examples/analog_hamiltonian_simulation/06_Analog_Hamiltonian_simulation_with_PennyLane.ipynb

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    "# Analog Hamiltonian simulation with PennyLane\n",
    "\n",
    "We are excited to announce that customers can now run analog Hamiltonian simulation (AHS) on Braket’s Rydberg atom devices via the [PennyLane-Braket SDK plug-in](https://amazon-braket-pennylane-plugin-python.readthedocs.io/en/latest/). Rydberg atom devices, such as [QuEra’s Aquila device](https://aws.amazon.com/blogs/quantum-computing/amazon-braket-launches-aquila-the-first-neutral-atom-quantum-processor-from-quera-computing/), feature customizable qubit geometry and time-dependent parameter control that allow you to engineer the system’s quantum evolution with high precision. This low-level control allows one to optimize the time-dependent parameters in an AHS program to simulate, for example, [quantum phases of matter](https://aws.amazon.com/blogs/quantum-computing/realizing-quantum-spin-liquid-phase-on-an-analog-hamiltonian-rydberg-simulator/) (see [here](https://github.com/aws/amazon-braket-examples/tree/main/examples/analog_hamiltonian_simulation) for more examples). However, searching for the optimal parameters can be tedious. With this new feature from the PennyLane-Braket plug-in, users can leverage the quantum machine learning techniques from [PennyLane](https://pennylane.ai/) to optimize their AHS programs for the Rydberg atom device.\n",
    "\n",
    "## Analog Hamiltonian simulation with Rydberg atoms\n",
    "\n",
    "AHS is an approach to study the properties of a quantum system by tuning the parameters of another quantum system that closely resembles the system of interest. In an AHS program, it is often required to find a set of parameters and minimize a cost function. Various methods to do this have been studied in the literature, including [stochastic optimizers](https://arxiv.org/abs/2202.09372), [Bayesian optimizations](https://arxiv.org/abs/2305.13365) and more. In this blog post, we demonstrate how to optimize the parameters for Rydberg atom devices using the [differentiable programming technique](https://pennylane.ai/qml/demos/tutorial_pulse_programming101), another recently released feature on PennyLane.\n",
    "\n",
    "As an example, let us consider a chain with nine spins, each of which can be in \"up\" or \"down\" states. We are interested in studying the so-called [anti-ferromagnetic (AFM) order](https://en.wikipedia.org/wiki/Antiferromagnetism), a naturally occurring phenomena in magnetic materials, where neighboring spins point in the opposite directions. To simulate the spin chain, we map each spin to an atom, and the ground and excited Rydberg states of each atom correspond to the \"down\" and \"up\" states of the spin, respectively. With this encoding, the AFM order of interest corresponds to an alternating pattern of ground and Rydberg states for the chain of nine atoms. We will show how to realize such a configuration in Rydberg system using PennyLane. \n",
    "\n",
    "We first create an arrangement with nine atoms by explicitly specifying their coordinates.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7cbb32fd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "\n",
    "tracker = Tracker().start()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dfa42aff-0358-4601-a4c1-89fe78aaa824",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 500x100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# For realizing the AFM order, the atomic spacing is typically\n",
    "# chosen between 6 and 7 micrometers. The interested readers are\n",
    "# encouraged to try other values of atomic spacing!\n",
    "a = 6.1  # μm\n",
    "num_atoms = 9\n",
    "coords = [[k * a, 0] for k in range(num_atoms)]\n",
    "\n",
    "plt.figure(figsize=(5, 1))\n",
    "\n",
    "plt.scatter([x for x, y in coords], [y for x, y in coords])\n",
    "\n",
    "# Add the labels for the atoms\n",
    "for idx, site in enumerate(coords):\n",
    "    plt.text(site[0], site[1], f\"  {idx}\", fontsize=10)\n",
    "\n",
    "plt.xlabel(\"μm\")\n",
    "plt.ylabel(\"μm\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7b8c5de-00a4-4e70-8d2a-af11a92e963b",
   "metadata": {},
   "source": [
    "We note that the atom spacing is specified in the unit of micrometers ($\\mu m$), following the convention of PennyLane. At the beginning of the AHS program, all the atoms are initialized in the ground state, and we aim to tune the time-dependent parameters of the system, including the amplitude of the Rabi frequency and detuning, to drive the system to the AFM state. An example of such an AHS program has been demonstrated in [this AHS example notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/02_Ordered_phases_in_Rydberg_systems.ipynb), where the time-series of the driving fields are specified as discrete sets of time-value pairs. Here, on the other hand, we will specify the time-series of the driving fields as continuous, differentiable functions.\n",
    "\n",
    "## Creating a differentiable Hamiltonian with PennyLane\n",
    "\n",
    "A [driving field]((https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/00_Introduction_of_Analog_Hamiltonian_Simulation_with_Rydberg_Atoms.ipynb)) in an AHS program consists of the amplitude (Rabi frequency), laser phase and the detuning of the driving laser field. To create a differentiable driving field, let us first specify some constraints, such as the maximum allowed values for the amplitude and detuning. We will set the laser phase to be constantly zero in this example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5eb06a9b-ff0b-496f-a124-1c3b37c63a4c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "amplitude_max = 2.51 MHz\n",
      "detuning_max  = 19.89 MHz\n",
      "time_max      = 4.0 μs\n"
     ]
    }
   ],
   "source": [
    "import pennylane.numpy as np\n",
    "\n",
    "# Rydberg interaction constant\n",
    "C6 = 862619.79  # MHz μm^6\n",
    "\n",
    "# Constraints for the driving fields with SI unit, the unit used by Braket\n",
    "amplitude_max = 1.58e7  # rad/second\n",
    "detuning_max = 1.25e8  # rad/second\n",
    "time_max_second = 4e-6  # second\n",
    "\n",
