examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb

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    "# Ordered phases in Rydberg systems\n",
    "\n",
    "In this example notebook, we show how one can prepare ordered phases in Rydberg systems, focusing on the 1D $Z_2$ phase and the 2D checkerboard phase. We will use an adiabatic time-evolution to prepare these many-body ground states.\n",
    "\n",
    "## Adiabatic evolution\n",
    "\n",
    "The adiabatic theorem of quantum mechanics states that \n",
    "\n",
    ">A physical system remains in its *instantaneous* eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. (Born & Fock, 1928)\n",
    "\n",
    "In other words, a slow-enough change in the parameters of the Hamiltonian will not induce transitions between its ground state and excited states: If the system starts in the ground state of the Hamiltonian at the beginning, it will smoothly transition into the ground state of the Hamiltonian at the end.\n",
    "\n",
    "The adiabatic theorem plays a key role in preparing the desired many-body ground states in the Rydberg system, the Hamiltonian of which can be expressed as\n",
    "\n",
    "\\begin{align}\n",
    "H(t) = \\sum_{k=1}^N \\frac{\\Omega(t)}{2}\\left(|g_k\\rangle\\langle r_k| + |r_k\\rangle\\langle g_k|\\right) - \\Delta_\\text{global}(t){n}_k + \\sum_{j=1}^{N-1}\\sum_{k=j+1}^N V_{jk}{n}_j{n}_k,\n",
    "\\end{align}\n",
    "\n",
    "where, for simplicity, we set the phase and the shifting field (See notebook 00 for detailed description of this Hamiltonian) to be zero throughout this notebook. We schedule the driving amplitude $\\Omega(t)$ to start from zero ($\\Omega(t=0)=0$). Hence, with negative detuning ($\\Delta_\\text{global}(t=0)<0$), the initial state where all atoms are in the ground state ($\\langle n_k\\rangle =0$) is the lowest energy eigenstate of the Hamiltonian, the many-body ground state.\n",
    "\n",
    "To arrive at a target Hamiltonian where the excited states of the atoms are favored, we ramp up the detuning $\\Delta_\\text{global}$ from large negative to large positive. During the ramp, we apply a large driving amplitude $\\Omega$ to open an energy gap between the first excited state and the ground state. According to the adiabatic theorem, if the ramping is slow enough, the system remains in the many-body ground state throughout the evolution. At the end of the AHS program, the Rabi frequency will be turned off and since $\\Delta_\\text{global}>0$, all the atoms tend to stay in the Rydberg state to lower the energy of the system. However, due to the strong Rydberg interaction, only one atom can be excited to the Rydberg state within its blockade radius.\n",
    "\n",
    "For a 1D chain of atoms, if we adjust the separation between the atoms such that only neighboring atoms are within the blockade radius, then we will arrive at a state where every second atom is excited, this is called the \"$Z_2$ phase\". For a 2D square array of atoms, a similar \"checkerboard phase\" emerges. The common feature of these phases is that the atoms are excited to the Rydberg states in an alternative pattern, complying with the blockade constraint, as shown in the figure below. In the figure, the shaded circles show *half* of the blockade radius such that sites with overlapped circles blockade each other. We show configurations, with black and white sites represent Rydberg and ground state atoms respectively, that comply with the blockade constraint. \n",
    "\n",
    "![Blockade_examples.png](Blockade_examples.png)\n",
    "\n",
    "We will realize these phases in this notebook. To begin, we import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9124196d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:06.629855Z",
     "start_time": "2023-08-29T21:43:06.051483Z"
    }
   },
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "tracker = Tracker().start()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "156c4218",
   "metadata": {},
   "source": [
    "In this notebook, we will use `matplotlib` package and `ahs_utils.py` module in the current working directory for visualization purposes and other functionalities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "08909afa",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:08.515925Z",
     "start_time": "2023-08-29T21:43:06.116118Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from braket.ahs.atom_arrangement import AtomArrangement\n",
    "\n",
    "from braket.ahs.analog_hamiltonian_simulation import AnalogHamiltonianSimulation\n",
    "from braket.ahs.driving_field import DrivingField\n",
    "\n",
    "from ahs_utils import show_register, show_global_drive, show_final_avg_density\n",
    "\n",
    "from braket.devices import LocalSimulator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b5eee4d",
   "metadata": {},
   "source": [
    "## 1D $Z_2$ phase \n",
    "\n",
    "Here we consider a 1D chain of 9 atoms with neighboring atoms separated by $6.1\\mu m$. The setup of the system can be generated as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6702f2b8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:08.726486Z",
     "start_time": "2023-08-29T21:43:08.517068Z"
    }
   },
