Hwu1BshyBildi2np0qXSrVs3KVq0qFnJPWPGjC6P6wrv77//vvTs2dPsT5o0yaxdpuEjvehaaE8++aRLzdEPP/wgp06dkvDwcHNs6tSpUqRIEROkUut1AQCBgTBkcTNnzpT+/fubmh9tArIvfqrruHz//fdy7tw500ymtUe6aOqePXtM85Puq5o1a0qpUqUci5nqubqIadWqVV3W1dIFUKOjo83iqVrDdP78eencubPbMulisVu2bJEbN25I5cqVEz2ur6crzSutBVqwYIG5r8EnJCTE3F+/fr2j1itXrlzSsmVL2b17t8TFxZky2GmZDx065LLoq75nPTdr1qxmUVZd9DXh6zr75ZdfHIvK6ufhfI79fTdo0MB8drrIbbVq1aRQoUL3+U0BAFILYcjCtCZFa1Q0wOgPuAYjeyjQZiVtXtJgouFFa410lfv9+/eboKSPqXz58kmJEiXkxRdflGXLlknt2rXNj78ujqe1To8++qg5b9GiRTJr1iyzUF7evHlNYHIXhq5duybNmzc3IUVDw6+//irly5dP1FylZdWAowuabtiwwRxfvny5BAf/35+0NuddvHjRlFNri/Tc//mf/5Fjx465hKE1a9aY2i77+543b568/PLL5n3oZ6Kf0WeffSaPP/64y+sqDWvt2rUzYUhDkAao0qVLm/5N9gUB7e87d+7ckidPHnONvicta6NGjVLlewUAWCAM2Ww2uXnzpmTOnFkyZPC825N2sr2f8wPdnDlzpE6dOlKuXDlTO6Q/6ForUrBgQVPLobUqGiZee+01ad26tblGP3dtJrPXDKn33ntPdu7caQKMPQS8+uqr0rdvX5e+SFp7snjxYhMgkqJNcmfOnDE1KhoeNFhVqVIlydWGNTjpYxrqNLSEhoaa42PGjDEdqp3L6Ynx48ebfkYvvfSS2dfPQ9+XO5MnTzbl1DCpn9mlS5ekVq1a8uabb5rnsNMg+emnn0rTpk3NvvZtioyMJAwBgI/wq2SgTQzvvPOOlCxZ0jRhbNy40aPrJkyYYH6sMmXKJJUqVfJqPxJ/pcFQw5DW6CgNHLpp7cn90ufR5qzVq1fLwoULzYguDTI7duwwNT12WkOTXBBSeq2GKL1eab8fe3+ltKB/VwcPHpRbt26Zff270cDojgatPn36mHOUlllDVMIAprVF9iCkGjZs6BjxBgBIf34Vhv7973/L5cuX7+sHe9q0afL222/L559/bpp3OnToYGo5tHnFyrQmJSoqSu7cuWN+vHUrW7asadK5X1rjo81P33zzjRnNpU1D2hSkzWDaLGRXuHDhez6XNktps5uzhx9+WNKKdhjXkJ0/f37TdKbNYvoZuaM1PhrMnWm/Ih3J5nyNPdjZab+mv/76K5XeAQAgoJvJ/vnPf5pb/bHxlDZlaE2D/f/MtXlCazI0JE2cOFGsSn/kH3vssUTz5mizlM4n5Nyv5l60mapNmzYyevToZM9z1/k4Ie1PpIHXWcL9lNImUq0Rc5YwlERERJiOzvo3pjVd+veifYI++eSTRM+n/aW0acyZ7mv/IHvfJQCA7/OrmqH79eeff5rRRjqSx/kHWfe1U7BVacdi7dz80UcfOWqF7NvTTz9tglJStE9OwgChHYo1YGp/ImenT5++77LVq1fP0Tnb3j9M+xl5g04fkLD/z7p169yWWftMaROY9u9Jag4mLavWgjnT2jE9DgDwH+n6v6869FlHKyVHmxQ8qVFwRzu/Km3ycKYjmbQ/S1L0R935h11HRgUSHTGlw83d9YXRPj29evUyQcldp2Udaq4BUztNax8g7XStfbK0Jkk7D/fu3dv0zdKh8fq5fffdd/dVttdff928hjaxaW2ejlDT5rywsDB5UM8884x5fi2jBhbtO6ah2Pl96mvWr1/flEHL/69//ctlwseEna2rV69uPjNtUvvxxx9Np+2kwhMAwDelaxjSIcz6w5wcHa2TsF/G/UrYNKL7yQUs/XEfN26cBCrtO6VNWu5G1umkglo7pEPodTi5hhKtUbHTkKD9gnQWam0+0qYiDRDatDR37lzZtWuXqT3SgNCpUyfHdTrEPmHNkTvab0mD6vTp083zd+zYUYYMGWKGoic1+aGWoUuXLiaE2WkToI42dFa8eHHz3LNnz5aff/7ZBBgNfs5LfejweP2b1NFx2plaz23VqpXb19W+Tdo3SvsZadOi/p3q5+D89+rufWuI1Pfly1I6iScA+KMgm7ZD+Bntz6E/KNrEoSNzkqJ9TbTzqo5wcv5hfvbZZ01ziE7M52nNkL6ehoiEtSXaZKSdsbWTr/Mkg0BK8TcFAN6hv9/asuDu9zug+wzpKB77sGjtyFqhQgWXfiFaK6T7OoFgck1z+qE5bwAAIDD5VRjS/kX6f832WhsNPbrvPIx5wIABZuZiuxEjRpimDm3a0ZFSQ4cONUsy2CfVAwAA1uZXYeiLL74wHX+1H4bW3mjfFt3XiRjttN+IfX0q9dxzz5lZjUeNGmWWddA+LboEg44WAgAA8Ms+Q77U5kj/Dngbf1MA4B2W7TMEAABwPwhDXkIFG/hbAgD/RBh6QBkzZjS39hFswIO6fv26uXWeNwkAkHpYQOlBP8DgYMmWLZtcuHDB/Hi5m8gQ8LR2UYPQ+fPnzcAAe9AGAKQuwtAD0pmsdTV2nXhRVzEHHpQGoUKFCvFBAkAaIQx5gS77UKZMGZrK8MC0dpEaIQBIW4QhL9HmMZbjAADA/9DBBQAAWBphCAAAWBrNZPcxh5DOZAkAAPyD/Xf7XnMBEoY8cPXqVXMbHh7uje8GAACk8e+4LsuRFNYm80B8fLxZ8T5HjhxmKD3+P3FrQIyKikp2zRf4F77XwMV3G7j4bt3TGiENQkWKFEl2HkBqhjygHyCr3CdNgxBhKPDwvQYuvtvAxXebWHI1QnZ0oAYAAJZGGAIAAJZGGEKKhYSEyNixY80tAgffa+Diuw1cfLcPhg7UAADA0qgZAgAAlkYYAgAAlkYYAgAAlkYYgkeTVh04cED27Nkjd+7cSfE58D3Xrl2Tn3/+WU6cOJHkObdv35Zt27bJkSNH0rRseDDnz5+XzZs3y+XLl5M85/Tp07Jr165kz4Hv0f/W/vTTTw98DpzYgGQcPXrUVqFCBVv+/PltxYsXtxUuXNi2efPm+z4Hvmfu3Lm20NBQW9myZc1t06ZNbTExMY7HY2NjbWPGjLEVK1bMPP7ss8+ma3nhmV9//dXWtWtXW8GCBXUxJtvy5csTnXPr1i1b9+7dbVmyZLGVL1/e3L7zzjt8xD7u888/t9WsWdOWO3duW0hISIrPQWLUDCFZ3bt3lxIlSsiZM2fkjz/+kA4dOkinTp3k+vXr93UOfMvhw4elT58+MnXqVHP/1KlT5rsbPny445wLFy5I5syZZceOHVK3bt10LS88t3//fnn66aflt99+S/Kcd999V3744Qc5dOiQqUFYtmyZjBo1StauXctH7cP0+/roo4/M9/cg58ANNwEJMH777Tfzf5bOtTzR0dG2DBky2BYuXOjxOfA9o0ePNjU+zqZMmWLLli2b7a+//kp0fosWLagZ8jOXL19OsmaoZMmStuHDh7sci4iI4Dv2E59++uk9a308OQf/j5ohJGn37t3mtnr16o5jhQsXNuu02R/z5Bz4Hv1unL8zVatWLVObR9+gwF/Q8/jx426/f/7NwqoIQ0jSpUuXJFu2bJIlSxaX43nz5jWPeXoOfI9+N/odObPv870FNvv36+7757uHVRGGkKRMmTLJzZs3zUgxZzdu3DB9STw9B75Hv7e//vor0Xem+N4C/7tX7r5/vntYFWEISXrooYfk7t27cu7cOcex+Ph4OXv2rBQvXtzjc+B79HvTYdXO7Pt8b4GtUKFCZh0rd98/3z2sijCEJD3xxBPmP5o60sRuw4YNcuXKFWnWrJnH58D36Hejc5BcvHjRcWzp0qVSvnx5KVq0aLqWDakrY8aM0qhRI5d/s1q7u3LlSv7NwrKC07sA8F1hYWEyevRoefXVVyUoKEhCQ0Nl5MiRZij9Y4895vE58D3dunWTDz74QNq2bWu+u71798qsWbPk22+/dTlvy5YtpglUw63e6iR+Gn5r1qyZbmVH8v788085ePCgxMXFmX0dOp8rVy4zqEGnwFDjx483/yMzZMgQady4sUyfPt18r3/729/4eH2YToOhU14cO3bM8e9RVa5cWXLkyOHxOUiMVetxT5999pn5kbx165Y0b95cBg4cmKhvgSfnwLforMMTJ040MxDnyZNH+vXrl6hmoGHDholmFC9QoIAsWrQojUsLT61fv17GjBnjNgC/8sorjv2dO3eaeaaio6NNjaD+T4wGJviuyMhIMz9UQjNmzJAKFSp4fA4SIwwBAABLo88QAACwNMIQAACwNMIQAACwNMIQAACwNMIQAACwNMIQAACwNMIQAACwNMIQADjRiUO/+uorM+u2p65du2ausc/6nJavDeDBEYYApDld2FdnyV29erXLIr/21dQ1EMTExNzXc6b0uoRiY2PNbM0nT570+Bpd/kCv0QWK0/q1ATw4whCANPX666/Lww8/LG+++aZ8+OGHZp2zHj16yPXr183jWiuigSAqKuq+njel1wEAC7UCSNN1szQE6eKRdevWNcfi4+NlwYIFZuX0rFmzytKlS81xXUV93759kj9/fmnSpIl8/fXX5lxddf2hhx6SqlWrSqZMmcy5uiBlUtfZa1y2bt1q7lepUkUKFix4X+VO7rUTOnLkiFksUxdFrVSpUqLHH7QsALyPMAQgzWhIyZIli9SpU8dxLEOGDKZGR2ng+P777839H3/8UcLCwqRcuXIm1GjYuXv3rlk49rfffjNhRINPeHi4CUNJXacLCOsitBpMsmXLZoLIW2+95bJo6b0k99rO/v73v8vRo0elZMmSJvDp606ZMsXxuDfKAiAV2AAgjWzfvt0WFBRkGzBggG3v3r22+Pj4ROecOXPGpv9p0seTcvfuXVvHjh1tvXr1Sva648eP27Jnz25bv36949jOnTttWbJksR08eNDtc1+4cME8z+7duz1+7RMnTphrmjZtart165bjvWbIkMG2ceNGj8tyr9cGkDqoGQKQZmrVqiVffvmljBs3TqZNmyY5cuSQBg0amBqVZs2a3fP6AwcOyPHjx82oLW0G27hxY7Ln62vlzZvXdHBeuHChqUFSefLkkU2bNpnaI0958tqDBw92NJ/pe23YsKFpYnviiSe8WhYA3kUYApCmunTpYrbTp0/Ltm3bZM6cOdK8eXNZvny5tG7d2u01N27ckDZt2sju3btNh2ttBtOO0ufPn0/2tXRUlg5X/+abb1yOazjJly+fR+W9n9fWfkLOtKP4H3/84bWyAEgdhCEA6aJo0aLSsWNH6dChg1SsWFG++OKLJMPQvHnzTF8cDRahoaHm2McffyyRkZHJvkbOnDkld+7cZsh9St3Pa1++fDnRvj3oeKMsAFIHQ+sBpJno6GhTO+JMO03rsVy5cpl9e+DQeYPsdP4eDU/2x+ydkZ25u65ly5Zy8OBB2bBhg8u5V69eNZsnPHltuyVLljju63xH2pnbPmrOG2UBkDqCtONQKj03ALhYvHixDBs2TNq1ayfly5eX27dvmz41e/bskZ9++kkqVKhgztP+Mzriqn379mboudao1K5d24y60lokfR49X4e6X7x40fH8Ca/T0WT9+/c3tU4DBw6UUqVKmWHver1O+KjNWAnp82mfIG0W06Hvv/zyyz1fW5vA9LkKFChgRsZpOT799FMT8vR6ez+ie5Ul4WsDSBvUDAFIMxpSNEjoXD07d+40Q+01GB07dswRhNR3331nhqevWLHCdC6uVq2audWh7Vu2bJGnnnpKFi1aZJrYnCW8Tk2fPt3009GOz/raGpJ0SLu7IKRCQkJMnyYNYMqT186ePbu5RjtVFylSRHbs2CFt27Y11znPR3SvsiR8bQBpg5ohAABgadQMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAASyMMAQAAsbL/BVIkyud5KI1QAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success probability: 0.9999999999999989\n"
     ]
    }
   ],
   "source": [
    "@pl.qnode(dev)\n",
    "def circuit():\n",
    "    for i in range(n_bits):\n",
    "        pl.Hadamard(wires=i)\n",
    "    pl.PauliX(wires=flag_wire)\n",
    "    pl.Hadamard(wires=flag_wire)\n",
    "    pl.Snapshot(\"Uniform superposition\")\n",
    "    oracle(keys)\n",
    "    pl.Snapshot(\"State marked by oracle\")\n",
    "    diffusion_operator(wires)\n",
    "    pl.Snapshot(\"Amplitude after diffusion\")\n",
    "    return pl.probs(wires=wires)\n",
    "\n",
    "results = pl.snapshots(circuit)()\n",
    "# inspect the results; plot the amplitudes after the oracle and after diffusion\n",
    "for k, result in results.items():\n",
    "    print(f\"{k}: {result}\")\n",
    "\n",
    "y1 = np.sqrt(2) * np.real(results[\"State marked by oracle\"][::2])\n",
    "y2 = np.sqrt(2) * np.real(results[\"Amplitude after diffusion\"][::2])\n",