    "\n",
    "def angular_SI_to_MHz(angular_SI):\n",
    "    \"\"\"Converts a value in rad/s or (rad/s)/s into MHz or MHz/s\"\"\"\n",
    "    return angular_SI / (2 * np.pi) * 1e-6\n",
    "\n",
    "\n",
    "# Pennylane uses microseconds for time so the unit of time is converted from second to microsecond\n",
    "time_max = time_max_second * 1e6  # microsecond\n",
    "\n",
    "# Pennylane uses MHz for amplitude and detuning so their units are converted from rad/second to MHz\n",
    "amplitude_max = angular_SI_to_MHz(amplitude_max)  # MHz\n",
    "detuning_max = angular_SI_to_MHz(detuning_max)  # MHz\n",
    "\n",
    "print(f\"amplitude_max = {round(amplitude_max, 2)} MHz\")\n",
    "print(f\"detuning_max  = {round(detuning_max, 2)} MHz\")\n",
    "print(f\"time_max      = {time_max} μs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b04e6f1-424f-465c-8abc-9ee8f9eb3035",
   "metadata": {},
   "source": [
    "Following the convention of PennyLane, we have used megahertz (MHz) as the unit for the amplitude and detuning. Also, we have limited the maximum duration of the program, `time_max`, to be 4$\\mu s$, and introduced the Rydberg interaction constant $C_6$. These constants are specific to QuEra's Aquila, and they can be queried from Braket SDK, as shown in [this AHS example notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb). With these constants, the differentiable driving fields for the Rydberg atom device can be defined via [PennyLane's JAX interface](https://pennylane.ai/qml/demos/tutorial_jax_transformations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7ec45e20-ed22-4f1d-9540-db456794e5ed",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "# Set to float64 precision and remove jax CPU/GPU warning\n",
    "jax.config.update(\"jax_enable_x64\", True)\n",
    "jax.config.update(\"jax_platform_name\", \"cpu\")\n",
    "jax.config.update(\"jax_debug_nans\", True)\n",
    "\n",
    "\n",
    "def ryd_amplitude(p, t):\n",
    "    \"\"\"Parametrized function for amplitude\"\"\"\n",
    "    return p[0] * (1 - (1 - jnp.sin(jnp.pi * t / time_max) ** 2) ** (p[1] / 2))\n",
    "\n",
    "\n",
    "def ryd_detuning(p, t):\n",
    "    \"\"\"Parametrized function for detuning\"\"\"\n",
    "    return p[0] * jnp.arctan(p[1] * (t - time_max / 2)) / (jnp.pi / 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4d7fce4-f618-448f-aee1-e239203edaea",
   "metadata": {},
   "source": [
    "There are two important remarks for defining the differentiable functions in PennyLane. First, mathematical functions, such as trigonometric functions, should be explicitly defined as JAX functions for them to be differentiable. Second, the callable functions, such as `ryd_amplitude`, are defined to have signature `(p, t)`, which is required when defining the [ParametrizedHamiltonian](https://docs.pennylane.ai/en/latest/code/api/pennylane.pulse.ParametrizedHamiltonian.html) object for the Rydberg atom device (see `H_ryd` below). \n",
    "\n",
    "The function `ryd_amplitude` starts and ends at zero, as required for the amplitude of the Rabi frequency for QuEra's Aquila (see [this AHS example notebook](https://github.com/aws/amazon-braket-examples/blob/main/examples/analog_hamiltonian_simulation/01_Introduction_to_Aquila.ipynb) for more details). We start the detuning, as parametrized by `ryd_detuning`, at a negative value to ensure that the initial state (where all atoms are in the ground state) is the lowest energy state of the Hamiltonian. Upon gradually increasing the detuning to a positive value, the Rydberg system is adiabatically driven to the AFM order (see below for the cost function for the AFM order). As an example, we define a set of parameters for the driving fields and plot them.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1a1b703c-1a92-429c-8b3e-c0b9af708cf4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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7kvHvRweIHYmIiMjoGtUafJdwFe//fhnKCu0apkgfZzx9RyfcE8uCyRhYOJHBBEHAu78mAwAe6BOMLv6uIiciurXnx0Zh27k8HLxchIOXCzGsM/d2IiIi6yAIAvYkFyD+12SkFlQBAII8HLFwTGdMiQtiwWRELJzIYHuSC3AiowQKOymeu7OL2HGIWhTi5YQZA8Ow4XAG3t2RjCEd2WqViIgs38W8Crzxvws4mlYMAPBwssfToztjxsBQKOy4hsnYWDiRQdQaAe/u0I42zRkSgUB3R5ETEbXOglGd8N2pqzifU4H//ZGL+3qxdT4REVmmkup6rNyZgv+eyIJGAOR2UswdEoF5IzvC3ZEdZE2FhRMZZOuZHFzKr4K7oz3mjegodhyiVvN2UeDJ4ZFYuesSVu68hIk9Ajl9gYiILIpGI+C/J7Pw3o4UlNdqO+VN7BGIJROiEezpJHI668fCiVpNEAR8diANAPDkiEjuiUMW59FhEdhwJANZJTXYkaTE3bEdxI5ERETUKudzyrF063kkZpcBAKIDXLHsnm4Y1NFb3GA2hJdbqdUOXi5CSn4lnOUyTB8QJnYcIoM5ye0wY6D23+76g+kQBEHkRERERLdWW6/G29sv4t6PDiExuwwuCjssu6crfnl6KIumdsYRJ2q19Qe1o01/6xfC+bNksWYOCsO6/VdwNrsMCZml6BvuJXYkIiKiZh1JLcKSLeeQWVwDALg7NhCv3t0V/m4OIiezTSycqFWSlRU4eLkIUgkwd0iE2HGI2szHRYEpcUHYfDIb6w+msXAiIiKzU61qRPyvF/H1sSwAQKC7A/45uTtGR/uLnMy2caoetcrnB9MBAOO7ByLEi4sPybI9Nkxb/O+8kI+MomqR0xAREV13MqMEEz44qC+aZgwMxc7nhrNoMgMsnKhFBRV1+CkxB8D1D5xElqyTnytGRflCEIAvDqeLHYeIiAgNag3e25GMv316FJnFNejg7oD/PDYAb03qAVcHLpEwByycqEVfH8tEg1pAnzBPxIV6ih2HyCgeGxYJAPju1FV9S1ciIiIxZBRV44G1R/DJvisQBGBqn2DseG44hnTyETsa/QkLJ7oltUbAdwlXAQCzB4eLG4bIiAZ39EYXfxfUNqjxyx+5YschIiIb9VNiDiZ+cBBnr5bD3dEea6f3xoqpPeHGUSazw8KJbulwahHyyuvg7miPO7tybi1ZD4lEgql9QgBoR52IiIjaU12DGv/Ycg4LNyeiul6NARFe+HXhMIzvESh2NLoJFk50S9+eygYA3NerAxzsZSKnITKuSXFBkEklSMwuw+X8SrHjEBGRjcgqrsED645g0/EsSCTAM6M7YdPjA9HBw1HsaHQLLJzopsprGrDzQj4A4G99Q0ROQ2R8vq4KjI72AwD9lFQiIiJTOni5EPd8dAjncyrg5SzHxjn9sWhsFGRSidjRqAUsnOimfj6bg/pGDaIDXNGtg5vYcYhMYmqfYADAj6dz0KDWiJyGiIislSAI+OzAFcz64gTKaxvQM8QD254ZihFdfMWORq3EwoluSncFfmrfEEgkvApC1mlUtB98XOQoqlJhf0qh2HGIiMgKqRrVWPTtWby9PRkaAfhb32B888RABLpzap4lYeFEzUpWVuCPq+Wwk0owqVcHseMQmYy9TIpJvYIAXF/TR0REZCwl1fWY8flxbDmTA5lUgjfu64Z374/l2nELxMKJmvX9tS5jY2L84e2iEDkNkWlNvbaGb09yAYqrVCKnISIia3GlsAqTPzmMkxmlcHWww5dz+mPmoHDO5LFQLJzoBhqNgG3n8gAAU3oHiZyGyPSiAlzRPcgNjRpB3xCFiIjodiRkluL+tUeQWVyDEC9H/DhvMIZ25oa2loyFE93g7NUy5JXXwVkuw3AuWCQbMeHavhnbr100ICIiaqvdF/Mx/fNjKKvRNoHY8vch6OzvKnYsuk0snOgGv55XAgBGx/hz/i3ZjPHdtYXTkSvFKK2uFzkNERFZqm9PZeOJfyegrkGDkVG++O/jA+DDZQ9WgYUTNSEIgv6K+4TuASKnIWo/ET7OiA5whVojYNdFTtcjIiLDbTicjhe//wNqjYD7ewdj/cy+cJLbiR2LjISFEzWRlFuBq6W1cLSXYWSUn9hxiNqVbrrejmujrkRERK31yb5ULP/fBQDA48Mi8H9TY2Ev40dta8K/TWpCN9o0KtoXjnJO0yPbMqGHdpT14OVCVNQ1iJyGiIgsgSAIWLUzBe/tSAEALLyjM/4xIYad86wQCyfS+/M0vbuurfcgsiWd/FzRyc8FDWoBuzldj4iIWmH1rkv4YE8qAODl8