   "outputs": [
    {
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mpiY+97nPRZZlcccdd3zgfjNmzIiqqqr62xtvvNGIUwIAHPha5POLd+nSJUpKSmLdunUNtq9bty7Ky8t3e0x5efle7b8zKF9//fV46KGH9vgZhdatW0fr1q0/4ioAAPgweX2lslWrVjF06NBYtGhR/ba6urpYtGhRjBw5crfHjBw5ssH+ERELFy5ssP/OoFy5cmX89re/jc6dO+dnAQAA7JW8vlIZETF9+vSYNGlSDBs2LIYPHx633HJLbN68OS644IKIiDjvvPPiYx/7WMyaNSsiIi655JI44YQT4uabb47TTjst5s6dG08//XT8+7//e0TsCMqzzjorli1bFvfff3/U1tbWf96yU6dO0apVq3wvCQCAv5P3qDz77LNjw4YNcc0110RlZWUMHjw4HnjggfqTcVavXh3FxX99wfRTn/pUzJkzJ7761a/GV77ylfjEJz4RCxYsiCOPPDIiIt5666347//+74iIGDx4cIPHevjhh+PEE0/M95IAAPg7eb9OZVPUXK4XBQAUXnPpjv367G8AAJoGUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUdnEPPHEE3HcccdFu3btory8PC6++OLYtGlTocfKm9/85jcxefLkOPLII6OkpCT69etX6JHybsuWLXH77bfHmDFjokePHtGhQ4f45Cc/GXfccUfU1tYWery8uuGGG+LYY4+Nrl27Rps2beITn/hEXHrppbFhw4ZCj9YoNm7cGN26dYuioqK47777Cj1OXp144olRVFS0y+2UU04p9Gh5t3379rjhhhtiwIAB0aZNm+jevXucdtpp8eabbxZ6tJx77bXXdvs877xdeOGFhR4xb+rq6uLOO++MwYMHR/v27aN79+5x6qmnxhNPPFHo0QqmRaEH4K+WL18eo0aNioEDB8Z3vvOdePPNN+Pb3/52rFy5Mn79618Xery8mDNnTsybNy+GDBkSPXv2LPQ4jeJPf/pTXHTRRTFq1KiYPn16dOzYMR588MH4whe+EE8++WT85Cc/KfSIeVNRURGDBw+Oc845Jzp06BAvvfRS/PCHP4xf/vKXsXz58jjooIMKPWJeXXPNNbFly5ZCj9FoevXqFbNmzWqw7UD/c15TUxOnnXZaPPHEE3HhhRfGoEGD4i9/+Us89dRTUVVVFb169Sr0iDnVtWvX+L//9//usv2BBx6Iu+++O8aMGVOAqRrH5ZdfHt/5znfi85//fHzhC1+IjRs3xg9+8IM44YQT4vHHH4/hw4cXesTGlzVDVVVVWURkVVVVhR6lgVNPPTXr0aNHg7l++MMfZhGRPfjggwWcLH/eeuutbPv27VmWZdlpp52W9e3bt7ADNYINGzZkzz///C7bL7jggiwispUrVxZgqsK57777sojIfvaznxV6lLx67rnnshYtWmRf//rXs4jI7r333kKPlFcnnHBCdsQRRxR6jEb3zW9+M2vZsmX21FNPFXqUgho1alTWsWPH7L333iv0KHlRU1OTtW3bNjvrrLMabP/Tn/6URUR28cUXN9jeVLsj17z93URUV1fHwoUL4/Of/3x07Nixfvt5550X7du3j3vuuaeA0+VPz549o2XLloUeo1F16dIljjjiiF22f/azn42IiJdeeqmxRyqonR952LhxY0HnyLdLLrkkPvvZz8bxxx9f6FEa1fvvv39Af4Tnb9XV1cWtt94an/3sZ2P48OHx/vvvN6tXpndau3ZtPPzww3HmmWdGmzZtCj1OXtTU1MR7770X3bt3b7C9W7duUVxcHG3bti3QZIUlKpuI5557Lt5///0YNmxYg+2tWrWKwYMHxzPPPFOgyWgslZWVEbEjOg9kWZbF22+/HZWVlfHYY4/FxRdfHCUlJXHiiScWerS8uffee+OJJ56Ib33rW4UepVG98sorcdBBB0WHDh2ivLw8rr766qipqSn0WHnz4osvxpo1a2LQoEExZcqUOOigg+Kggw6KQYMGxcMPP1zo8RrN3Llzo66uLiZOnFjoUfKmbdu2MWLEiJg9e3bcfffdsXr16nj22Wfj/PPPj3/4h3+IKVOmFHrEgvCZyiZi7dq1ERHRo0ePXe7r0aNHPPbYY409Eo1o+/btccstt8TBBx8cxxxzTKHHyat169Y1+D7v1atXzJkzJwYMGFDAqfLnvffeiy996Utx2WWXRb9+/eK1114r9EiN4uMf/3icdNJJcdRRR8XmzZvjvvvui+uuuy5eeeWVmDdvXqHHy4uVK1dGRMR3v/vd6NSpU/zgBz+IiB0nqJ1yyimxdOnSGDRoUCFHbBR333139OjRI04++eRCj5JXd911V5x99tnx+c9/vn5b//794/HHH4/+/fsXcLLCEZX58O67EQsXRrzzTkSnThGf/nREhw57POS9996LiIjWrVvvcl+bNm3q72+yPsKaDwg5Wve0adPixRdfjF/+8pfRosV+8McyYd2dOnWKhQsXxtatW+OZZ56J//qv/9o/3h79iGu+8cYbo6amJr7yla80wpB58BHX/Z//+Z8Nfn3uuefGlClT4oc//GFcdtllceyxx+Zr4tz4COve+X387rvvxjPPPBO9e/eOiIiTTz45DjnkkPjWt74Vd911V95H/8hy8PfZK6+8EhUVFXHZZZdFcfF+8mboR1x3hw4d4ogjjoiRI0fGqFGjorKyMm688cYYN25cPPbYYwf8u067VegPdRZC3j4wu2lTll1ySZa1a5dlEX+9tWu3Y/umTR946L333ptFRLZ48eJd7vvnf/7nrLy8PLez5krCmv/efnWiTg7X/a1vfSuLiOwb3/hG3sbNmRyue6fHH388i4jsF7/4Rc7HzYmENa9atSpr27Zt9qMf/ah+28MPP7x/nKiTh+d6xYoVTf97PQd/j5900km73HfSSSdlBx98cP7mTpHD5/qaa67JIiJ7+umn8zZuziSsu6amJjvyyCOzadOmNdj+yiuvZC1btsy+/OUvN9jeXE7UaZSovO2227K+fftmrVu3zoYPH/6hZ8Xdc8892WGHHZa1bt06O/LII7Nf/vKXDe6vq6vLrr766qy8vDxr06ZNNmrUqOyVV17Z63ny8uRu2pRlxxyTZSUlDb85d95KSnbc/wHfpL/73e+yiMjmzZu3y33HHXdcNmTIkNzNmiuJa/57+01U5nDdP/7xj7OioqLsX//1Xxth8EQ5fr7/Vo8ePbJzzjknD0MnSlzzueeemx1yyCHZn/70p2zVqlXZqlWrsp/97GdZRGTf//73s1WrVmW1tbWNvKi9kKfnevPmzVlEZJdddlmeBk+UuO6d/0Da3ffy2WefnZWVleV7Bfsux8/1IYcckh122GF5HjoHEte9aNGiLCKy3/zmN7vcN2jQoOwf//EfG2wTlTkyd+7crFWrVtmPfvSj7IUXXsguvPDCrKysLFu3bt1u93/88cezkpKS7Fvf+lb24osvZl/96lezli1bZs8991z9PjfeeGNWWlqaLViwIPvDH/6QfeYzn8kOPvjgvb50QV6e3Esu+eBvzr/9Jr3kkt0evnHjxqxFixbZ5Zdf3mD7tm3bsvbt22f/8i//krtZcyVxzX9vv4nKHK17wYIFWUlJSTZ+/PimGRZ/L8fP99/6h3/4h+zUU0/N+cjJEtd8wgknZBGxx9tf/vKXxlzR3snTc/3cc89lEZHdcMMNeRk7WeK6q6urs5YtW2bHH3/8Lvcdf/zx2Sc+8Yn8zv9R5PC5fvLJJ7OIyL7+9a/nfexkieueM2dOFhHZr3/9613uGzhwYDZixIgG20RljgwfPjybOnVq/a9ra2uznj17ZrNmzdrt/p/73Oey0047rcG2ESNGZP/7f//vLMt2vEpZXl6e3XTTTfX3b9y4MWvduvVeX+cu509udfWuL59/0K1duyx7993dfplTTjkl69GjR1ZdXV2/7T/+4z8+8Bu3oHK05r+1X0Rljtb96KOPZm3atMlOOumkbOvWrY28iI8gB+vetGlTtnnz5l2277xO5dVXX90YK9l7OVjzY489ls2fP7/B7Rvf+EYWEdmXv/zlbP78+fXXaW0ycrDuqqqqXb6v6+rqsrPPPjuLiKyioqKxVrP3cvRn+4wzzshKSkqyl156qX7biy++mJWUlGRf+MIXGms1eyfHf49ffPHFWURkr776aiMt4CPKwbqffvrpLCKySZMmNdheUVGRFRcX7/LuU3OJyryeEbB9+/aoqKiIGTNm1G8rLi6O0aNHx5IlS3Z7zJIlS2L69OkNto0dOzYWLFgQERGrVq2KysrKGD16dP39paWlMWLEiFiyZEmcc845u3zNbdu2xbZt2+p/XV1dnbKsXS1cGLG31yLbsiXiN7+JOPPMXe66/vrr41Of+lSccMIJMWXKlHjzzTfj5ptvjjFjxjS9H22WozU/++yz8d///d8REfHqq69GVVVVXHfddRERcfTRR8fpp5+es5FzIgfrfv311+Mzn/lMFBUVxVlnnRX33ntvg/sHDRrU9M4QzcG6V65cGaNHj46zzz47BgwYEMXFxfH000/HXXfdFf369YtLLrkkD4MnyMGajzvuuF12LSsri4iIY445JsaNG5c4ZB7kYN3Lli2LCRMmxIQJE+KQQw6J9957L+bPnx+PP/54TJkyJYYMGZKHwRPl6O+0G264IRYtWhQnn3xyXHzxxRER8b3vfS86derU9E7WytGaIyJqa2tj3rx5ceyxx8bHP/7xHA6ZBzlY99ChQ+PTn/50/OQnP4nq6uoYM2ZMrF27Nv7t3/4t2rZtG5deemnu594P5DUq33777aitrd3l4qDdu3ePFStW7PaYysrK3e6/8xp+O/+7p33+3qxZs+Laa6/9SGvYK++8k5P9hwwZEr/97W/jiiuuiMsuuyw6dOgQkydP3uXHnDUJOVrzsmXL4uqrr26wbeevJ02a1PSiMgfrXrVqVVRVVUVExNSpU3e5f+bMmU0vKnOw7l69esX48ePjoYceip/85CdRU1MTffv2jWnTpsVVV10VnTt3ztGwOZKj7/H9Tg7W3bdv3zj++ONj/vz5UVlZGcXFxTFw4MC48847m+71+3L0fB9++OHx6KOPxhVXXBHXXXddFBcXx8knnxw33XRTfOxjH8vBoDmUw+/x3/72t7Fu3bq46qqrEodqBDla989//vP49re/HXPnzo0HHnggWrVqFccff3x84xvfiMMOOywHg+5/9oNrl6SbMWNGg1c/q6ur6y/1kBOdOuVs/+OOOy4ef/zxxIEaQY7WfP7558f555+fPk9jycG6TzzxxMiyLEcDNZIcrLtLly711+3bL+Twz/XfavLPfw7WffDBB+9/PwUsh8/3kCFDYuHChYkDNYIcrnns2LFN+/v6b+Vo3W3bto2rr756lxdGmrO8XkSqS5cuUVJSEuvWrWuwfd26dVFeXr7bY8rLy/e4/87/7svXbN26dXTs2LHBLac+/emIdu32bt927SLGjMnt4xdCc1xzhHXvjQNl3c1xzRHWvTcOlHU3xzVHNN91N4K8RmWrVq1i6NChsWjRovptdXV1sWjRohg5cuRujxk5cmSD/SMiFi5cWL//wQcfHOXl5Q32qa6ujqeeeuoDv2bedegQceGFESUle96vpGTHfu3bN85c+dQc1xxh3c1p3c1xzRHW3ZzW3RzXHNF8190Y8n0m0Ny5c7PWrVtns2fPzl588cVsypQpWVlZWVZZWZll2Y7ruF155ZX1+z/++ONZixYtsm9/+9vZSy+9lM2cOXO3lxQqKyvLfv7zn2fPPvtsdsYZZxT+kkJ5vIZfk9Uc15xl1t2c1t0c15xl1t2c1t0c15xljb7u5nL2d96jMsuy7N/+7d+yPn36ZK1atcqGDx+ePfnkk/X3nXDCCbuckn/PPfdkhx56aNaqVavsiCOO+MCLn3fv3j1r3bp1NmrUqOzll1/e63ma4k/U2W81xzVnmXU3p3U3xzVnmXU3p3U3xzVnWaOuu7lEZVGW7S+frM2d6urqKC0tjaqqqtx/vjIiYtOmHZcg2PlzRMeMOfBfPm+Oa46w7ua07ua45gjrbk7rbo5rjmiUdee9O5oIUXkAP7kAQOE1l+7I64k6AAA0D6ISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkohIAgGSiEgCAZKISAIBkeYvKd955JyZOnBgdO3aMsrKymDx5cmzatGmPx2zdujWmTp0anTt3jvbt28f48eNj3bp19ff/4Q9/iAkTJkTv3r2jbdu2MXDgwLj11lvztQQAAPZS3qJy4sSJ8cILL8TChQvj/vvvj8WLF8eUKVP2eMxll10Wv/jFL+Lee++NRx99NNasWRNnnnlm/f0VFRXRrVu3uOuuu+KFF16Iq666KmbMmBG33XZbvpYBAMBeKMqyLMv1F33ppZfi8MMPj6VLl8awYcMiIuKBBx6If/qnf4o333wzevbsucsxVVVV0bVr15gzZ06cddZZERGxYsWKGDhwYCxZsiSOPfbY3T7W1KlT46WXXoqHHnpor+errq6O0tLSqKqqio4dO36EFQIA7J3m0h15eaVyyZIlUVZWVh+UERGjR4+O4uLieOqpp3Z7TEVFRdTU1MTo0aPrtw0YMCD69OkTS5Ys+cDHqqqqik6dOu1xnm3btkV1dXWDGwAAuZOXqKysrIxu3bo12NaiRYvo1KlTVFZWfuAxrVq1irKysgbbu3fv/oHHPPHEEzFv3rwPfVt91qxZUVpaWn/r3bv33i8GAIAPtU9ReeWVV0ZRUdEebytWrMjXrA08//zzccYZZ8TMmTNjzJgxe9x3xowZUVVVVX974403GmVGAIDmosW+7PzFL34xzj///D3u079//ygvL4/169c32P7+++/HO++8E+Xl5bs9rry8PLZv3x4bN25s8GrlunXrdjnmxRdfjFGjRsWUKVPiq1/96ofO3bp162jduvWH7gcAwEezT1HZtWvX6Nq164fuN3LkyNi4cWNUVFTE0KFDIyLioYceirq6uhgxYsRujxk6dGi0bNkyFi1aFOPHj4+IiJdffjlWr14dI0eOrN/vhRdeiJNPPjkmTZoU119//b6MDwBAnuTl7O+IiFNPPTXWrVsXd955Z9TU1MQFF1wQw4YNizlz5kRExFtvvRWjRo2Kn/70pzF8+PCIiPg//+f/xK9+9auYPXt2dOzYMS666KKI2PHZyYgdb3mffPLJMXbs2LjpppvqH6ukpGSvYnen5nIWFgBQeM2lO/bplcp9cffdd8e0adNi1KhRUVxcHOPHj4/vfe979ffX1NTEyy+/HFu2bKnf9t3vfrd+323btsXYsWPj+9//fv399913X2zYsCHuuuuuuOuuu+q39+3bN1577bV8LQUAgA+Rt1cqm7Lm8i8GAKDwmkt3+NnfAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJMtbVL7zzjsxceLE6NixY5SVlcXkyZNj06ZNezxm69atMXXq1OjcuXO0b98+xo8fH+vWrdvtvn/+85+jV69eUVRUFBs3bszDCgAA2Ft5i8qJEyfGCy+8EAsXLoz7778/Fi9eHFOmTNnjMZdddln84he/iHvvvTceffTRWLNmTZx55pm73Xfy5MkxaNCgfIwOAMA+KsqyLMv1F33ppZfi8MMPj6VLl8awYcMiIuKBBx6If/qnf4o333wzevbsucsxVVVV0bVr15gzZ06cddZZERGxYsWKGDhwYCxZsiSOPfbY+n3vuOOOmDdvXlxzzTUxatSo+Mtf/hJlZWV7PV91dXWUlpZGVVVVdOzYMW2xAAB70Fy6Iy+vVC5ZsiTKysrqgzIiYvTo0VFcXBxPPfXUbo+pqKiImpqaGD16dP22AQMGRJ8+fWLJkiX121588cX4+te/Hj/96U+juHjvxt+2bVtUV1c3uAEAkDt5icrKysro1q1bg20tWrSITp06RWVl5Qce06pVq11ecezevXv9Mdu2bYsJEybETTfdFH369NnreWbNmhWlpaX1t969e+/bggAA2KN9isorr7wyioqK9nhbsWJFvmaNGTNmxMCBA+Pzn//8Ph9XVVVVf3vjjTfyNCEAQPPUYl92/uIXvxjnn3/+Hvfp379/lJeXx/r16xtsf//99+Odd96J8vLy3R5XXl4e27dvj40bNzZ4tXLdunX1xzz00EPx3HPPxX333RcRETs/DtqlS5e46qqr4tprr93t127dunW0bt16b5YIAMBHsE9R2bVr1+jateuH7jdy5MjYuHFjVFRUxNChQyNiRxDW1dXFiBEjdnvM0KFDo2XLlrFo0aIYP358RES8/PLLsXr16hg5cmRERPy///f/4r333qs/ZunSpfEv//Iv8dhjj8XHP/7xfVkKAAA5tE9RubcGDhwYp5xySlx44YVx5513Rk1NTUybNi3OOeec+jO/33rrrRg1alT89Kc/jeHDh0dpaWlMnjw5pk+fHp06dYqOHTvGRRddFCNHjqw/8/vvw/Htt9+uf7x9OfsbAIDcyktURkTcfffdMW3atBg1alQUFxfH+PHj43vf+179/TU1NfHyyy/Hli1b6rd997vfrd9327ZtMXbs2Pj+97+frxEBAMiRvFynsqlrLteLAgAKr7l0h5/9DQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAEAyUQkAQDJRCQBAMlEJAECyFoUeoBCyLIuIiOrq6gJPAgAc6Hb2xs7+OFA1y6h89913IyKid+/eBZ4EAGgu3n333SgtLS30GHlTlB3o2bwbdXV1sWbNmujQoUMUFRXl5TGqq6ujd+/e8cYbb0THjh3z8hjsG89J0+M5aXo8J02P56Tp2dfnJMuyePfdd6Nnz55RXHzgfvKwWb5SWVxcHL169WqUx+rYsaO/BJoYz0nT4zlpejwnTY/npOnZl+fkQH6FcqcDN5cBAGg0ohIAgGSiMk9at24dM2fOjNatWxd6FP6H56Tp8Zw0PZ6Tpsdz0vR4TnavWZ6oAwBAbnmlEgCAZKISAIBkohIAgGSiEgCAZKISAIBkojIPbr/99ujXr1+0adMmRowYEb///e8LPVKztnjx4jj99NOjZ8+eUVRUFAsWLCj0SM3arFmz4phjjokOHTpEt27dYty4cfHyyy8Xeqxm74477ohBgwbV/4SQkSNHxq9//etCj8X/uPHGG6OoqCguvfTSQo/SrH3ta1+LoqKiBrcBAwYUeqwmQ1Tm2Lx582L69Okxc+bMWLZsWRx99NExduzYWL9+faFHa7Y2b94cRx99dNx+++2FHoWIePTRR2Pq1Knx5JNPxsKFC6OmpibGjBkTmzdvLvRozVqvXr3ixhtvjIqKinj66afj5JNPjjPOOCNeeOGFQo/W7C1dujR+8IMfxKBBgwo9ChFxxBFHxNq1a+tvv/vd7wo9UpPhOpU5NmLEiDjmmGPitttui4iIurq66N27d1x00UVx5ZVXFng6ioqKYv78+TFu3LhCj8L/2LBhQ3Tr1i0effTR+F//638Vehz+RqdOneKmm26KyZMnF3qUZmvTpk0xZMiQ+P73vx/XXXddDB48OG655ZZCj9Vsfe1rX4sFCxbE8uXLCz1Kk+SVyhzavn17VFRUxOjRo+u3FRcXx+jRo2PJkiUFnAyarqqqqojYETA0DbW1tTF37tzYvHlzjBw5stDjNGtTp06N0047rcH/r1BYK1eujJ49e0b//v1j4sSJsXr16kKP1GS0KPQAB5K33347amtro3v37g22d+/ePVasWFGgqaDpqquri0svvTT+8R//MY488shCj9PsPffcczFy5MjYunVrtG/fPubPnx+HH354ocdqtubOnRvLli2LpUuXFnoU/seIESNi9uzZcdhhh8XatWvj2muvjeOPPz6ef/756NChQ6HHKzhRCRTM1KlT4/nnn/eZpCbisMMOi+XLl0dVVVXcd999MWnSpHj00UeFZQG88cYbcckll8TChQujTZs2hR6H/3HqqafW/+9BgwbFiBEjom/fvnHPPff4mEiIypzq0qVLlJSUxLp16xpsX7duXZSXlxdoKmiapk2bFvfff38sXrw4evXqVehxiIhWrVrFIYccEhERQ4cOjaVLl8att94aP/jBDwo8WfNTUVER69evjyFDhtRvq62tjcWLF8dtt90W27Zti5KSkgJOSEREWVlZHHroofHqq68WepQmwWcqc6hVq1YxdOjQWLRoUf22urq6WLRokc8lwf/IsiymTZsW8+fPj4ceeigOPvjgQo/EB6irq4tt27YVeoxmadSoUfHcc8/F8uXL62/Dhg2LiRMnxvLlywVlE7Fp06b44x//GD169Cj0KE2CVypzbPr06TFp0qQYNmxYDB8+PG655ZbYvHlzXHDBBYUerdnatGlTg39Frlq1KpYvXx6dOnWKPn36FHCy5mnq1KkxZ86c+PnPfx4dOnSIysrKiIgoLS2Ntm3bFni65mvGjBlx6qmnRp8+feLdd9+NOXPmxCOPPBIPPvhgoUdrljp06LDL54wPOuig6Ny5s88fF9CXvvSlOP3006Nv376xZs2amDlzZpSUlMSECRMKPVqTICpz7Oyzz44NGzbENddcE5WVlTF48OB44IEHdjl5h8bz9NNPx0knnVT/6+nTp0dExKRJk2L27NkFmqr5uuOOOyIi4sQTT2yw/cc//nGcf/75jT8QERGxfv36OO+882Lt2rVRWloagwYNigcffDA+/elPF3o0aDLefPPNmDBhQvz5z3+Orl27xnHHHRdPPvlkdO3atdCjNQmuUwkAQDKfqQQAIJmoBAAgmagEACCZqAQAIJmoBAAgmagEACCZqAQAIJmoBAAOOIsXL47TTz89evbsGUVFRbFgwYK8Pt7Xvva1KCoqanAbMGBAXh+zqRGVAMABZ/PmzXH00UfH7bff3miPecQRR8TatWvrb7/73e8a7bGbAj+mEQA44Jx66qlx6qmnfuD927Zti6uuuip+9rOfxcaNG+PII4+Mb37zm7v8CNl90aJFiygvL//Ix+/vvFIJADQ706ZNiyVLlsTcuXPj2WefjX/+53+OU045JVauXPmRv+bKlSujZ8+e0b9//5g4cWKsXr06hxM3fX72NwBwQCsqKor58+fHuHHjIiJi9erV0b9//1i9enX07Nmzfr/Ro0fH8OHD44Ybbtjnx/j1r38dmzZtisMOOyzWrl0b1157bbz11lvx/PPPR4cOHXK1lCbN298AQLPy3HPPRW1tbRx66KENtm/bti06d+4cERErVqyIgQMH7vHrXHHFFXHjjTdGRDR4q33QoEExYsSI6Nu3b9xzzz0xefLkHK+gaRKVAECzsmnTpigpKYmKioooKSlpcF/79u0jIqJ///7x0ksv7fHr7AzQ3SkrK4tDDz00Xn311fSB9xOiEgBoVj75yU9GbW1trF+/Po4//vjd7tOqVaukSwJt2rQp/vjHP8a55577kb/G/kZUAgAHnE2bNjV4lXDVqlWxfPny6NSpUxx66KExceLEOO+88+Lmm2+OT37yk7Fhw4ZYtGhRDBo0KE477bR9frwvfelLcfrpp0ffvn1jzZo1MXPmzCgpKYkJEybkcllNmhN1AIADziOPPBInnXTSLtsnTZoUs2fPjpqamrjuuuvipz/9abz11lvRpUuXOPbYY+Paa6+No446ap8f75xzzonFixfHn//85+jatWscd9xxcf3118fHP/7xXCxnvyAqAQBI5jqVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACQTlQAAJBOVAAAkE5UAACT7/4hpM3Yt7jPPAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "register = AtomArrangement()\n",
    "separation = 6.1e-6  # in meters \n",
    "num_atoms = 9\n",
    "\n",
    "for k in range(num_atoms):\n",
    "    register.add([k * separation, 0])\n",
    "    \n",
    "show_register(register)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33174b8a",
   "metadata": {},
   "source": [
    "In order to prepare the $Z_2$ ordered state for the atomic chain, we shall design an AHS program that drives the system adiabatically. As described above, we start from $\\Omega(t=0)=0$ with $\\Delta(t=0)<0$, followed by turning on $\\Omega(t)$ and ramping up $\\Delta(t)$. We will turn off the driving amplitude at the end of the program. This program can be specified as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "12184869",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:08.726631Z",
     "start_time": "2023-08-29T21:43:08.719473Z"
    }
   },
   "outputs": [],
   "source": [
    "time_points = [0, 2.5e-7, 2.75e-6, 3e-6]\n",
    "amplitude_min = 0\n",
    "amplitude_max = 1.57e7  # rad / s\n",
    "\n",
    "detuning_min = -5.5e7  # rad / s\n",
    "detuning_max = 5.5e7  # rad / s\n",
    "\n",
    "amplitude_values = [amplitude_min, amplitude_max, amplitude_max, amplitude_min]  # piecewise linear\n",
    "detuning_values = [detuning_min, detuning_min, detuning_max, detuning_max]  # piecewise linear\n",
    "phase_values = [0, 0, 0, 0]  # piecewise constant\n",
    "\n",
    "\n",
    "drive = DrivingField.from_lists(time_points, amplitude_values, detuning_values, phase_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee92d637",
   "metadata": {},
   "source": [
    "We can plot the waveforms of these driving fields to make sure that they are correctly specified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e8d369e3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:09.288470Z",
     "start_time": "2023-08-29T21:43:08.729040Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_global_drive(drive);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecd5fce7",
   "metadata": {},
   "source": [
    "Finally, we construct out AHS program from the atomic registers, and the Hamiltonian defined above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ef5318d9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:09.296363Z",
     "start_time": "2023-08-29T21:43:09.290265Z"
    }
   },
   "outputs": [],
   "source": [
    "ahs_program = AnalogHamiltonianSimulation(\n",
    "    register=register, \n",
    "    hamiltonian=drive\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37e89b67",
   "metadata": {},
   "source": [
    "Before running the program on Quera's Aquila device (See notebook 01), we can first run it on the local simulator to make sure the outcome is the expected $Z_2$ state. Below we have explicitly specified the values of `steps` and `shots`, which are the number of time steps in the simulation and the number of sampling for the final stats, respectively. One could increase the accuracy of the result by increasing the values of these arguments, at the expense of longer runtime. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "18447781",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:12.091558Z",
     "start_time": "2023-08-29T21:43:09.295999Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "device = LocalSimulator(\"braket_ahs\")\n",
    "result = device.run(ahs_program, shots=1000, steps=100).result()\n",
    "show_final_avg_density(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daf77070",
   "metadata": {},
   "source": [
    "We see that the average Rydberg density approximately forms the $Z_2$ pattern. The discrepancy can be attributed to finite size of the system and nonadiabaticity throughout the evolution. We expect that as one increase the system size and the duration of the AHS program, the final Rydberg density will approach the ideal $Z_2$ pattern.\n",