    "bit_strings = [f\"{x:0{n_bits}b}\" for x in range(len(y1))]\n",
    "pos = np.arange(len(y1))\n",
    "plt.bar(pos - 0.2, y1, width=0.4, color=\"#70CEFF\", label=\"After oracle\")\n",
    "plt.bar(pos + 0.2, y2, width=0.4, color=\"#C756B2\", label=\"After diffusion\")\n",
    "plt.xticks(pos, bit_strings)\n",
    "plt.axhline(0, color=\"black\", linewidth=0.8)\n",
    "plt.xlabel(\"State label\")\n",
    "plt.ylabel(\"Probability amplitude\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(\"Success probability:\", results[\"execution_results\"][1])\n",
    "assert np.isclose(results[\"execution_results\"][1], 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9a3e5b3",
   "metadata": {},
   "source": [
    "# Exercise 5: Grover's algorithm\n",
    "\n",
    "Now use **four data qubits** and search for the single marked key $0101$. Build Grover's algorithm from the oracle and diffusion functions above.\n",
    "\n",
    "For $N=2^n$ possible inputs and $M=1$ marked key, let $\\theta=\\arcsin\\sqrt{M/N}$. A suitable number of iterations is\n",
    "\n",
    "$$r_{\\mathrm{opt}}\\approx\\operatorname{round}\\left(\\frac{\\pi}{4\\theta}-\\frac12\\right).$$\n",
    "\n",
    "**Step 5a.** Set up the new circuit and calculate how many iterations to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3de9e0fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suggested Grover iterations: 3\n"
     ]
    }
   ],
   "source": [
    "n_bits = 4\n",
    "wires = list(range(n_bits))\n",
    "flag_wire = n_bits\n",
    "dev = pl.device(\"default.qubit\", wires=n_bits + 1)\n",
    "keys = [[0,1,0,1]]\n",
    "N = 2**n_bits\n",
    "M = 1\n",
    "theta = np.arcsin(np.sqrt(M / N))\n",
    "r_opt = int(np.round(np.pi / (4 * theta) - 0.5))\n",
    "print(\"Suggested Grover iterations:\", r_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b4d4285",
   "metadata": {},
   "source": [
    "**Step 5b.** Complete the circuit: prepare a uniform superposition on the data qubits and $|-\\rangle$ on the extra qubit, then repeat the oracle and diffusion operations `iterations` times. Measure only the data qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0e81f0f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "@pl.qnode(dev)\n",
    "def circuit(iterations):\n",
    "    for i in range(n_bits):\n",