dF47s4uLJqsFAsn0ktWViKjuAZyOylGR3OaHtkm3dq+7ec4XY+IiG5tze/Xi6ZX7+6Kp0Z0FDkRmRILJ9LTddMb0cUXLgouZCTbNP7aOqf9lwpRpWoUOQ0REZmrD3dfxprfLwMAlk6MwaNDI0RORKbGwon0diZpC6fx7KZHNiw6wBXh3k6ob9TgwKVCseMQEZEZ+uJQOlbuugQAWDI+Go8NixQ5EbUHFk4EAMgrr0WyshISCdhNj2yaRCLB6Gh/AMC+lAKR0xARkbn5PuEq3vhF2z1v0Z1d8CSn59kMFk4EANifor2y3jPYA17OcpHTEIlrZJQvAO10PUEQRE5DRETm4rckJV764Q8AwGNDI/D06E4iJ6L2xMKJAAD7rhVOozjaRIT+EV5wtJchv0KFi3mVYschIiIzcCK9BE//9wzUGgFT+wTjlYlsOW5rRC2c4uPj0a9fP7i6usLPzw+TJk1CSkpKi8/77rvvEB0dDQcHB/To0QPbt29vh7TWq0GtwaHUIgDXr7QT2TIHexkGd/QGAOy7xOl6RES2LrWgEo9/dQr1jRqM7eqP+Ck9WDTZIFELp/3792P+/Pk4duwYdu3ahYaGBowdOxbV1dU3fc6RI0cwbdo0PProozhz5gwmTZqESZMm4fz58+2Y3LqcyihFlaoR3s5y9AhyFzsOkVnQXUTYl8wGEUREtqygsg6zvjiJ8toG9A71wAfT4mAn46QtWyRqz+kdO3Y0ub1x40b4+fkhISEBw4cPb/Y577//Pu666y688MILAIA333wTu3btwkcffYR169aZPLM10l1RH97FF1Ipr54QAbomKUlIyCpFeW0D3B3txY5ERETtrKa+EXM3nkROWS3CvZ3w+ax+cLCXiR2LRGJW5XJ5eTkAwMvL66aPOXr0KMaMGdPk2Lhx43D06NFmH69SqVBRUdHki5rSNYbgND2i60K8nNDR1xlqjYDD16ayEhGR7dBoBCz65izO51TAy1mOjXP6s4GWjTObwkmj0eDZZ5/FkCFD0L1795s+TqlUwt/fv8kxf39/KJXKZh8fHx8Pd3d3/VdISIhRc1s6XRtyqQQY3pmFE9Gf6Vrzsy05EZHtWf37JexIUkIuk2L9zD4I93EWOxKJzGwKp/nz5+P8+fPYvHmzUV93yZIlKC8v139lZ2cb9fUtna6bXs8QD3jyKgpRE/p1TilsS05EZEt+SszBh3tSAQBvT+mBPmE3nw1FtkPUNU46CxYswC+//IIDBw4gODj4lo8NCAhAfn5+k2P5+fkICAho9vEKhQIKhcJoWa2N7kr6yC5sQ070V7q25AWVKlzIq0C3DmyeQkRk7c5dLceL32v3anpieCQe6HPrz6ZkO0QdcRIEAQsWLMCWLVuwZ88eREREtPicQYMGYffu3U2O7dq1C4MGDTJVTKul1gg4cqUYADCC65uIbqCwu96W/NBlrnMiIrJ2pdX1eOrrBKgaNRgV5YuX7ooWOxKZEVELp/nz5+Prr7/Gpk2b4OrqCqVSCaVSidraWv1jZs6ciSVLluhvL1y4EDt27MDKlSuRnJyM119/HadOncKCBQvE+CNYtKTcclTWNcLVwY5tyIluYtC1wuloWrHISYiIyJTUGgELv0lETlktwrydsOahOMjYbZj+RNTCae3atSgvL8fIkSMRGBio//rmm2/0j8nKykJeXp7+9uDBg7Fp0yZ89tln6NmzJ77//nts3br1lg0lqHlHr402DYjw4hsD0U3oCqeT6SVoUGtETkNERKby/u+XcOBSIRzspVg3ow+3oaAbiLrGqTWLrfft23fDsalTp2Lq1KkmSGRbdFfQB0Z6i5yEyHzFBLjBw8keZTUNOJdTjt6hnmJHIiIiI9ubXIAPrjWDiJ/SAzGBbiInInNkNl31qH01qDU4mV4C4PoVdSK6kVQqwYAIbTcl3SgtERFZj7zyWiz6NhEAMHNQGCbHsRkENY+Fk406l1OO6no1PJzsERPAqypEtzLo2qjsMa5zIiKyKo1qDRZuTkRpTQO6B7nhlYkxYkciM8bCyUb9eX2TlOubiG5pUEcfAMCpjFLUN3KdExGRtfhgTypOpJfAWS7Dh9N6Q2EnEzsSmTEWTjZKd+V8ENc3EbWoi78LvJ3lqG1Q4+zVMrHjEBGRERy5UoQP91wGoN3kNsLHWeREZO5YONmg+kYNTmWUArh+JZ2Ibk4ikeibqHCdExGR5SuvacDz356FIAB/6xuM+3oFiR2JLAALJxt09moZahvU8HaWo4u/i9hxiCzCwI4snMg0Xn/9dUgkkiZf0dHcdJPIlF796TzyyusQ7u2EZfd0EzsOWQhR25GTOHQf/AZGekMi4fomotbQTWtNyCpFXYMaDvacB0/G061bN/z+++/623Z2PD0TmcpPiTn4+WwuZFIJVj/YC84K/r5R6/Bfig3SF05sQ07Uah19neHrqkBhpQpnssrYxp+Mys7ODgEBAWLHILJ6uWW1eHXreQDA/FGdEMe9+cgAnKpnY+obNTiddW19ExtDELWaRCLR/84cT+d0PTKuy5cvo0OHDoiMjMT06dORlZV108eqVCpUVFQ0+SKilgmCgJd++AMVdY3oGeyOp0d3EjsSWRgWTjbmfG45VI0aeDnL0dGX3WOIDNEvXHtlMiGzVOQkZE0GDBiAjRs3YseOHVi7di3S09MxbNgwVFZWNvv4+Ph4uLu7679CQkLaOTGRZfrmZDYOXi6Cwk6KVQ/2gr2MH4PJMPwXY2MSrnXT6x3qyfVNRAbqE+YFADiTVQa1RhA5DVmL8ePHY+rUqYiNjcW4ceOwfft2lJWV4dtvv2328UuWLEF5ebn+Kzs7u50TE1mevPJa/HPbRQDA82O7oKMvm2OR4bjGycborpT3DeecXiJDRQW4wlVhh0pVI1KUlejawU3sSGSFPDw80KVLF6SmpjZ7v0KhgEKhaOdURJZLEAQs+fEcKlWNiAv1wKNDI8WORBaKI042RBAEnNIVTmEsnIgMJZNK0CvUAwCQkFkibhiyWlVVVbhy5QoCAwPFjkJkFX44nYN9KYWQ20mx4oFYyKSccUNtw8LJhmSV1KCoSgW5TIruQe5ixyGySH2uXXQ4xXVOZCSLFy/G/v37kZGRgSNHjmDy5MmQyWSYNm2a2NGILF5RlQpv/nIBAPDsmM7o5OcqciKyZJyqZ0NOXVvf1D3IjXvQELVR32vrnHS/T0S36+rVq5g2bRqKi4vh6+uLoUOH4tixY/D19RU7GpHFe+uXCyivbUDXQDc8MYxT9Oj2sHCyIfppeuFeIichsly9Qj0glQA5ZbVQltchwN1B7Ehk4TZv3ix2BCKrdPByIbYm5kIqAeKn9IAdu+jRbeK/IBuiW5PRh+ubiNrMRWGHmEBtU4hTXOdERGSW6hrUWHpto9uZg8LRM8RD3EBkFVg42Yjy2gZcyq8CoG1FTkRtp7v4wP2ciIjM04d7LiOzuAYBbg54fmwXseOQlWDhZCNOZ2k/4IV7O8HXlW1siW4HCyciIvN1pbAKnx1IAwAsv68bXB3sRU5E1oKFk43QbXyr28CTiNpOt04wKbcCNfWNIqchIiIdQRDw+s9JaFALGB3th3HdAsSORFakTYVTQ0MDsrOzkZKSgpISzvG3BLq1GNz4luj2BXk4ItDdAWqNgMTsMrHjEBHRNTvOK3HwchHkMimW3dNV7DhkZVpdOFVWVmLt2rUYMWIE3NzcEB4ejpiYGPj6+iIsLAyPP/44Tp48acqs1EYNag3OZpcD4Ma3RMain67HtuRERGahpr5Rv2fTkyMiEebtLHIisjatKpxWrVqF8PBwbNiwAWPGjMHWrVuRmJiIS5cu4ejRo1i2bBkaGxsxduxY3HXXXbh8+bKpc5MBLuVXorZBDVcHO3T0dRE7DpFV0DVZOXu1TNwgREQEAPhk7xXkltchyMMRfx/ZSew4ZIVatY/TyZMnceDAAXTr1q3Z+/v374+5c+di7dq12LhxIw4ePIjOnTsbNSi1nW60qWewB6RSichpiKyDrrVtYnY5BEGARMLfLSIisWSX1OgbQrx6d1c4ymUiJyJr1KrC6b///W+rXszBwQFPPfXUbQUi4zt7bQ1GzxB3cYMQWZFuHdxgJ5WgqEqlv8JJ5kmj0WD//v04ePAgMjMzUVNTA19fX8TFxWHMmDEICQkROyIR3ab4Xy+iXq3BkE7eGNfNX+w4ZKUMbg7x1Vdf4cKFCzccr6urw1dffWWUUGRcuqlEPYM9RM1BZE0c7GWIDnQFcP3iBJmX2tpavPXWWwgJCcGECRPw66+/oqysDDKZDKmpqVi2bBkiIiIwYcIEHDt2TOy4RNRGx9OKsf2cElKJdrSJMwDIVAwunGbPno0BAwbghx9+aHK8vLwcc+bMMVowMo5qVSMu5VcCAHpx12wio9JdjGDhZJ66dOmCP/74A+vXr0dFRQWOHj2KH374AV9//TW2b9+OrKwsXLlyBcOGDcNDDz2E9evXix2ZiAyk1gh441pDiGn9QxEd4CZyIrJmbWpHvnz5cjzyyCN4/fXXjRyHjO18Tjk0AhDo7gA/Nwex4xBZlevrnMpEzUHN27lzJ7799ltMmDAB9vbNb4AZFhaGJUuW4PLlyxg9enQ7JySi2/XD6atIyq2Aq8IOi+7sInYcsnJtKpxmzJiBPXv24NNPP8UDDzyA2tpaY+ciI+E0PSLT0Y3inssph1ojiBuGbhATE9Pqx9rb26Njx44mTENExlatasT//ZYCAHjmjs7wdlGInIisncGFk27e6MCBA3H8+HGkpqZi8ODByMjIMHY2MgJ9Rz1O0yMyuo6+LnCWy1BTr0ZqQZXYcegWIiMjMWfOHKhUqibHi4qKEBkZKVIqIrodnx9MR0GlCmHeTpg5OEzsOGQDDC6cBOH6VdXQ0FAcOXIE4eHhuPPOO40ajIwjkR31iExGJpWgR7D2d4vrnMxbRkYGDh8+jGHDhkGpVOqPq9VqZGZmipiMiNqisFKFTw9cAQC8MC4KCju2HyfTM7hwWrZsGVxcrm+i6uTkhC1btuC5557D8OHDjRqObk9hpQo5ZbWQSIAeQSyciExBv86JG+GaNYlEgh07diA4OBh9+vTByZMnxY5ERLfh/d2XUFOvRs9gd0zsESh2HLIRbSqcnJycbji+fPly7N271yihyDj+uPZBrqOvC1wdml8YTUS3h531LIMgCHBxccGPP/6ImTNnYsSIEfj666/FjkVEbXClsAr/PZENAFgyIYbtx6ndtGoDXAD4+eefW3yMRCLBPffcc1uByHj0G9+yMQSRyehGnJKVlahrUMPBntNFzNGfP1jFx8ejW7duePzxxzFt2jQRUxFRW6zYkQK1RsCYGD8MjPQWOw7ZkFYXTpMmTWpyWyKRNFnvpDumVquNEoxuX+JVbWOIXlzfRGQyHdwd4OOiQFGVCkm55egT5iV2JGrGX89XM2bMQMeOHTF58mSREhFRW5zOKsWOJO1mty/dFS12HLIxrZ6qp9Fomnw5OTkhNTW1yTEWTeZDEITrI07sqEdkMhKJRH9xIvFaF0syPxqNBn5+fk2ODRo0CGfPnsWePXtESkVEhhAEASt2aNuP3987GJ39XUVORLamTfs4kfnLKqlBeW0D5DIpd9EmMjGuc7Jc/v7+GDFihNgxiKgVDqcW42haMeQyKZ7lZrckglZP1SPLci5He+U7JtAVcjvWx0SmpGtJfj6XI07mJi4urlULx0+fPt0OaYiorQRBwIrfkgEA0weGIsjDUeREZItYOFmp8zkVAIBubENOZHLdOmh/z9KLqlGlaoSLgm+t5uLP63MFQUB8fDyeeuopeHlxLRqRJfktKR9nr5bDSS7D/FGdxI5DNqrNZ3eJRML2j2Ys6dqV7+4dWDgRmZqvqwIBbg5QVtThYl4F+oXzQ7m5WLZsWZPbK1euxMKFCxEZGSlSIiIylFojYOVO7dqmR4dGwMdFIXIislWtLpw8PT2bFEpVVVWIi4uDVNp0GlhJSYnx0lGbCIKgn6rHjW+J2kf3IHcoK+pw7mo5CyciIiP639lcXC6ogrujPR4bxoseJJ5WF05r1qwxYQwyppyyWpTVNMBOKkGXABex4xDZhO5Bbvj9Yj7XORERGVGjWoP3d18GADwxPBLujvYiJyJb1urCadasWabMQUakW9/Uxd8VCjtuxknUHnTTYpOu/f4REdHt25qYi/Siang5yzFrcLjYccjGcQWzFTrPaXpE7U7XWe9yQSVq69VwlPOihTn44IMPmtxubGzExo0b4ePj0+T4M888056xiKgVGtQafHBttOnJ4ZFsvEOia/W/wNYupE1LS2v1Nz9w4ABWrFiBhIQE5OXlYcuWLU06IP3Vvn37MGrUqBuO5+XlISAgoNXf19rppgp1D+L+TUTtxc9VAR8XBYqqVLiorEDvUE+xIxGA1atXN7kdEBCAf//7302OSSQSFk5EZujH01eRVVIDHxc5HhkUJnYcotYXThkZGQgLC8PDDz98w+7rbVVdXY2ePXti7ty5mDJlSqufl5KSAje360WBsfJYA0EQ9CNO3TniRNRuJBIJegS5YW9KIZJyylk4mYn09HSxIxBRG9Q3avDhnlQAwFMjOsJJztEmEl+r/xV+8803+OKLL7Bq1SqMHz8ec+fOxYQJE27oqmeI8ePHY/z48QY/z8/PDx4eHm3+vtYsv0KFoqp6yKQSxARyxImoPXUPcsfelEJ9V0siImqbH05fxdXSWvi6KjBjIEebyDy0unCaOnUqpk6dipycHGzcuBHPPfccnnzySTzyyCN49NFH0blzZ1PmbKJXr15QqVTo3r07Xn/9dQwZMqTdvre50402dfJ1gYM911gQtSfdRrjn2SDCbHz11VetetzMmTNNnISIWqtBrcHHe6+PNvHzDJkLg8c9g4KC8Morr+CVV17B/v378frrr2PFihUoKiqCp6dpp6YEBgZi3bp16Nu3L1QqFT7//HOMHDkSx48fR+/evZt9jkqlgkql0t+uqLDuDzTX1zdxmh5Re9M1iLiUXwlVo5pdLc3A7Nmz4eLiAjs7OwiC0OxjJBIJCyciM7LldA6ultbCx0WBh/uHih2HSK9NE0br6urw/fff44svvsDx48cxdepUODk5GTvbDaKiohAVFaW/PXjwYFy5cgWrV6++YbGvTnx8PJYvX27ybObi+vomTtMjam8d3B3g6WSP0poGpCgrERvsIXYkmxcTE4P8/HzMmDEDc+fORWxsrNiRiOgWGtUafHRttOnJ4ZHsUEpmxaAFSsePH8cTTzyBgIAArFq1ClOmTEFOTg42b94MhUJhqoy31L9/f6Smpt70/iVLlqC8vFz/lZ2d3Y7p2p9uihBbkRO1P4lEoh/t5XQ985CUlIRt27ahtrYWw4cPR9++fbF27Vqrn31AZKm2JuYiq6QG3s5yTB/I0SYyL60unLp164a7774bjo6O2L9/P06fPo0FCxaYfHpeSxITExEYGHjT+xUKBdzc3Jp8WavCShWUFXWQSMDGEEQi0RdOuWwQYS4GDBiATz/9FHl5eXjmmWfw7bffIjAwENOnT28ylZuIxNX4p7VNjw+PZCc9Mjut/hd58eJFODs746uvvrrptDgAKCkpafU3r6qqajJalJ6ejsTERHh5eSE0NBRLlixBTk6OfnHvmjVrEBERgW7duqGurg6ff/459uzZg507d7b6e1qzC3naK6gRPs5w5iZxRKLofq1BRBI765kdR0dHzJw5E+Hh4Vi2bBk2b96Mjz76SLQZE0TU1C9/5CG9qBqeTvZ4hJ30yAy1+tP1hg0bjP7NT5061WRD20WLFgEAZs2ahY0bNyIvLw9ZWVn6++vr6/H8888jJycHTk5OiI2Nxe+//97spri26EKutnDSdfYiovbXtYN2tDdZWYlGtQZ2srZv2UDGk5OTgy+//BIbNmxAdXU1ZsyYgbVr14o+a4KItDQaQT/a9OjQCF4AJrPU6n+Vs2bNMvo3Hzly5E27HAHAxo0bm9x+8cUX8eKLLxo9h7XQjTh15TQ9ItGEeTnBSS5DTb0aGcXV6OTnKnYkm/btt99iw4YN2L9/P8aNG4eVK1di4sSJkMm44JzInOy8oMTlgiq4Othh5uBwseMQNatVhZMgCJBIJKbOQrfpwrU1Fbor3kTU/qTXNp9OyCxFUm4FCyeRPfTQQwgNDcVzzz0Hf39/ZGRk4OOPP77hcc8884wI6YgI0H7O1HXSmzUoHG4O9iInImpeqwqnbt264bXXXsOUKVMgl8tv+rjLly9j1apVCAsLw8svv2y0kNSymvpGpBVVAwBiAvlBjUhMMYGuSMgsxYW8CtzXK0jsODYtNDQUEokEmzZtuuljJBIJCyciEe27VIjzORVwtJdh7tAIseMQ3VSrCqcPP/wQL730Ev7+97/jzjvvRN++fdGhQwc4ODigtLQUFy5cwKFDh5CUlIQFCxZg3rx5ps5Nf5GirIQgAD4uCvi5Oogdh8imdQ3UrjPUrTsk8WRkZIgdgYhuQRAEfLxHO9o0fUAovJxvfoGeSGytKpzuuOMOnDp1CocOHcI333yD//znP8jMzERtbS18fHwQFxeHmTNnYvr06VxoK5KLeZUAOE2PyBzofg91v5dERNS84+klOJVZCrlMiseHR4odh+iWDGpZMnToUAwdOtRUWeg2XMi7tr6JjSGIRBfl7wqpBCiqUqGgso6jwCLZvHkzHnrooVY9Njs7G1lZWRgyZIiJUxHRn+k66U3tGwx/N75Xknljn1wroZsSxPVNROJzlMsQ4eMMgNP1xLR27VrExMTgvffew8WLF2+4v7y8HNu3b8fDDz+M3r17o7i4WISURLbr3NVyHLxcBJlUgqdGdBQ7DlGLWDhZAbVGQLJSOyWoG6fqEZmFrtf2U9NtE0Dtb//+/Xj33Xexa9cudO/eHW5ubujcuTN69OiB4OBgeHt7Y+7cuQgNDcX58+dx7733ih2ZyKZ8sk872nRPbCBCvJxETkPUMu4uZgUyi6tRU6+Gg70UET4uYschIminzf7vbC5HnER277334t5770VRUREOHTp0w/rcuLg4SKW8hkjU3lILqrAjSQkAmDeyk8hpiFqHhZMV0C1Ajwpwg0zK/baIzMH1BhEsnMyBj48PJk2aJHYMIrrm0/1XIAjAmBh/RAVwmQFZBl5mswLXG0PwjYfIXOjWG6YVVaOmvlHkNERE5iOnrBZbzuQAAP4+imubyHK0qXC6cuUKli5dimnTpqGgoAAA8OuvvyIpKcmo4ah1dFOB2FGPyHz4uTrAx0UBQdDus0ZERFqfH0xDo0bAoEhv9A7lNjZkOQwunPbv348ePXrg+PHj+PHHH1FVVQUAOHv2LJYtW2b0gNQy3eJz7uFEZF50v5NsEEFEpFVSXY/NJ7IBAPNGcrSJLIvBhdPLL7+Mt956C7t27YJcfn1359GjR+PYsWNGDUctK65SIb9CBYlEu8aJiMyHbhSYDSKIiLS+PJKB2gY1uge5YVhnH7HjEBnE4MLp3LlzmDx58g3H/fz8UFRUZJRQ1Hq6xhBhXk5wUbDXB5E50a1z4ogTERFQrWrEl0czAADzRnSCRMKGVmRZDP6k7eHhgby8PERERDQ5fubMGQQFBRktGLWOrmNXDNc3EZkd3YhTirISGo0AKbteimbRokXNHpdIJHBwcECnTp1w3333wcvLq52TEdmO/57IQllNAyJ8nHFX9wCx4xAZzODC6aGHHsJLL72E7777DhKJBBqNBocPH8bixYsxc+ZMU2SkW7ioZOFEZK4ifJwht5Oipl6N7NIahHk7ix3JZp05cwanT5+GWq1GVFQUAODSpUuQyWSIjo7GJ598gueffx6HDh1C165dRU5LZH3qGzX4/GA6AODJ4ZHcPoUsksFT9d5++21ER0cjJCQEVVVV6Nq1K4YPH47Bgwdj6dKlpshIt5B8bapeNPdAIDI7djIpuvhrN6XWTaslcdx3330YM2YMcnNzkZCQgISEBFy9ehV33nknpk2bhpycHAwfPhzPPfec2FGJrNLWxBwoK+rg56rA5N6coUSWyeDCSS6XY/369bhy5Qp++eUXfP3110hOTsa///1vyGQyU2Skm2hQa5BaoO1qyBEnIvMUfa1pS7KS65zEtGLFCrz55ptwc7v+Xunu7o7XX38d7733HpycnPDaa68hISFBtIwff/wxwsPD4eDggAEDBuDEiROiZSEyJo1GwLr9VwAAjw6NgMKOnxfJMrW5m0BoaChCQ0ONmYUMlF5UjXq1Bi4KOwR5OIodh4iaoRsNTuaIk6jKy8tRUFBwwzS8wsJCVFRoi1oPDw/U19eLEQ/ffPMNFi1ahHXr1mHAgAFYs2YNxo0bh5SUFPj5+YmSichYdl3MR1phNVwd7PDwAH52JMvVqsLpZotqm7Nq1ao2hyHD6BpDRAW4ctE5kZnSjQZf5IiTqO677z7MnTsXK1euRL9+/QAAJ0+exOLFizFp0iQAwIkTJ9ClSxdR8q1atQqPP/445syZAwBYt24dtm3bhi+++AIvv/yyKJmIjEEQBHyyTzvaNHNQGFwd7EVORNR2rSqczpw50+T26dOn0djYeMMC2z59+hg/Id3URa5vIjJ7ut/PzOIaVKsa4cxtA0Tx6aef4rnnnsNDDz2ExsZGAICdnR1mzZqF1atXAwCio6Px+eeft3u2+vp6JCQkYMmSJfpjUqkUY8aMwdGjR294vEqlgkql0t/WjZgRmaNjaSU4m10GhZ0UswdHtPwEIjPWqjP43r179f+/atUquLq64ssvv4SnpycAoLS0FHPmzMGwYcNMk5KalcyOekRmz9tFAT9XBQoqVUjJr0TvUE+xI9kkFxcXrF+/HqtXr0ZaWhoAIDIyEi4uLvrH9OrVS5RsRUVFUKvV8Pf3b3Lc398fycnJNzw+Pj4ey5cvb694RLdl7bW1TX/rGwJfV4XIaYhuj8HNIVauXIn4+Hh90QQAnp6eeOutt7By5UqjhqNb062Z0G2ySUTmKfraxQ2ucxKfi4sLYmNjERsb26RosiRLlixBeXm5/is7O1vsSETNSsotx4FLhZBKgMeHRYodh+i2GTxnpKKiAoWFhTccLywsRGUlPxS0l9Lqeigr6gAAXfxZOBGZs5gAVxy4VMjOeiKqrq7GO++8g927d6OgoAAajabJ/bpRKDH4+PhAJpMhPz+/yfH8/HwEBNy4SahCoYBCwSv3ZP7W7df+Xt0d2wGh3k4ipyG6fQYXTpMnT8acOXOwcuVK9O/fHwBw/PhxvPDCC5gyZYrRA1LzkpXaIjXEy5ELLYnMXHQgO+uJ7bHHHsP+/fvxyCOPIDAwEBKJ+TTUkcvl6NOnD3bv3q1vVKHRaLB7924sWLBA3HBEbZRZXI1tf+QCAJ4cwdEmsg4GF07r1q3D4sWL8fDDD6OhoUH7InZ2ePTRR7FixQqjB6Tm6a5c6/aIISLzpfs9vaisgCAIZvWh3Vb8+uuv2LZtG4YMGSJ2lGYtWrQIs2bNQt++fdG/f3+sWbMG1dXV+i57RJbmswNp0AjAyChfdOvgLnYcIqMwuHBycnLCJ598ghUrVuDKFe2Cv44dO8LZ2dno4ejm9Oub2FGPyOx19HWBnVSCyrpG5JbXcd81EXh6esLLy0vsGDf14IMPorCwEK+99hqUSiV69eqFHTt23NAwgsgSFFTW4buEqwCAeSM6ipyGyHgMbg6h4+zsrF9gy6Kp/en2hIlmRz0isye3k6KTn7YRwcVcrnMSw5tvvonXXnsNNTU1Yke5qQULFiAzMxMqlQrHjx/HgAEDxI5E1CYbDmegvlGD3qEe6B9hvhcsiAxl8IjTqFGjbjnNZM+ePbcViFqm1ghIUeo66rFwIrIEMYFuSFZWIllZgTFdOYrQ3lauXIkrV67A398f4eHhsLdvujb09OnTIiUjsi4VdQ34+mgmAGDeyE6cmkxWxeDC6a/7XDQ0NCAxMRHnz5/HrFmzjJWLbiGjuBqqRg0c7WUI9WKXGiJLoNsI96KSDSLEoGu6QESm9Z9jWahUNaKznwvuiPYTOw6RURlcOOl2WP+r119/HVVVVbcdiFqmW9/UJcAVMimv5BBZAt202ot5nKonhmXLlokdgcjq1TWo8a9D6QCAp0Z0hJSfUcjKtHmN01/NmDEDX3zxhbFejm5B31GP+zcRWQxdI5eMomrUNahFTkNEZHzfJVxFUZUKQR6OuLdXB7HjEBmdwSNON3P06FE4ODgY6+XoFnR7OOn2hiEi8+frqoCnkz1KaxqQWlCF7kFsz2tqXl5euHTpEnx8fODp6XnLtRYlJSXtmIzI+jSqNfh0v7bb8uPDImAvM9q1eSKzYXDh9NdNbgVBQF5eHk6dOoVXX33VaMHo5nQjTlFsRU5kMSQSCaICXHEsrQQX8ypYOLWD1atXw9VV+z65Zs0accMQWbn//ZGLq6W18HaW48F+oWLHITIJgwsnNze3JlftpFIpoqKi8MYbb2Ds2LFGDUc3qlI1IrukFgA3vyWyNNEBbjiWVqLvikmm9eeGRWxeRGQ6Go2Atfu0o01zh0bAUS4TORGRaRhcOG3cuNEEMai1LuVrP3D5uSrg5SwXOQ0RGULXWS8ln4