    "\n",
    "The $Z_2$ phase can be characterized by the density correlation $g_{ij}$ of the $i$-th and the $j$-th atom, which is defined as\n",
    "\n",
    "\\begin{align}\n",
    "g_{ij} = \\langle n_i n_j\\rangle - \\langle n_i\\rangle\\langle n_j\\rangle,\n",
    "\\end{align}\n",
    "\n",
    "where $\\langle\\cdot\\rangle$ is the average over the shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4ba0163e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:12.099341Z",
     "start_time": "2023-08-29T21:43:12.094610Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_density_correlation_Z2(result):\n",
    "    post_sequences = np.array([list(measurement.post_sequence) for measurement in result.measurements])\n",
    "    return np.cov(post_sequences.T)\n",
    "\n",
    "gij = get_density_correlation_Z2(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c405519e",
   "metadata": {},
   "source": [
    "The Rydberg density correlation function can be visualized as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dd0c5d4a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:12.352200Z",
     "start_time": "2023-08-29T21:43:12.106118Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(gij, cmap='bwr', vmin=-0.25, vmax=+0.25)\n",
    "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n",
    "plt.xlabel(\"atom index\")\n",
    "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n",
    "plt.ylabel(\"atom index\")\n",
    "plt.title('Rydberg density correlation')\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "276bb5b6",
   "metadata": {},
   "source": [
    "For more explanation and interpretation of the Rydberg density correlation functions, see \"Probing many-body dynamics on a 51-atom quantum simulator\" by [Bernien et al. (2017)](https://arxiv.org/abs/1707.04344). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc7d3074",
   "metadata": {},
   "source": [
    "## 2D checkerboard phase \n",
    "\n",
    "In two dimension, Rydberg system can exhibit the checkerboard phase, which is analogous to the $Z_2$ phase in 1D. For simplicity, here we create a $3\\times 3$ square lattice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "22477060",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:12.549865Z",
     "start_time": "2023-08-29T21:43:12.357234Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "register_2D = AtomArrangement()\n",
    "separation = 6.7e-6  # in meters \n",
    "\n",
    "for k in range(3):\n",
    "    for l in range(3):\n",
    "        register_2D.add((k * separation, l * separation))\n",
    "\n",
    "show_register(register_2D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb0fcacf",
   "metadata": {},
   "source": [
    "We will use the same driving field as the one for generating the $Z_2$ phase. We then assemble the 2D array with the driving field, and run the AHS program on the local simulator. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "df3a2aae",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:17.368586Z",
     "start_time": "2023-08-29T21:43:12.603198Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0ZamioqIKlzNnzqi0tNTl/ZSWlmrLli2Kj4//vzBeXoqPj9f69esr3GbJkiWKi4tTYmKigoOD1apVK02YMOGyv2dVUlJyUVYAAGBdpstNvXr1VL9+/YuWevXqyd/fX7fccouSk5PlcDguu59jx46prKxMwcHB5caDg4NVUFBQ4Tb79u3T559/rrKyMi1btkyvvfaapkyZojfffPOSn5OSkqLAwEDnEh4ebvaQAQDAdcT0Zak5c+bolVde0cCBA51PJN64caM+/vhjvfrqqzp69Kjefvtt+fr66uWXX3ZrWIfDoaCgIH344Yfy9vZW+/btdejQIb311ltKTk6ucJukpCTZ7Xbn66KiIgoOAAAWZrrcfPzxx5oyZYr69u3rHOvVq5dat26tDz74QJmZmbr55ps1fvz4y5abhg0bytvbu9zPOEi//JRDSEhIhduEhoaqZs2a8vb2do61aNFCBQUFKi0tlY+Pz0Xb+Pr6ytfX1+xhAgCA65Tpy1Lr1q1T27ZtLxpv27atc65Mp06dlJeXd9n9+Pj4qH379srMzHSOORwOZWZmKi4ursJtOnbsqD179pS75LVr1y6FhoZWWGwAAMCNx3S5CQ8Pr/A3pGbNmuW83HP8+HHVr1//ivuy2+2aMWOGPv74Y+3cuVPPPfeciouLnXdP9e/fX0lJSc71n3vuOZ04cULDhg3Trl27tHTpUk2YMEGJiYlmDwMAAFiU6ctSb7/9th555BEtX75cHTp0kCRt3rxZOTk5+vzzzyVJmzZtUr9+/a64r379+uno0aMaO3asCgoKFBUVpYyMDOck47y8PHl5/V//Cg8P14oVKzRixAi1adNGjRo10rBhw/TSSy+ZPQwAAGBRpstN7969lZubqw8++EC5ubmSpAceeECLFy92PnPmueeec3l/Q4YM0ZAhQyp8b/Xq1ReNxcXFacOGDWZjAwCAG4SpcnP+/Hndf//9Sk9PV0pKSlVlAgAAqDRTc25q1qyp7du3V1UWAACAq2Z6QvGTTz5Z4YRiAACA6sD0nJuff/5Zs2fP1tdff6327durdu3a5d5PTU11WzgAAACzTJeb7777Tu3atZP0yzNmfs1ms7knFQAAQCWZLjerVq2qihwAAABuYXrOzQV79uzRihUr9NNPP0mSDMNwWygAAIDKMl1ujh8/rm7duun2229Xjx49lJ+fL0l6+umnNXLkSLcHBAAAMMN0uRkxYoRq1qypvLw81apVyzner18/ZWRkuDUcAACAWabn3Hz11VdasWKFGjduXG78tttu04EDB9wWDAAAoDJMn7kpLi4ud8bmghMnTsjX19ctoQAAACrLdLnp3Lmz/va3vzlf22w2ORwOTZ48WV27dnVrOAAAALNMX5aaPHmyunXrps2bN6u0tFQvvviivv/+e504cULffPNNVWQEAABwmekzN61atdKuXbvUqVMn/e53v1NxcbH+8Ic/aNu2bbr11lurIiMAAIDLTJ+5kaTAwEC98sor7s4CAABw1SpVbk6ePKlZs2Zp586dkqSWLVtq0KBBatCggVvDAQAAmGX6stSaNWsUERGhqVOn6uTJkzp58qSmTp2qJk2aaM2aNVWREQAAwGWmz9wkJiaqX79+ev/99+Xt7S1JKisr0/PPP6/ExETt2LHD7SEBAABcZfrMzZ49ezRy5EhnsZEkb29v2e127dmzx63hAAAAzDJdbtq1a+eca/NrO3fu1J133umWUAAAAJXl0mWp7du3O/956NChGjZsmPbs2aO77rpLkrRhwwZNnz5dEydOrJqUAAAALnKp3ERFRclms8kwDOfYiy++eNF6jz/+uPr16+e+dAAAACa5VG5++OGHqs4BAADgFi6Vm1tuuaWqcwAAALiFS+VmyZIlLu+wd+/elQ4DAABwtVwqN3369Cn3+r/n39hsNuc/l5WVuScZAABAJbh0K7jD4XAuX331laKiorR8+XKdOnVKp06d0rJly9SuXTtlZGRUdV4AAIDLMv2E4uHDhys9PV2dOnVyjiUkJKhWrVr