    "        pl.Hadamard(wires=i)\n",
    "    pl.PauliX(wires=flag_wire)\n",
    "    pl.Hadamard(wires=flag_wire)\n",
    "    for _ in range(iterations):\n",
    "        oracle(keys)\n",
    "        diffusion_operator(wires)\n",
    "    return pl.probs(wires=wires)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3091315b",
   "metadata": {},
   "source": [
    "**Inspect the result.** Try one and two iterations, then the suggested number $r_{\\mathrm{opt}}$. Plot the final distribution and check whether the most likely outcome is the marked key. You do **not** need to plot a success-probability curve over many iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3ac712e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After 1 iteration(s): P(0101) = 0.4727\n",
      "After 2 iteration(s): P(0101) = 0.9084\n",
      "After 3 iteration(s): P(0101) = 0.9613\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Most likely outcome: 0101\n"
     ]
    },
    {
     "data": {
      "image/png": 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CYII=",
      "text/plain": [
       "<Figure size 2800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bit_strings = [f\"{x:0{n_bits}b}\" for x in range(2**n_bits)]\n",
    "marked_index = int(\"\".join(map(str, keys[0])), 2)\n",
    "\n",
    "for iterations in [1, 2, r_opt]:\n",
    "    results = circuit(iterations)\n",
    "    print(f\"After {iterations} iteration(s): P(0101) = {results[marked_index]:.4f}\")\n",
    "\n",
    "results = circuit(r_opt)\n",
    "plt.figure(figsize=(8, 3.5))\n",
    "plt.bar(bit_strings, results, color=\"#70CEFF\")\n",
    "plt.xticks(rotation=\"vertical\")\n",
    "plt.xlabel(\"State label\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(f\"Grover after {r_opt} iterations\")\n",
    "plt.show()\n",
    "print(\"Most likely outcome:\", bit_strings[int(np.argmax(results))])\n",
    "# draw the final circuit\n",
    "pl.drawer.use_style(\"black_white\")\n",
    "pl.draw_mpl(circuit)(r_opt);\n",
    "assert bit_strings[int(np.argmax(results))] == \"0101\"\n",
    "assert np.isclose(results[marked_index], 0.9613189697265625)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pennylane (3.14.7)",
   "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": "3.14.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}