WTGDQaDVJTU1FQUACNRtPkvuHDh4uUisjy7U4uwKX8Krgo7DBjYJjYcYhMxuDCKTIyEidPnoS3t3eT42VlZejduzfS0tKMFo5upOuox41viSzP9c56LJza27Fjx/Dwww8jMzMTgiA0uU8ikUCtZsMOorYQBAGf7EsFADwyKAzujvYtPIPIchlcOGVkZDR7glGpVMjJyTFKKLq5FF1HPa5vIrI4XfxdIJEARVUqFFWp4OOiEDuSzXjqqafQt29fbNu2DYGBgdyUk8hIjl4pxpmsMijspJg7JELsOEQm1erC6eeff9b//2+//QZ39+sLm9VqNXbv3o3w8HCjhqMb6TbPjGIrciKL4yS3Q6iXEzKLa5CirIRPJxZO7eXy5cv4/vvv0alTJ7GjEFmVj/ZqR5se6hcCX1e+p5F1a3XhpNt1XSKR3LDI1t7eHuHh4Vi5cqVRw1FTgiDoF5WzFTmRZYoOcEVmcQ2SlZUY0slH7Dg2Y8CAAUhNTWXhRGRECZmlOHKlGPYyCZ4Y0VHsOEQm1+rCSbeQNiIiAidPnoSPD0/47S2/QoXy2gbIpBJ08nMROw4RtUFUgBt+S8rXT7ul9vH000/j+eefh1KpRI8ePWBv33QdRmxsrEjJiCzXx9dGm6bEBSPIw1HkNESmZ/Aap/T0dFPkoFa4eO2DVoSPMxR2bPVJZIl06xOT2ZK8Xd1///0AgLlz5+qPSSQSCILA5hBEbXA+pxx7kgsglQDzRnK0iWxDqwqnDz74AE888QQcHBzwwQcf3PKxzzzzjFGC0Y300/TYGILIYul+fy/lV0KtESCTsklBe+BFPyLj0nXSu6dnB4T7OIuchqh9tKpwWr16NaZPnw4HBwesXr36po+TSCQsnEyIhROR5QvzdoaDvRR1DRpkldQggh842kVYGPeWITKWy/mV+PW8EgDw95FcN0i2o1WF05+v1PGqnXgu5ulakXMPJyJLJZNK0MXfFX9cLUdyXgULp3by1Vdf3fL+mTNntlMSIsv30d5UCAIwrps/ongxl2yIwWucjOnAgQNYsWIFEhISkJeXhy1btui7993Mvn37sGjRIiQlJSEkJARLly7F7Nmz2yWvmBrUGlwprAIAvkkRWbgoXeGkrMT4HoFix7EJCxcubHK7oaEBNTU1kMvlcHJyYuFE1EpXCqvwv7O5AIBn7ugschqi9tWqwmnRokWtfsFVq1a1+rHV1dXo2bMn5s6diylTprT4+PT0dEycOBFPPfUU/vOf/2D37t147LHHEBgYiHHjxrX6+1qitMJqNKgFuCjsEOzJzjVElixK3yCCnfXaS2lp6Q3HLl++jHnz5uGFF14QIRGRZfp4Tyo0AjAmxh/dOri3/AQiK9KqwunMmTOtejFDd2IfP348xo8f3+rHr1u3DhEREfr9omJiYnDo0CGsXr3a6gsn3QesqABX7nhPZOFiArXTbVPYWU9UnTt3xjvvvIMZM2YgOTlZ7DhEZi+jqBpbE3MAAAs52kQ2qFWF0969e02do1WOHj2KMWPGNDk2btw4PPvsszd9jkqlgkql0t+uqLDMK7y6D1icpkdk+XS/x5klNaipb4STXNRZ0zbNzs4Oubm5Yscgsggf79WONo2O9kOPYI42ke25rbN1dnY2ACAkJMQoYVqiVCrh7+/f5Ji/vz8qKipQW1sLR8cbp7DFx8dj+fLl7ZLPlHR7vsSwcCKyeD4uCvi4KFBUpcKl/Cr0CvEQO5LV+/nnn5vcFgQBeXl5+OijjzBkyBCRUhFZjqziGvx4Rjva9PRodtIj22Rw4dTY2Ijly5fjgw8+QFWVtlmBi4sLnn76aSxbtuyG3djFtmTJkiZrtCoqKtqt0DOm6yNO7KhHZA2iA1xxKFWFFGUFC6d28NfGQxKJBL6+vhg9erR++jcR3dwHey5DrREwvIsv4kI9xY5DJAqDC6enn34aP/74I9577z0MGjQIgHYK3euvv47i4mKsXbvW6CF1AgICkJ+f3+RYfn4+3Nzcmh1tAgCFQgGFQmGyTO2hvLYBOWW1ADhVj8haaAunIlzM4zqn9qDRaMSOQGSx0ouq8ePpqwCARXd2ETkNkXikhj5h06ZN2LhxI5588knExsYiNjYWTz75JP71r39h06ZNpsioN2jQIOzevbvJsV27dukLOGt1KV/7waqDuwPcHc1rRI+I2iaaDSLa1RtvvIGampobjtfW1uKNN94QIRGR5fhg92VoBOCOaD+OkJNNM7hwUigUCA8Pv+F4REQE5HK5Qa9VVVWFxMREJCYmAtC2G09MTERWVhYA7TS7P++t8dRTTyEtLQ0vvvgikpOT8cknn+Dbb7/Fc889Z+gfw6Ik6za+DeQ0PSJrEf2nluSCIIicxvotX75cP738z2pqaqxiHSyRqaQWVOKna530nuNoE9k4gwunBQsW4M0332zSqU6lUuGf//wnFixYYNBrnTp1CnFxcYiLiwOg3S8qLi4Or732GgAgLy9PX0QB2uJs27Zt2LVrF3r27ImVK1fi888/t4FW5OyoR2RtOvm5QCoBSmsaUFipavkJdFsEQWh2K4ezZ8/Cy8tLhEREluH93dpOemO7+qN7EDvpkW0zeI3TmTNnsHv3bgQHB6Nnz54AtCee+vp63HHHHU02sv3xxx9v+VojR4685ZXWjRs3Nvuc1u4rZS10hVM0Cyciq+FgL0OEjzOuFFbjorISfm4OYkeySp6enpBIJJBIJOjSpUuT4kmtVqOqqgpPPfWUiAmJzFeKshK//KFt1//sGI42ERlcOHl4eOD+++9vcswSu9RZCkEQ9GsgotlRj8iqRAe64UphNVKUFRjRxVfsOFZpzZo1EAQBc+fOxfLly+Hufv2KuVwuR3h4uNWvkyVqq//bmQJBACb0CEDXDvwMQmRw4bRhwwZT5KCbuFpaiypVI+xlEkT6Oosdh4iMKNrfFduQh2R21jOZWbNmAdBO9R4yZAjs7LjZMFFrnMkqxa4L+ZBK2EmPSMfgNU7UvnSjTR19XWAv418XkTXRNXxJZmc9kxsxYgQyMzOxdOlSTJs2DQUFBQCAX3/9FUlJSSKnIzI//7czBQBwf+9gdPLjUgEioA2FU3FxMebPn4+uXbvCx8cHXl5eTb7IuJKV2o56MeyoR2R1dOsWUwuq0KDmPkOmtH//fvTo0QPHjx/Hjz/+qO+wd/bsWSxbtkzkdETm5XBqEQ6nFsNeJsHCMZ3FjkNkNgyes/DII48gNTUVjz76KPz9/ZvtUkTGc5Ed9YisVrCnI1wUdqhSNSK9qBpd/Pl7biovv/wy3nrrLSxatAiurtd/zqNHj8ZHH30kYjIi8yIIAt77TTvaNH1AGII9nURORGQ+DC6cDh48iEOHDuk76pFppbCjHpHVkkgkiApwRUJmKZKVlSycTOjcuXPNbtLu5+eHoqIiERIRmaffkvJxNrsMjvYyzB/VSew4RGbF4Kl60dHRqK2tNUUW+ou6BjXSi6oBsKMekbXSjSbrNrom0/Dw8EBeXt4Nx8+cOYOgoCAREhGZnwa1Bu/tSAYAPDo0Ar6uCpETEZkXgwunTz75BK+88gr279+P4uJiVFRUNPki40ktqIJaI8DDyR7+bnzzIrJGMdcKpxQ2iDCphx56CC+99BKUSiUkEgk0Gg0OHz6MxYsXY+bMmWLHIzIL35zMRlpRNbyc5XhyRKTYcYjMTpv2caqoqMDo0aObHNftyq5Wq40WztbpOm1F+btyLRmRlYoKYGe99vD2229j/vz5CAkJgVqtRteuXaFWq/Hwww9j6dKlYscjEl21qhFrfr8MAFh4R2e4OtiLnIjI/BhcOE2fPh329vbYtGkTm0OYWAo76hFZPd1UvZyyWpTXNsDdkR9WTEEul2P9+vV49dVXcf78eVRVVSEuLg6dO7NjGBEArD+YhqIqFcK8nTCtf6jYcYjMksGF0/nz53HmzBlERUWZIg/9ycU8NoYgsnbujvYI8nBETlktUpSV6B/BbR1MKTQ0FKGh/FBI9GcFlXX47EAaAODFcdGQ23HfSKLmGFw49e3bF9nZ2Syc2gH3cCKyDdEBrsgpq0WysoKFkxEtWrSo1Y9dtWqVCZMQmbfVuy6hpl6NniEemNAjQOw4RGbL4MLp6aefxsKFC/HCCy+gR48esLdvOq0kNjbWaOFsWUFlHYqq6iGVgC2KiaxcTKAbdicX4CI76xnVmTNnmtw+ffo0Ghsb9Rf+Ll26BJlMhj59+ogRj8gsJOWWY/PJbADAqxNjuASD6BYMLpwefPBBAMDcuXP1xyQSCZtDGJluml64jzMc5TKR0xCRKelGlS/ksUGEMe3du1f//6tWrYKrqyu+/PJLeHp6AgBKS0sxZ84cDBs2TKyIRKISBAFv/nIBggDcHRuIvuEc8Sa6FYMLp/T0dFPkoL/Q7enCaXpE1i86UDuqfElZCbVGgEzKK77GtnLlSuzcuVNfNAGAp6cn3nrrLYwdOxbPP/+8iOmIxLHzQj6OpZVAbifFy+OjxY5DZPYMLpzCwsJMkYP+QjdlJ4aNIYisXri3MxzspahtUCOzuBqRvi5iR7I6FRUVKCwsvOF4YWEhKis50ke2R9WoxtvbLwIAnhgWiWBPJ5ETEZk/gwsnnQsXLiArKwv19fVNjt977723HYquT9XjiBOR9ZNJJYgKcMPZ7DJczKtk4WQCkydPxpw5c7By5Ur0798fAHD8+HG88MILmDJlisjpiNrfxsMZyCyuga+rAvNGdhQ7DpFFMLhwSktLw+TJk3Hu3Dn92iYA+sWEXON0+1SNalwprALAwonIVsQEuOJsdhmSlRWYGBsodhyrs27dOixevBgPP/wwGhoaAAB2dnZ49NFHsWLFCpHTEbUvZXkd3t+t3ez2xXFRcFa0+To6kU0xuFH/woULERERgYKCAjg5OSEpKQkHDhxA3759sW/fPhNEtD2pBVVo1Ahwc7BDoLuD2HGIqB3oLpKws55pODk54ZNPPkFxcTHOnDmDM2fOoKSkBJ988gmcnZ3FjkfUrv65/SJq6tWIC/XA/b2DxY5DZDEMvsRw9OhR7NmzBz4+PpBKpZBKpRg6dCji4+PxzDPP3ND+lQz352l6bAtKZBt0G11fZGc9k3J2dua2GWTTjl4pxv/O5kIiAd68rzukbEZD1GoGjzip1Wq4umpP8D4+PsjNzQWgbRqRkpJi3HQ2ih31iGxP9LXf95yyWpTXNoichoisUYNag2U/nwcATB8Qiu5B7iInIrIsBhdO3bt3x9mzZwEAAwYMwHvvvYfDhw/jjTfeQGRkpNED2qKLSl3hxI56RLbC3dEeQR6OAK5fPCEiMqYvj2TgUn4VPJ3ssXhslNhxiCyOwYXT0qVLodFoAABvvPEG0tPTMWzYMGzfvh0ffPCB0QPaGkEQ2FGPyEbpLpZwnRMRGVtOWS1W7boEAHjprmh4OMlFTkRkeQxe4zRu3Dj9/3fq1AnJyckoKSmBp6cn1+MYQWGlCiXV9ZBKgC7+HHEisiUxgW74/WIBkpVc50RExiMIApb9dB419Wr0DfPE3/qGiB2JyCIZpf+kl5eXMV6GAFy4dqU5wscZDvYykdMQUXtiZz0iMoUd55X4/WIB7GUSxE/pwYYQRG1k8FQ9Mi1O0yOyXbrOein5lVBrBJHTEJE1qKhrwLKfkwAAT43oiM6czULUZiyczEyykh31iGxVmLczHO1lqGvQIL2oWuw4RGQF3tuRjIJKFcK9nTB/VCex4xBZNBZOZiYpV1s4dWXhRGRzZFIJoq6NOl3gdD2bER4eDolE0uTrnXfeETsWWYGjV4rx9bEsAMA/J/fgEgCi28TCyYzU1quRVlgFAOjWgYUTkS3S/e4n5ZaLnITa0xtvvIG8vDz919NPPy12JLJwNfWNeOmHPwAA0/qHYEgnH5ETEVk+ozSHIOO4qKyARgB8XBTwc3MQOw4RiaBbB+2GlBdyOeJkS1xdXREQECB2DLIiK35LQVZJDTq4O+AfE2LEjkNkFTjiZEZ00/Q42kRku66POFVAENggwla888478Pb2RlxcHFasWIHGxkaxI5EFO5VRgo1HMgAA8ffHwtXBXtxARFaCI05m5MK1qTksnIhsV1SAK2RSCUqq66GsqEOgu6PYkcjEnnnmGfTu3RteXl44cuQIlixZgry8PKxatarZx6tUKqhUKv3tigqOTtJ1NfWNWPzdWQgC8Le+wRjRxVfsSERWgyNOZuT6iJO7yEmISCwO9jJ08nUBACTl8AOxpXr55ZdvaPjw16/k5GQAwKJFizBy5EjExsbiqaeewsqVK/Hhhx82KY7+LD4+