685//XOEzcAAAAK4V0w/x27t3r+rVq3fReGBgoPbv3++GSAAAAJVnutx06NBBdrtdhYWFzrHCwkKNHj1aMTExbg0HAABglulyM3v2bOXn5+vmm29WZGSkIiMjdfPNN+vQoUOaNWtWVWQEAABwmek5N5GRkdq+fbtWrlypnJwcSVKLFi0UHx9f7q4pAAAATzBdbvbt26emTZuqe/fu6t69e1VkAgAAqDTTl6UiIyPVtWtXffLJJ/rPf/5TFZkAAAAqzXS52bp1q9q0aSO73a6QkBA988wz+vbbb6siGwAAgGmmy01UVJTeffddHT582Dm5uHPnzmrVqpVSU1N19OjRqsgJAADgEtPl5oIaNWroD3/4g/7+979r0qRJ2rNnj0aNGqXw8HD1799f+fn57swJAADgkkqXm82bN+v5559XaGioUlNTNWrUKO3du1crV67U4cOH9bvf/c6dOQEAAFxi+m6p1NRUffTRR8rNzVWPHj30t7/9TT169JCX1y89qUmTJpozZ44iIiLcnRUAAOCKTJeb999/X0899ZQGDhyo0NDQCtcJCgrigX4AAMAjTJeb3bt3Vzien5+v8ePHa9q0afLx8dGAAQOuOhwAAIBZpsrN999/r1WrVsnX11ePPPKI6tWrp2PHjmn8+PFKT09X06ZNqyonAACAS1yeULxkyRK1bdtWQ4cO1TPPPKPo6GitWrVKLVq00M6dO/XFF1/o+++/r8qsAAAAV+RyuXnzzTeVmJiooqIipaamat++fRo6dKiWLVumjIwM3X///VWZEwAAwCUul5vc3FwlJiaqTp06euGFF+Tl5aV33nlHHTp0qMp8AAAAprhcbs6cOaOAgABJkre3t/z9/ZljAwAAqh1TE4pXrFihwMBASZLD4VBmZqa+++67cuv07t3bfekAAABMMlVu/vv27meeeabca5vNprKysqtPBQAAUEkulxuHw1GVOQAAANyi0r8tBQAAUB1RbgAAgKVQbgAAgKVQbgAAgKVQbgAAgKVUqtycOnVKM2fOVFJSkk6cOCFJ2rp1qw4dOuTWcAAAAGaZes6NJG3fvl3x8fEKDAzU/v37NXjwYDVo0ECLFi1SXl6e/va3v1VFTgAAAJeYPnNjt9s1cOBA7d69W35+fs7xHj16aM2aNW4NBwAAYJbpcrNp06aLnkwsSY0aNVJBQYFbQgEAAFSW6XLj6+uroqKii8Z37dql3/zmN24JBQAAUFmmy03v3r31xhtv6Pz585J++T2pvLw8vfTSS3rooYfcHhAAAMAM0+VmypQpOnv2rIKCgvTTTz/p3nvvVWRkpOrWravx48dXKsT06dMVEREhPz8/xcbGauPGjS5tN3/+fNlsNvXp06dSnwsAAKzH9N1SgYGBWrlypbKysrR9+3adPXtW7dq1U3x8fKUCLFiwQHa7Xenp6YqNjVVaWpoSEhKUm5uroKCgS263f/9+jRo1Sp07d67U5wIAAGsyXW4u6NSpkzp16nTVAVJTUzV48GANGjRIkpSenq6lS5dq9uzZGjNmTIXblJWV6YknntDrr7+utWvX6tSpU1edAwAAWIPpcjN16tQKx202m/z8/BQZGal77rlH3t7eV9xXaWmptmzZoqSkJOeYl5eX4uPjtX79+ktu98YbbygoKEhPP/201q5de9nPKCkpUUlJifN1RZOhAQCAdZguN++8846OHj2qc+fOqX79+pKkkydPqlatWqpTp46OHDmipk2batWqVQoPD7/svo4dO6aysjIFBweXGw8ODlZOTk6F22RlZWnWrFnKzs52KW9KSopef/11l9YFAADXP9MTiidMmKAOHTpo9+7dOn78uI4fP65du3YpNjZW7777rvLy8hQSEqIRI0a4PeyZM2f0xz/+UTNmzFDDhg1d2iYpKUmnT592LgcPHnR7LgAAUH2YPnPz6quvauHChbr11ludY5GRkXr77bf10EMPad++fZo8ebJLt4U3bNhQ3t7eKiwsLDdeWFiokJCQi9bfu3ev9u/fr169ejnHHA7HLwdSo4Zyc3PL5ZJ+eS6Pr6+vqWMEAADXL9NnbvLz8/Xzzz9fNP7zzz87n1AcFhamM2fOXHFfPj4+at++vTIzM51jDodDmZmZiouLu2j95s2ba8eOHcrOznYuvXv3VteuXZWdnX3Fy2AAAMD6TJ+56dq1q5555hnNnDlTbdu2lSRt27ZNzz33nO677z5J0o4dO9SkSROX9me32zVgwABFR0crJiZGaWlpKi4udt491b9/fzVq1EgpKSny8/NTq1atym1fr149SbpoHAAA3JhMl5tZs2bpj3/8o9q3b6+aNWtK+uWsTbdu3TRr1ixJUp06dTRlyhSX9tevXz8dPXpUY8eOVUFBgaKiopSRkeGcZJyXlycvL9MnmAAAwA3KdLkJCQnRypUrlZOTo127dkmSmjVrpmbNmjnX6dq1q6l9DhkyREOGDKnwvdWrV1922zlz5pj6LAAAYG2Vfohf8+bN1bx5c3dmAQAAuGqVKjc//vijlixZory8PJWWlpZ7LzU11S3BAAAAKsN0ucnMzFTv3r3VtGlT5eTkqFWrVtq/f78Mw1C7du2qIiMAAIDLTM/UTUpK0qhRo7Rjxw75+flp4cKFOnjwoO6991498sgjVZERAADAZabLzc6dO9W/f39Jvzw476efflKdOnX0xhtvaNKkSW4PCAAAYIbpclO7dm3nPJvQ0FDt3bvX+d6xY8fclwwAAKASTM+5ueuuu5SVlaUWLVqoR48eGjlypHbs2KFFixbprrvuqoqMAAAALjNdblJTU3X27FlJ0uuvv66zZ89qwYIFuu2227hTCgAAeJypclNWVqYff/xRbdq0kfTLJar09PQqCQYAAFAZpubceHt7q3v37jp58mRV5QEAALgqpicUt2rVSvv27auKLAAAAFfNdLl58803NWrUKH355ZfKz89XUVFRuQUAAMCTTE8o7tGjhySpd+/estlsznHDMGSz2VRWVua+dAAAACaZLjerVq2qihwAAABuYbrc3HvvvVWRAwAAwC1Mz7mRpLVr1+rJJ5/U3XffrUOHDkmS/ud//kdZWVluDQcAAGCW6XKzcOFCJSQkyN/fX1u3blVJSYkk6fTp05owYYLbAwIAAJhRqbul0tPTNWPGDNWsWdM53rFjR23dutWt4QAAAMwyXW5yc3N1zz33XDQeGBioU6dOuSMTAABApZkuNyEhIdqzZ89F41lZWWratKlbQgEAAFSW6XIzePBgDRs2TN9++61sNpsOHz6suXPnatSoUXruueeqIiMAAIDLTN8KPmbMGDkcDnXr1k3nzp3TPffcI19fX40aNUovvPBCVWQEAABwmelyY7PZ9Morr2j06NHas2ePzp49q5YtW6pOnTpVkQ8AAMAU05elPvnkE507d04+Pj5q2bKlYmJiKDYAAKDaMF1uRowYoaCgID3++ONatmwZvyUFAACqFdPlJj8/X/Pnz5fNZlPfvn0VGhqqxMRErVu3riryAQAAmGK63NSoUUMPPvig5s6dqyNHjuidd97R/v371bVrV916661VkREAAMBlpicU/1qtWrWUkJCgkydP6sCBA9q5c6e7cgEAAFRKpX4489y5c5o7d6569OihRo0aKS0tTb///e/1/fffuzsfAACAKabP3Dz66KP68ssvVatWLfXt21evvfaa4uLiqiIbAACAaabLjbe3tz777DMlJCTI29u73HvfffedWrVq5bZwAAAAZpkuN3Pnzi33+syZM/r00081c+ZMbdmyhVvDAQCAR1Vqzo0krVmzRgMGDFBoaKjefvtt3XfffdqwYYM7swEAAJhm6sxNQUGB5syZo1mzZqmoqEh9+/ZVSUmJFi9erJYtW1ZVRgAAAJe5fOamV69eatasmbZv3660tDQdPnxYf/3rX6syGwAAgGkun7lZvny5hg4dqueee0633XZbVWYCAACoNJfP3GRlZenMmTNq3769YmNjNW3aNB07dqwqswEAAJjmcrm56667NGPGDOXn5+uZZ57R/PnzFRYWJofDoZUrV+rMmTNVmRMAAMAlpu+Wql27tp566illZWVpx44dGjlypCZOnKigoCD17t27KjICAAC4rNK3gktSs2bNNHnyZP3444/69NNP3ZUJAACg0q6q3Fzg7e2tPn36aMmSJe7YHQAAQKW5pdwAAABUF5QbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKZQbAABgKdWi3EyfPl0RERHy8/NTbGysNm7ceMl1Z8yYoc6dO6t+/fqqX7++4uPjL7s+AAC4sXi83CxYsEB2u13JycnaunWr7rzzTiUkJOjIkSMVrr969Wo99thjWrVqldavX6/w8HB1795dhw4dusbJAQBAdeTxcpOamqrBgwdr0KBBatmypdLT01WrVi3Nnj27wvXnzp2r559/XlFRUWrevLlmzpwph8OhzMzMCtcvKSlRUVFRuQUAAFiXR8tNaWmptmzZovj4eOeYl5eX4uPjtX79epf2ce7cOZ0/f14NGjSo8P2UlBQFBgY6l/DwcLdkBwAA1ZNHy82xY8dUVlam4ODgcuPBwcEqKChwaR8vvfSSwsLCyhWkX0tKStLp06edy8GDB686NwAAqL5qeDrA1Zg4caLmz5+v1atXy8/Pr8J1fH195evre42TAQAAT/FouWnYsKG8vb1VWFhYbrywsFAhISGX3fbtt9/WxIkT9fXXX6tNmzZVGRMAAFxHPHpZysfHR+3bty83GfjC5OC4uLhLbjd58mSNGzdOGRkZio6OvhZRAQDAdcLjl6XsdrsGDBig6OhoxcTEKC0tTcXFxRo0aJAkqX///mrUqJFSUlIkSZMmTdLYsWM1b948RUREOOfm1KlTR3Xq1PHYcQAAgOrB4+WmX79+Onr0qMaOHauCggJFRUUpIyPDOck4Ly9PXl7/d4Lp/fffV2lpqR5++OFy+0lOTtZf/vKXaxkdAABUQx4vN5I0ZMgQDRkypML3Vq9eXe71/v37qz4QAAC4bnn8IX4AAADuRLkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWQrkBAACWUi3KzfTp0xURESE/Pz/FxsZq48aNl13/73//u5o3by4/Pz+1bt1ay5Ytu0ZJAQBAdVfD0wEWLFggu92u9PR0xcbGKi0tTQkJCcrNzVVQUNBF669bt06PPfaYUlJS9OCDD2revHnq06ePtm7dqlatWnngCIBrL