Hu7u7vqvkBBuZkrXvbXtIjKKaxDo7oBXJnYVOw6RVeGIk5loUGuQrNTu4cQRJyLb1q2DG1LyK5GUW4ExXf3FjkNt8Pzzz2P27Nm3fExkZGSzxwcMGIDGxkZkZGQgKirqhvuXLFmCRYsW6W9XVFSweCIAwO6L+dh0XNtFb+XUnnB35BQ9ImNi4WQmrhRWob5RAxeFHUK9nMSOQ0Qi6trBDT+eyWFnPQvm6+sLX9+2TZFKTEyEVCqFn59fs/crFAooFIrbiUdWqKhKpe+i99jQCAxmFz0io2PhZCZ0U3K6BrpBKpWInIaIxKSbrpvEznpW7+jRozh+/DhGjRoFV1dXHD16FM899xxmzJgBT09PseORhRAEAS//cA5FVfWI8nfF4nE3jlQS0e1j4WQm9Bvfcpoekc3TvQ/klNWirKYeHk5ykRORqSgUCmzevBmvv/46VCoVIiIi8NxzzzWZikfUki+PZOD3i/mQy6RY/WAvbnRLZCIsnMxEEjvqEdE17o72CPFyRHZJLS7kVnDKjRXr3bs3jh07JnYMsmDnc8rx9nZto5ElE6J5AZbIhNhVzwwIgoALeeyoR0TXdQvkdD0iurUqVSMWbDqNerUGd3b1x+zB4WJHIrJqLJzMQHZJLSrrGiGXSdHZ30XsOERkBq5vhMsGEUR0I0EQsHTLOWQU16CDuwNWPBALiYRrpIlMiYWTGdB9MOoS4AJ7Gf9KiAjoFqQrnDjiREQ3+vp4FrYm5kImleCDaXFcC0nUDvgp3QzoN74N5DQ9ItLSTdu9UliF2nq1yGmIyJwkZJbijf8lAQBeuisKfcO9RE5EZBtYOJkBfWOIIC7oJCItP1cFfFzk0AhAspKjTkSkVVipwt//k4AGtYDx3QPw+LDmN1ImIuNj4SQyQRBwLoeNIYioKYlEon9POJ/DdU5EBDSoNXj6v6eRX6FCR19nrJjak+uaiNoRCyeR5ZXXoahKBTuphK3IiaiJnsHawunsVRZORAS8+csFHEsrgbNchk8f6QMXBXeVIWpPZlE4ffzxxwgPD4eDgwMGDBiAEydO3PSxGzduhEQiafLl4ODQjmmN64+rZQCALv6u3LCOiJqIDfYAcP19gohs17+PZeKro5mQSIDVD/ZCJz9XsSMR2RzRC6dvvvkGixYtwrJly3D69Gn07NkT48aNQ0FBwU2f4+bmhry8PP1XZmZmOyY2Lt2V5NhgTtMjoqZ07wupBVWoVjWKnIaIxHIktQiv/6xtBrF4bBTGdgsQORGRbRK9cFq1ahUef/xxzJkzB127dsW6devg5OSEL7744qbPkUgkCAgI0H/5+/u3Y2LjOqcvnDzEDUJEZsfPzQEBbg7QCGxLTmSr0gqr8PdNp6HWCLivVwf8fWRHsSMR2SxRC6f6+nokJCRgzJgx+mNSqRRjxozB0aNHb/q8qqoqhIWFISQkBPfddx+SkpJu+liVSoWKioomX+ZCEAT9FByOOBFRc3TvDZyuR2R7iqpUmL3hJMpqGtAzxAPv3s9NbonEJGrhVFRUBLVafcOIkb+/P5RKZbPPiYqKwhdffIGffvoJX3/9NTQaDQYPHoyrV682+/j4+Hi4u7vrv0JCQoz+52irjOIaVNQ1QmEnRVQA5yoT0Y16hngAYIMIIltTU9+IRzeeRFZJDUK9nPCvWX25FppIZKJP1TPUoEGDMHPmTPTq1QsjRozAjz/+CF9fX3z66afNPn7JkiUoLy/Xf2VnZ7dz4pvTXUHu2sEN9jKL+6sgonbAESci29Oo1uCZ/57B2avl8HCyx8Y5/eDjohA7FpHNE7WPpY+PD2QyGfLz85scz8/PR0BA6xY+2tvbIy4uDqmpqc3er1AooFCY55vN2WztFeSeXN9ERDcRG+QBAMgsrkFZTT08nOTiBiIikxIEAf/Ycg6/XyyA3E6Kz2f2RaSvi9ixiAgijzjJ5XL06dMHu3fv1h/TaDTYvXs3Bg0a1KrXUKvVOHfuHAIDA00V02R0V5B7BHF9ExE1z93JHmHeTgCAPzhdj8iqCYKAt7dfxLenrkIqAT54KA59w73EjkVE14g+P2zRokVYv349vvzyS1y8eBHz5s1DdXU15syZAwCYOXMmlixZon/8G2+8gZ07dyItLQ2nT5/GjBkzkJmZiccee0ysP0KbNKo1+i5ZPUNYOBHRzem6bp7LYeFEZM0+2XcF6w+mAwDeuT8Wd3Vn23EicyL6ltMPPvggCgsL8dprr0GpVKJXr17YsWOHvmFEVlYWpNLr9V1paSkef/xxKJVKeHp6ok+fPjhy5Ai6du0q1h+hTVILq1DboIaLwg6RPhyCJ6Kb6xnsjv+dzcXZ7DKxoxCRiWw4nI4Vv6UAAJZOjMHf+ppPMysi0hK9cAKABQsWYMGCBc3et2/fvia3V69ejdWrV7dDKtP649r6pu5BbpBK2VqUiG5ON+LEqXpE1umroxlY/r8LAIBnRnfCY8MiRU5ERM0RfaqerTp7bX0TG0MQUUu6B7lBKgGUFXUoqKgTOw4RGdF/jmfitZ+0+1E+NaIjnruzi8iJiOhmWDiJRHflOJaFExG1wEluh85+2r3euJ8TkfX4+lgmXtlyHgDwxPBIvHRXFDe4JTJjLJxEUFuvxsU8NoYgotbTvVeczioVOQkRGcPnB9OwdKu2aJo7JAJLxkezaCIycyycRJCYXYZGjYAANwcEeTiKHYeILEDfMG1L4oQMFk5ElkwQBLz/+2W8te0iAGDeyI549e4YFk1EFsAsmkPYmoTMEgBAn3BPvlESUav0CfcEoF0fWd+ogdyO172ILI1Go92n6fND2pbji8d2wYLRnUVORUStxTOvCE5laq8Y9w3zFDkJEVmKSB9neDnLoWrU4Hwu1zkRWZr6Rg0WfZuoL5qWToxh0URkYVg4tTONRsBpfeHE3cCJqHUkEgl6h2ovtnC6HpFlqVI14tEvT2JrYi7spBKs+ltPthwnskAsnNrZ5YIqVNQ1wkkuQ0ygq9hxiMiC9L02Xe/Utem+RGT+8spr8bd1R3HwchGc5DJ8PqsvpvQOFjsWEbUB1zi1M90Hnl4hHrCTsW4lotbTTe9NyCyFIAhcI0lk5s7nlOPRL08iv0IFHxc5/jWrH3qGeIgdi4jaiJ/c25luig3XNxGRoboHuUMuk6Koqh6ZxTVixyGiW/gtSYmp644iv0KFLv4u2PL3ISyaiCwcC6d2pmsM0Sec65uIyDAO9jL0CNbu56R7LyEi86LRCFi96xKe/HcCahvUGNbZB9/PG4wQLyexoxHRbWLh1I4KKuuQVVIDiQSIC/UQOw4RWaA/T9cjIvNSWdeAJ/6dgPd3XwYAzB4cjg2z+8HNwV7kZERkDFzj1I503fSi/F35JkpEbdJHXzixQQSROUlRVmLefxKQVlgNuZ0Ub0/ugQf6sAkEkTVh4dSOTunWN4VzfRMRtY2ucLqUX4Xymga4O/EiDJHYvk+4iqVbz6GuQYNAdwesm9GH65mIrBCn6rWjU9y/iYhuk7eLApE+zgCA01mcrkckppr6Rrz4/Vks/u4s6ho0GN7FF9ueGcaiichKsXBqJ9WqRpzPKQdw/YoxEVFb6N5DjqUXi5yEyHadu1qOuz84hG9PXYVEAiy6sws2zu4HL2e52NGIyEQ4Va+dHE8vRqNGQIiXIzvrENFtGdzJG98lXMXh1CKxoxDZHLVGwOcH0/B/O1PQoBYQ4OaAVQ/2xOCOPmJHIyITY+HUTg5e1n7AGdrJV+QkRGTphnTSfkBLyq1ASXU9r3ATtZPM4mos/u4sTl5bs3xXtwC8c38PeDjxd5DIFnCqXjvRXRke1plXpIjo9vi5OiA6wBWCABy5wlEnIlPTaAT8+1gm7lpzECczSuEsl+GdKT2wdkZvFk1ENoQjTu0gv6IOl/KrIJEAgyK9xY5DRFZgSCcfJCsrcehyEe6O7SB2HCKrlVZYhZd/PIcT6dotAAZGemHFAz057Z7IBrFwageHrk3T6xHkDk9OqSEiIxja2Qf/OpSOg5eLIAgCJBKJ2JGIrEqDWoP1B9Ow5vfLqG/UwNFehhfvisKsQeGQSvn7RmSLWDi1g0OpuvVNnKZHRMYxIMILcpkUOWW1yCiuQcS1FuVEdPuOpxVj6dbzuFxQBUA7zf7tyT04ykRk41g4mZggCNcLJ65vIiIjcZLboXeYB46lleBQahELJyIjKKiswzu/JuPH0zkAAC9nOV6ZEIMpvYM4qktELJxM7VJ+FQorVXCwl3L/JiIyqqGdfLSF0+VCPDIwTOw4RBZL1ajGxsMZ+HBPKqpUjZBIgGn9Q/HiuCg2fyAiPRZOJnbwciEAoH+ENxR2MpHTEJE1GdrZF/+38xKOXClGo1oDOxkbpRIZQhAE/JaUj3d+vYiM4hoAQM9gd7x+bzfEhfJiJxE1xcLJxHTT9IZxfRMRGVmPIHe4O9qjvLYBf+SUozc/6BG12umsUry97SJOZWr3ZPJxUeClu6Jwf+9gNn8gomaxcDIhVaMax9O07Uu5vomIjE0mlWBwR2/8el6Jg5eKWDgRtcLl/Eqs3HkJO5KUAACFnRSPDYvAUyM6wtXBXuR0RGTOWDiZ0KHLRahtUMPfTYEof1ex4xCRFRoZ5Ytfzyux84ISC8d0FjsOkdnKKq7Bmt2XsOVMDgQBkEiA+3sH4/mxXRDo7ih2PCKyACycTGjbH3kAgPHdAznsT0QmcWfXAPxjy3kk5VYgo6ga4eyuR9RERlE1Ptqbii1ncqDWCACAu7oFYNHYLujCi5pEZAAWTiaialRj14V8AMDE2ECR0xCRtfJylmNwR28cvFyEbefyMH9UJ7EjEZmFS/mVWLfvCn46m6svmIZ38cXzd3ZBzxAPccMRkUVi4WQihy4XoVLVCH83Bfpw3QERmdCEHoE4eLkI21k4EeF0VinW7ruiv3gJaKe0LryjMzvlEdFtYeFkItvOcZoeEbWPcd0CsHSrdrpeZnE1wrw5XY9si1ojYNeFfHx+ME3fJU8iAcZ1DcC8kR05wkRERsHCyQT+PE1vQg9O0yMi0/JylmNQpDcOpWqn6/19JEedyDZU1DXgu1NX8dXRDGRe24fJXibBpF5BeHJER3TycxE5IRFZExZOJnA4tQiVdY3wc1WgbxinBRCR6U2MDcShVO10PRZOZO0u5Vfi62OZ+CHhKqrr1QAAd0d7zBgYilmDwuHn5iByQiKyRiycTGDbH9q9ISb04DQ9Imofuul653MqkFVcg1BvJ7EjERlVXYMavyUp8Z/jWTiRXqI/3tnPBbOHhGNyXBCc5PxYQ0Smw3cYI6tv1GDXheuFExFRe/jzdL1fzuVy1ImsRoqyEt+czMaPZ66irKYBgHbz5ztj/PHIoDAM7ugNiYQXKYnI9Fg4Gdm2c7moqNN20+M0PSJqT3dfm673zclsPDm8I2Qc8SYLVVZTj5/P5uL7hKv442q5/niguwP+1jcE0/qHIsCd0/GIqH2xcDIiQRDw2YF0AMDMQeGcpkdE7ereXh3wzo5kZBbXYNcFJe7qzlFvshyqRjX2Jhdgy5kc7E0uRL1aAwCwk0owOtoP0/qHYngXX14QICLRsHAyosOpxbiYVwEnuQzTB4SKHYeIbIyT3A6PDAzDh3tS8dmBNBZOZuCf//wntm3bhsTERMjlcpSVld3wmKysLMybNw979+6Fi4sLZs2ahfj4eNjZWf8pulGtwdG0YvzvbC52nFeioq5Rf19MoBum9gnGfb06wNtFIWJKIiIt639XbkefHUwDAPytbwg8nOQipyEiWzRzUDg+3Z+G01llSMgsQZ8wL7Ej2bT6+npMnToVgwYNwr/+9a8b7ler1Zg4cSICAgJw5MgR5OXlYebMmbC3t8fbb78tQmLTa1RrcDy9BNvO5eG380oUV9fr7wtwc8B9cR0wqVcQYgLdRExJRHQjFk5GkqyswIFLhZBKgEeHRogdh4hslK+rApPjgvDNqWx8diANnz7CwklMy5cvBwBs3Lix2ft37tyJCxcu4Pfff4e/vz969eqFN998Ey+99BJef/11yOXWcRGurkGNw6lF+C1Jid8vFqDkT8WSp5M9JvQIxD09O6BfuBen4hGR2WLhZCSfH9SubRrfPRAhXmwDTETieWxYBL45lY2dF/KRUVSNcB9nsSPRTRw9ehQ9evSAv7+//ti4ceMwb948JCUlIS4uTsR0t6ekuh57kwvw+8V8HLhUqN9vCdAWS+O6BWB8j0AM7ugNe5lUxKRERK3DwskIsktq8FNiDgDtBxYiIjF19nfF6Gg/7EkuwNp9V/DuA7FiR6KbUCqVTYomAPrbSqWy2eeoVCqoVCr97YqKCtMFNIAgCLiYV4m9KQXYm1yA01ml0AjX7w90d8DYrv4Y2y0AAyK8YMdiiYgsDAun29Sg1uDZbxLRoBYwMNILcaFsQU5E4ntqREfsSS7AN6eycWdXf4zp6t/yk6hVXn75Zbz77ru3fMzFixcRHR1tku8fHx+vnwIotrKaehy8XIQDlwpx4HIh8itUTe7vGuiGMTF+uCPGH7HB7txviYgsGgun27Rq1yUkZJbC1cEOKx7oKXYcIiIAQP8IL8wdEoEvDqdj8fdnsf2ZYejg4Sh2LKvw/PPPY/bs2bd8TGRkZKteKyAgACdOnGhyLD8/X39fc5YsWYJFixbpb1dUVCAkJKRV3+921TWocTqrFIcuF+FQahHO5ZRD+NOokqO9DEM6eWNklB9GRfshiP/miMiKmEXh9PHHH2PFihVQKpXo2bMnPvzwQ/Tv3/+mj//uu+/w6quvIiMjA507d8a7776LCRMmtGNirQOXCrF23xUAwLv3x3JtExGZlZfHR+NUZgn+uFqOhZvP4L+PD+T0KCPw9fWFr6+vUV5r0KBB+Oc//4mCggL4+fkBAHbt2gU3Nzd07dq12ecoFAooFO3Tnru+UYM/rpbhWFoxjlwpxqnMUtQ3apo8pou/C0Z08cWILn7oG+4JB3tZu2QjImpvohdO33zzDRYtWoR169ZhwIABWLNmDcaNG4eUlBT9SeTPjhw5gmnTpiE+Ph533303Nm3ahEmTJuH06dPo3r17u2TWaATsv1SIF74/CwCYMTAUE3pwvxQiMi9yOyk+nBaHiR8cwsmMUiz58RxeGBcFPzcHsaPZjKysLJSUlCArKwtqtRqJiYkAgE6dOsHFxQVjx45F165d8cgjj+C9996DUqnE0qVLMX/+/HYrjv6stl6NM9mlOJleihMZxUjILEVdQ9NCyc9VgSGdfDC0kw+GdvaBP/89EZGNkAjCnwfZ29+AAQPQr18/fPTRRwAAjUaDkJAQPP3003j55ZdvePyDDz6I6upq/PLLL/pjAwcORK9evbBu3boWv19FRQXc3d1RXl4ONzfD9ohQNarx05lcrD+YhssFVQCA6ABXbJ0/hFfYiMhs/fJHLhZsOgMAkMukmBTXAY8Pi0Rnf1eDX+t23kNt0ezZs/Hll1/ecHzv3r0YOXIkACAzMxPz5s3Dvn374OzsjFmzZuGdd95p9Qa4t/N3UlylwsmMEpzKKMWpzFIk5ZajQd30Y4G3sxwDIr0wMNIbgzv6oKOvM9cqEZHVMOQ9VNQRp/r6eiQkJGDJkiX6Y1KpFGPGjMHRo0ebfc7Ro0ebzO0GtK1bt27d2uzjjdl96PWfL+C/J7IAAC4KO0zrH4KnRnRk0UREZu3u2A5wltvho72pSMgsxbenruK7hKs49NJorkExsY0bN950DyedsLAwbN++vX0C/cWm41lYuetSk2MBbg7oF+GF/hFeGBDhhc5+LiyUiIggcuFUVFQEtVrdbCvW5OTkZp9zs9atN2vbaszuQw/3D8Xe5ALMHRqOh/qHws3B3iivS0RkaqOitYv1EzJLsP5AOho1GhZNhH4RXojyd0WfcE/0C/dE3zAvBHs6slAiImqG6GucTM2Y3Yd6BLvj0EujuLiaiCxWnzAv9HnEC41qTcsPJqs3MNIbvz03XOwYREQWQdTCycfHBzKZTN96VSc/P/+mbVgDAgIMeryxuw+xaCIia8D3MiIiIsOIeuaUy+Xo06cPdu/erT+m0Wiwe/duDBo0qNnnDBo0qMnjAW3r1ps9noiIiIiI6HaJPlVv0aJFmDVrFvr27Yv+/ftjzZo1qK6uxpw5cwAAM2fORFBQEOLj4wEACxcuxIgRI7By5UpMnDgRmzdvxqlTp/DZZ5+J+ccgIiIiIiIrJnrh9OCDD6KwsBCvvfYalEolevXqhR07dugbQGRlZUEqvT4wNnjwYGzatAlLly7FP/7xD3Tu3Blbt25ttz2ciIiIiIjI9oi+j1N74x4kRERtx/dQ88O/EyKitjPkPZSrg4mIiIiIiFrAwomIiIiIiKgFLJyIiIiIiIhawMKJiIiIiIioBSyciIiIiIiIWsDCiYiIiIiIqAWi7+PU3nTd1ysqKkROQkRkeXTvnTa2k4VZ43mNiKjtDDmv2VzhVFlZCQAICQkROQkRkeWqrKyEu7u72DEIPK8RERlDa85rNrcBrkajQW5uLlxdXSGRSAx+fkVFBUJCQpCdnc2NBluBPy/D8WdmGP68DHc7PzNBEFBZWYkOHTpAKuVsb3PA81r74s/LcPyZGYY/L8O113nN5kacpFIpgoODb/t13Nzc+I/ZAPx5GY4/M8Pw52W4tv7MONJkXnheEwd/Xobjz8ww/HkZztTnNV4uJCIiIiIiagELJyIiIiIiohawcDKQQqHAsmXLoFAoxI5iEfjzMhx/Zobhz8tw/JnRn/Hfg2H48zIcf2aG4c/LcO31M7O55hBERERERESG4ogTERERERFRC1g4ERERERERtYCFExERERERUQtYOBEREREREbWAhZMBPv74Y4SHh8PBwQEDBgzAiRMnxI5ktg4cOIB77rkHHTp0gEQiwdatW8WOZNbi4+PRr18/uLq6ws/PD5MmTUJKSorYscza2rVrERsbq9/sbtCgQfj111/FjmUx3nnnHUgkEjz77LNiRyER8bzWejyvGYbnNcPxvHZ72uO8xsKplb755hssWrQIy5Ytw+nTp9GzZ0+MGzcOBQUFYkczS9XV1ejZsyc+/vhjsaNYhP3792P+/Pk4duwYdu3ahYaGBowdOxbV1dViRzNbwcHBeOedd5CQkIBTp05h9OjRuO+++5CUlCR2NLN38uRJfPrpp4iNjRU7ComI5zXD8LxmGJ7XDMfzWtu123lNoFbp37+/MH/+fP1ttVotdOjQQYiPjxcxlWUAIGzZskXsGBaloKBAACDs379f7CgWxdPTU/j888/FjmHWKisrhc6dOwu7du0SRowYISxcuFDsSCQSntfajuc1w/G81jY8r7WsPc9rHHFqhfr6eiQkJGDMmDH6Y1KpFGPGjMHRo0dFTEbWqry8HADg5eUlchLLoFarsXnzZlRXV2PQoEFixzFr8+fPx8SJE5u8n5Ht4XmN2hvPa4bhea312vO8Zmfy72AFioqKoFar4e/v3+S4v78/kpOTRUpF1kqj0eDZZ5/FkCFD0L17d7HjmLVz585h0KBBqKurg4uLC7Zs2YKuXbuKHctsbd68GadPn8bJkyfFjkIi43mN2hPPa63H85ph2vu8xsKJyMzMnz8f58+fx6FDh8SOYvaioqKQmJiI8vJyfP/995g1axb279/Pk0wzsrOzsXDhQuzatQsODg5ixyEiG8LzWuvxvNZ6YpzXWDi1go+PD2QyGfLz85scz8/PR0BAgEipyBotWLAAv/zyCw4cOIDg4GCx45g9uVyOTp06AQD69OmDkydP4v3338enn34qcjLzk5CQgIKCAvTu3Vt/TK1W48CBA/joo4+gUqkgk8lETEjtiec1ai88rxmG57XWE+O8xjVOrSCXy9GnTx/s3r1bf0yj0WD37t2cd0pGIQgCFixYgC1btmDPnj2IiIgQO5JF0mg0UKlUYscwS3fccQfOnTuHxMRE/Vffvn0xffp0JCYmsmiyMTyvkanxvGYcPK/dnBjnNY44tdKiRYswa9Ys9O3bF/3798eaNWtQXV2NOXPmiB3NLFVVVSE1NVV/Oz09HYmJifDy8kJoaKiIyczT/PnzsWnTJvz0009wdXWFUqkEALi7u8PR0VHkdOZpyZIlGD9+PEJDQ1FZWYlNmzZh3759+O2338SOZpZcXV1vWFvg7OwMb29vrjmwUTyvGYbnNcPwvGY4ntcMI8p5zWT9+qzQhx9+KISGhgpyuVzo37+/cOzYMbEjma29e/cKAG74mjVrltjRzFJzPysAwoYNG8SOZrbmzp0rhIWFCXK5XPD19RXuuOMOYefOnWLHsihsR048r7Uez2uG4XnNcDyv3T5Tn9ckgiAIpinJiIiIiIiIrAPXOBEREREREbWAhRMREREREVELWDgRERERERG1gIUTERERERFRC1g4ERERERERtYCFExERERERUQtYOBEREREREbWAhRORgfbt2weJRIKysjJRvv/u3bsRExMDtVptlNd7+eWX8fTTTxvltYiIyPLwvEbUOtwAl+gWRo4ciV69emHNmjX6Y/X19SgpKYG/vz8kEkm7Z+rTpw8WLVqE6dOnG+X1ioqKEBkZicTERERGRhrlNYmIyDzxvEbUdhxxIjKQXC5HQECAKCeXQ4cO4cqVK7j//vuN9po+Pj4YN24c1q5da7TXJCIiy8HzGlHrsHAiuonZs2dj//79eP/99yGRSCCRSJCRkXHDlIaNGzfCw8MDv/zyC6KiouDk5IQHHngANTU1+PLLLxEeHg5PT08888wzTaYhqFQqLF68GEFBQXB2dsaAAQOwb9++W2bavHkz7rzzTjg4ODTJOWnSpCaPe/bZZzFy5Ej97e+//x49evSAo6MjvL29MWbMGFRXV+vvv+eee7B58+Y2/6yIiMj88bxGdHvsxA5AZK7ef/99XLp0Cd27d8cbb7wBAPD19UVGRsYNj62pqcEHH3yAzZs3o7KyElOmTMHkyZPh4eGB7du3Iy0tDffffz+GDBmCBx98EACwYMECXLhwAZs3b0aHDh2wZcsW3HXXXTh37hw6d+7cbKaDBw/i4YcfNujPkZeXh2nTpuG9997D5MmTUVlZiYMHD+LPs3T79++Pq1evIiMjA+Hh4Qa9PhERWQae14huDwsnoptwd3eHXC6Hk5MTAgICbvnYhoYGrF27Fh07dgQAPPDAA/j3v/+N/Px8uLi4oGvXrhg1ahT27t2LBx98EFlZWdiwYQOysrLQoUMHAMDixYuxY8cObNiwAW+//Xaz3yczM1P/+NbKy8tDY2MjpkyZgrCwMABAjx49mjxG95qZmZk8wRARWSme14huDwsnIiNwcnLSn1wAwN/fH+Hh4XBxcWlyrKCgAABw7tw5qNVqdOnSpcnrqFQqeHt73/T71NbWNpnO0Bo9e/bEHXfcgR49emDcuHEYO3YsHnjgAXh6euof4+joCEB7hZGIiIjnNaIbsXAiMgJ7e/smtyUSSbPHNBoNAKCqqgoymQwJCQmQyWRNHvfnk9Jf+fj4oLS0tMU8f55zLpPJsGvXLhw5cgQ7d+7Ehx9+iFdeeQXHjx9HREQEAKCkpASAdsoGERERz2tEN2JzCKJbkMvlRttX4s/i4uKgVqtRUFCATp06Nfm61fSJuLg4XLhw4Ybj+fn5TW6npaU1uS2RSDBkyBAsX74cZ86cgVwux5YtW/T3nz9/Hvb29ujWrdtt/smIiMic8bxG1HYccSK6hfDwcBw/fhwZGRlwcXGBl5eXUV63S5cumD59OmbOnImVK1ciLi4OhYWF2L17N2JjYzFx4sRmnzdu3Dh8+eWXNxw/fvw41q9fjzvuuAN79uzBb7/9ho4dOyI9PR0FBQXYvXs3xo4dCz8/Pxw/fhyFhYWIiYnRP//gwYMYNmyYfmoDERFZJ57XiNqOI05Et7B48WLIZDJ07doVvr6+yMrKMtprb9iwATNnzsTzzz+PqKgoTJo0CSdPnkRoaOhNnzN9+nQkJSUhJSWlyfFRo0bhhx9+QExMDNavX48NGzYgLy8PK1asgJubGw4cOIAJEyagS5cuWLp0KVauXInx48frn79582Y8/vjjRvuzERGReeJ5jajtJMKfezcSkdl74YUXUFFRgU8//RSAdr+LsrIybN26tU2v9+uvv+L555/HH3/8ATs7DkITEVH74nmNLAVHnIgszCuvvIKwsDD9gtzbVV1djQ0bNvDkQkREouB5jSwFR5yILNztXpkjIiIyJzyvkbli4URERERERNQCTtUjIiIiIiJqAQsnIiIiIiKiFrBwIiIiIiIiagELJyIiIiIiohawcCIiIiIiImoBCyciIiIiIqIWsHAiIiIiIiJqAQsnIiIiIiKiFrBwIiIiIiIiasH/A0DLKgNKbwHfAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_time = np.linspace(0, time_max, 100)\n",
    "\n",
    "# These parameters are chosen arbitrarily for demonstration purpose.\n",
    "# The readers are encouraged to try out other parameters!\n",