2LMUk9HuKL9E3t6OsI1x/dSfVX37+ZG/V6qisfLTWpqqgYPHqxBgwZJktLT07V06VLNnj1bY8aMuWj9d999V/fff79Gjx4tSRo3bpxWrlypadOmKT09/Zpmt7rq/n8GEv+HAAC4mEfLTWlpqbZs2aKkpCTnmJeXl+Lj47V+/foKt1m/fr3sdnu5sYSEBC1evLjC9UtKSlRSUuJ8ffr0aUlSUVHRVaavmKPkXJXs151cPXaO5doy8++klY6HY7m2bsRjkar/8VjpWKSq+W/shX0ahnHllQ0POnTokCHJWLduXbnx0aNHGzExMRVuU7NmTWPevHnlxqZPn24EBQVVuH5ycrIhiYWFhYWFhcUCy8GDB6/YLzx+WaqqJSUllTvT43A4dOLECd10002y2WweTHZlRUVFCg8P18GDBxUQEODpOPgVvpvqie+l+uK7qZ6up+/FMAydOXNGYWFhV1zXo+WmYcOG8vb2VmFhYbnxwsJChYSEVLhNSEiIqfV9fX3l6+tbbqxevXqVD+0BAQEB1f5fuhsV3031xPdSffHdVE/Xy/cSGBjo0noevRXcx8dH7du3V2ZmpnPM4XAoMzNTcXFxFW4TFxdXbn1JWrly5SXXBwAANxaPX5ay2+0aMGCAoqOjFRMTo7S0NBUXFzvvnurfv78aNWqklJQUSdKwYcN07733asqUKerZs6fmz5+vzZs368MPP/TkYQAAgGrC4+WmX79+Onr0qMaOHauCggJFRUUpIyNDwcHBkqS8vDx5ef3fCaa7775b8+bN06uvvqqXX35Zt912mxYvXmzJZ9z4+voqOTn5ostq8Dy+m+qJ76X64rupnqz6vdgMw5V7qgAAAK4P1eLnFwAAANyFcgMAACyFcgMAACyFcgMAACyFclONTZ8+XREREfLz81NsbKw2btzo6Ug3tJSUFHXo0EF169ZVUFCQ+vTpo9zcXE/HQgUmTpwom82m4cOHezrKDe/QoUN68sknddNNN8nf31+tW7fW5s2bPR3rhldWVqbXXntNTZo0kb+/v2699VaNGzfOtd9tug5QbqqpBQsWyG63Kzk5WVu3btWdd96phIQEHTlyxNPRblj//Oc/lZiYqA0bNmjlypU6f/68unfvruLiYk9Hw69s2rRJH3zwgdq0aePpKDe8kydPqmPHjqpZs6aWL1+uf//735oyZYrq16/v6Wg3vEmTJun999/XtGnTtHPnTk2aNEmTJ0/WX//6V09HcwtuBa+mYmNj1aFDB02bNk3SL09uDg8P1wsvvKAxY8Z4OB0k6ejRowoKCtI///lP3XPPPZ6OA0lnz55Vu3bt9N577+nNN99UVFSU0tLSPB3rhjVmzBh98803Wrt2raej4L88+OCDCg4O1qxZs5xjDz30kPz9/fXJJ594MJl7cOamGiotLdWWLVsUHx/vHPPy8lJ8fLzWr1/vwWT4tdOnT0uSGjRo4OEkuCAxMVE9e/Ys978deM6SJUsUHR2tRx55REFBQWrbtq1mzJjh6VjQLw/EzczM1K5duyRJ//rXv5SVlaUHHnjAw8ncw+NPKMbFjh07prKyMudTmi8IDg5WTk6Oh1Lh1xwOh4YPH66OHTta8unY16P58+dr69at2rRpk6ej4H/t27dP77//vux2u15++WVt2rRJQ4cOlY+PjwYMGODpeDe0MWPGqKioSM2bN5e3t7fKyso0fvx4PfHEE56O5haUG6ASEhMT9d133ykrK8vTUSDp4MGDGjZsmFauXCk/Pz9Px8H/cjgcio6O1oQJEyRJbdu21Xfffaf09HTKjYd99tlnmjt3rubNm6c77rhD2dnZGj58uMLCwizx3VBuqqGGDRvK29tbhYWF5cYLCwsVEhLioVS4YMiQIfryyy+1Zs0aNW7c2NNxIGnLli06cuSI2rVr5xwrKyvTmjVrNG3aNJWUlMjb29uDCW9MoaGhatmyZbmxFi1aaOHChR5KhAtGjx6tMWPG6NFHH5UktW7dWgcOHFBKSoolyg1zbqohHx8ftW/fXpmZmc4xh8OhzMxMxcXFeTDZjc0wDA0ZMkRffPGF/vGPf6hJkyaejoT/1a1bN+3YsUPZ2dnOJTo6Wk888YSys7MpNh7SsWPHix6XsGvXLt1yyy0eSoQLzp07V+5HqSXJ29tbDofDQ4ncizM31ZTdbteAAQMUHR2tmJgYpaWlqbi4WIMGDfJ0tBtWYmKi5s2bp//3//6f6tatq4KCAklSYGCg/P39PZzuxla3bt2L5j7Vrl1bN910E3OiPGjEiBG6++67NWHCBPXt21cbN27Uhx9+qA8//NDT0W54vXr10vjx43XzzTfrjjvu0LZt25SamqqnnnrK09HcglvBq7Fp06bprbfeUkFBgaKiojR16lTFxsZ6OtYNy2azVTj+0UcfaeDAgdc2DK6oS5cu3ApeDXz55ZdKSkrS7t271aRJE9ntdg0ePNjTsW54Z86c0WuvvaYvvvhCR44cUVhYmB577DGNHTtWPj4+no531Sg3AADAUphzAwAALIVyAwAALIVyAwAALIVyAwAALIVyAwAALIVyAwAALIVyAwAALIVyAwAALIVyA6BSbDabFi9eLEnav3+/bDabsrOzPZrpcnJycnTXXXfJz89PUVFRno4DoApRboAbzMCBA9WnTx+37jM8PFz5+fnV+neckpOTVbt2beXm5pb7UVozrocSB4AfzgTgBt7e3goJCfF0jMvau3evevbsyS9SAzcAztwAN7guXbpo6NChevHFF9WgQQOFhIToL3/5S7l1du/erXvuuUd+fn5q2bKlVq5cWe79is5ofP/993rwwQcVEBCgunXrqnPnztq7d6/z/ZkzZ6pFixby8/NT8+bN9d577znfKy0t1ZAhQxQaGio/Pz/dcsstSklJueQxOBwOvfHGG2rcuLF8fX0VFRWljIwM5/s2m01btmzRG2+8IZvNdtHxXZCRkaFOnTqpXr16uummm/Tggw+Wy9ykSRNJUtu2bWWz2dSlSxeXPv/C3+ezzz5T586d5e/vrw4dOmjXrl3atGmToqOjVadOHT3wwAM6evSoc7vVq1crJiZGtWvXVr169dSxY0cdOHDgkn8HAP/LAHBDGTBggPG73/3O+free+81AgICjL/85S/Grl27jI8//tiw2WzGV199ZRiGYZSVlRmtWrUyunXrZmRnZxv//Oc/jbZt2xqSjC+++MIwDMP44YcfDEnGtm3bDMMwjB9//NFo0KCB8Yc//MHYtGmTkZuba8yePdvIyckxDMMwPvnkEyM0NNRYuHChsW/fPmPhwoVGgwYNjDlz5hiGYRhvvfWWER4ebqxZs8bYv3+/sXbtWmPevHmXPKbU1FQjICDA+PTTT42cnBzjxRdfNGrWrGns2rXLMAzDyM/PN+644w5j5MiRRn5+vnHmzJkK9/P5558bCxcuNHbv3m1s27bN6NWrl9G6dWujrKzMMAzD2LhxoyHJ+Prrr438/Hzj+PHjLn3+hb9P8+bNjYyMDOPf//63cddddxnt27c3unTpYmRlZRlbt241IiMjjWeffdYwDMM4f/68ERgYaIwaNcrYs2eP8e9//9uYM2eOceDAAbNfOXDDodwAN5iKyk2nTp3KrdOhQwfjpZdeMgzDMFasWGHUqFHDOHTokPP95cuXX7bcJCUlGU2aNDFKS0srzHDrrbdeVFbGjRtnxMXFGYZhGC+88IJx3333GQ6Hw6VjCgsLM8aPH3/RMTz//PPO13feeaeRnJzs0v4uOHr0qCHJ2LFjh2EYFx+nq59/YbuZM2c63//0008NSUZmZqZzLCUlxWjWrJlhGIZx/PhxQ5KxevVqU5kBGAaXpQCoTZs25V6HhobqyJEjkqSdO3cqPDxcYWFhzvfj4uIuu7/s7Gx17txZNWvWvOi94uJi7d27V08//bTq1KnjXN58803nJaCBAwcqOztbzZo109ChQ/XVV19d8rOKiop0+PBhdezYsdx4x44dtXPnzssf+H/ZvXu3HnvsMTVt2lQBAQGKiIiQJOXl5bnl83/9dw4ODpYktW7dutzYhb97gwYNNHDgQCUkJKhXr1569913lZ+fb+p4gBsV5QbARSXEZrPJ4XBUen/+/v6XfO/s2bOSpBkzZig7O9u5fPfdd9qwYYMkqV27dvrhhx80btw4/fTTT+rbt68efvjhSudxVa9evXTixAnNmDFD3377rb799ltJv8wBcodf/51tNluFY7/+u3/00Udav3697r77bi1YsEC33367828E4NIoNwAuq0WLFjp48GC5swZX+g9smzZttHbtWp0/f/6i94KDgxUWFqZ9+/YpMjKy3HJhwq4kBQQEqF+/fpoxY4YWLFighQsX6sSJExftLyAgQGFhYfrmm2/KjX/zzTdq2bKly8d5/Phx5ebm6tVXX1W3bt3UokULnTx5stw6Pj4+kqSysjK3f/6ltG3bVklJSVq3bp1atWqlefPmXfU+AavjVnAAlxUfH6/bb79dAwYM0FtvvaWioiK98sorl91myJAh+utf/6pHH31USUlJCgwM1IYNGxQTE6NmzZrp9ddf19ChQxUYGKj7779fJSUl2rx5s06ePCm73a7U1FSFhoaqbdu28vLy0t///neFhISoXr16FX7e6NGjlZycrFtvvVVRUVH66KOPlJ2drblz57p8nPXr19dNN92kDz/8UKGhocrLy9OYMWPKrRMUFCR/f39lZGSocePG8vPzU2BgoFs+/7/98MMP+vDDD9W7d2+FhYUpNzdXu3fvVv/+/Su9T+BGQbkBcFleXl764osv9PTTTysmJkYRERGaOnWq7r///ktuc9NNN+kf//iHRo8erXvvvVfe3t6Kiopyzkv505/+pFq1aumtt97S6NGjVbt2bbVu3VrDhw+XJNWtW1eTJ0/W7t275e3trQ4dOmjZsmXy8qr4ZPPQoUN1+vRpjRw5UkeOHFHLli21ZMkS3XbbbaaOc/78+Ro6dKhatWqlZs2aaerUqc7bvSWpRo0amjp1qt544w2NHTtWnTt31urVq93y+f+tVq1aysnJ0ccff6zjx48rNDRUiYmJeuaZZyq9T+BGYTMMw/B0CAAAAHdhzg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALAUyg0AALCU/w+ubwGD5Gj1ZQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ahs_program_2D = AnalogHamiltonianSimulation(\n",
    "    register=register_2D, \n",
    "    hamiltonian=drive\n",
    ")\n",
    "\n",
    "result_2D = device.run(ahs_program_2D, shots=1000, steps=200).result()\n",
    "show_final_avg_density(result_2D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08e49477",
   "metadata": {},
   "source": [
    "We see that the overall pattern mimics the checkerboard pattern, but the central site suffers strong discrepancy. This is due to the finite size of the system and the finite duration of the AHS program, which cause non-adiabatic errors.\n",
    "\n",
    "For more explanation and interpretation of the 2-d results, see \"Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator\" by [Ebadi et al. (2020)](http://arxiv.org/abs/2012.12281). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ffc633",
   "metadata": {},
   "source": [
    "## Realizing $Z_2$ and checkerboard phase on a QPU\n",
    "\n",
    "In previous sections, we have demonstrated two AHS programs for realizing many-body ground states. The results from the local simulator show that the results of the programs meet our expectations. Here we will run the same AHS program on the Aquila device. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "525d3c27",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note: </b> Some atoms may be missing even if the shot was successful. We recommend comparing <code>pre_sequence</code> of each shot with the requested atom filling in the AHS program specification.  \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "31901542",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:43:18.579380Z",
     "start_time": "2023-08-29T21:43:17.366197Z"
    }
   },
   "outputs": [],
   "source": [
    "from braket.aws import AwsDevice \n",
    "device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/quera/Aquila\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "07a73135",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:46:21.296356Z",
     "start_time": "2023-08-29T21:43:18.582585Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_1D_aquila = device.run(ahs_program, shots=100).result()\n",
    "show_final_avg_density(result_1D_aquila)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69fc4e5d",
   "metadata": {},
   "source": [
    "We can calculate the density correlation function for the result obtained from Aquila"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e07e91f5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:46:21.516981Z",
     "start_time": "2023-08-29T21:46:21.297846Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gij_aquila = get_density_correlation_Z2(result_1D_aquila)\n",
    "\n",
    "plt.imshow(gij_aquila, cmap='bwr', vmin=-0.25, vmax=+0.25)\n",
    "plt.xticks(range(num_atoms), [f'{i}' for i in range(num_atoms)])\n",
    "plt.xlabel(\"atom index\")\n",
    "plt.yticks(range(num_atoms), [f'{j}' for j in range(num_atoms)])\n",
    "plt.ylabel(\"atom index\")\n",
    "plt.title('Rydberg density correlation')\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fcc2c8b3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:49:24.113062Z",
     "start_time": "2023-08-29T21:46:21.519925Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_2D_aquila = device.run(ahs_program_2D, shots=100).result()\n",
    "show_final_avg_density(result_2D_aquila)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c5e689d",
   "metadata": {},
   "source": [
    "In summary, in this notebook we have demonstrated how to realize the 1D $Z_2$ phase and 2D checkerboard phase via adiabatic transition on the Rydberg systems. These are interesting many body phases in their own right, and serve as the starting points for the more involved use cases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "eba213ef",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:49:24.283780Z",
     "start_time": "2023-08-29T21:49:24.115038Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum Task Summary\n",
      "{'arn:aws:braket:us-east-1::device/qpu/quera/Aquila': {'shots': 200, 'tasks': {'COMPLETED': 2}}}\n",
      "Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).\n",
      "Estimated cost to run this example: 2.60 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Quantum Task Summary\")\n",
    "print(tracker.quantum_tasks_statistics())\n",
    "print('Note: Charges shown are estimates based on your Amazon Braket simulator and quantum processing unit (QPU) task usage. Estimated charges shown may differ from your actual charges. Estimated charges do not factor in any discounts or credits, and you may experience additional charges based on your use of other services such as Amazon Elastic Compute Cloud (Amazon EC2).')\n",
    "print(f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a6a296d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-08-29T21:49:24.286066Z",
     "start_time": "2023-08-29T21:49:24.282530Z"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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   "codemirror_mode": {
    "name": "ipython",
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     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   "types_to_exclude": [
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