    "amplitude_param = [amplitude_max, 10]\n",
    "detuning_param = [detuning_max * 2 / 3, 1.45]\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "axes[0].plot(vis_time, [ryd_amplitude(amplitude_param, t) for t in vis_time])\n",
    "axes[0].set_xlabel(\"time (μs)\")\n",
    "axes[0].set_ylabel(\"amplitude (MHz)\")\n",
    "axes[1].plot(vis_time, [ryd_detuning(detuning_param, t) for t in vis_time])\n",
    "axes[1].set_ylabel(\"detuning (MHz)\")\n",
    "axes[1].set_xlabel(\"time (μs)\")\n",
    "fig.subplots_adjust(wspace=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c33f2a76-77e9-4fb5-9484-131d0d2bffeb",
   "metadata": {},
   "source": [
    "We construct the parametrized function for the global driving field for the Rydberg atoms out of the amplitude and detuning functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "61166af7-c3f1-40f8-88f0-6451903d1e82",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "\n",
    "global_drive = qml.pulse.rydberg_drive(\n",
    "    amplitude=ryd_amplitude, phase=0, detuning=ryd_detuning, wires=range(len(coords))\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f236b78a-ebbc-4eb7-a62c-6bf926b708d1",
   "metadata": {},
   "source": [
    "For simplicity, we have fixed the `phase`, another time-dependent parameter for Rydberg devices, to be zero. The full Rydberg Hamiltonian is the sum of the driving field and the Rydberg interaction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "499e1f61-5ba9-4149-a0c2-5f03b7356368",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "H_ryd = global_drive + qml.pulse.rydberg_interaction(coords, interaction_coeff=C6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9e0ce72-e72f-4f24-94a4-0162f6446ec7",
   "metadata": {},
   "source": [
    "## Simulating anti-ferromagnetic order with Rydberg atoms\n",
    "\n",
    "We have created a time-dependent, parameterized Rydberg Hamiltonian. Now let us check if it can realize the AFM order. For that, we define the following parametrized AHS program.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69f63279-8fc4-4c5d-8ee6-4af44f1ff080",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ts = [0, time_max]\n",
    "\n",
    "\n",
    "def program(detuning_param, amplitude_param=amplitude_param, ts=ts):\n",
    "    qml.evolve(H_ryd)([amplitude_param, detuning_param], ts)\n",
    "    return qml.counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3708356e-a99b-4a3e-8e05-9e4f0522bc91",
   "metadata": {},
   "source": [
    "Here [qml.evolve](https://docs.pennylane.ai/en/stable/code/api/pennylane.evolve.html) returns a [ParametrizedEvolution](https://docs.pennylane.ai/en/stable/code/api/pennylane.pulse.ParametrizedEvolution.html) object which has the same set of parameters as the parametrized Hamiltonian `H_ryd`. The `program` takes in the parameters for detuning, the only necessary parameters, and outputs the measurement outcome of the AHS program. Below, we will optimize the parameters of the detuning while keeping those for the amplitude fixed. The AHS program can be run on the PennyLane simulator as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "49a0c3a8-7abb-406c-8c51-b80a59027e78",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "shots = 1000\n",
    "\n",
    "# Introduce the PennyLane local simulator\n",
    "simulator_pl = qml.device(\"default.qubit.jax\", wires=len(coords), shots=shots)\n",
    "\n",
    "# Define the qnode that runs the AHS program\n",
    "program_pl = qml.QNode(program, simulator_pl, interface=\"jax\")\n",
    "\n",
    "# Run the program with a specific set of parameters for the detuning\n",
    "counts_pl = program_pl(detuning_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda789ce-b909-43c6-bd68-e75e8833d244",
   "metadata": {},
   "source": [
    "We plot the probability of Rydberg state for each site, averaged over all the shots, for the results from the PennyLane and AWS local simulators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1c72a0c6-4c75-42e6-a098-a443acf867bf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_prob(counts):\n",
    "    \"\"\"Helper function for calculating the Rydberg probability averaged over all the shots\"\"\"\n",
    "    prob = np.zeros(9)\n",
    "    total_shots = 0  # Total number of shots in the counts\n",
    "    for key, val in counts.items():\n",
    "        prob += np.array([int(bit) for bit in [*key]]) * val\n",
    "        total_shots += val\n",
    "    prob /= total_shots\n",
    "    return prob\n",
    "\n",
    "\n",
    "prob_pl = get_prob(counts_pl)\n",
    "\n",
    "fig, axs = plt.subplots(1, 1)\n",
    "axs.bar(range(len(coords)), prob_pl)\n",
    "axs.set_xlabel(\"Indices of atoms\")\n",
    "axs.set_ylabel(\"Average probability\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6968da0e-eaf4-4a30-a5ad-093f71b9e368",
   "metadata": {},
   "source": [
    "Below we will focus on the PennyLane local simulator, which supports the JAX interface for differentiable programming. \n",
    "\n",
    "For a chain of atoms, the average Rydberg probability of the ideal AFM order forms an alternating pattern of zeros and ones. In particular, atoms in the odd-index and even-index sites tend to be in the ground and Rydberg states, respectively. From the above plots, we see that the AHS program approximately produces the AFM state of interest. The discrepancy, which is more prominent at the center of the chain, can be attributed to the non-adiabaticity during the evolution. The AFM order obtained can be improved further by tuning, the detuning field, however,but manually searching through the parameter space is expensive. We now show that the differentiable programming can be helpful in this scenario. \n",
    "\n",
    "## Cost function for anti-ferromagnetic order\n",
    "\n",
    "To optimize the AHS program, we need to define a cost function, which characterizes the \"quality\" of the AFM order. The cost function is defined as follows (the label of atoms starts from $0$)\n",
    "\\begin{align}\n",
    "H_\\text{cost} = \\sum_{i=0}^7\\left(x_i-\\frac{1}{2}\\right)\\left(x_{i+1}-\\frac{1}{2}\\right).\n",
    "\\end{align}\n",
    "We will use binary variables $x_i$ to represent the states of the atoms: $x_i=1$ when the $i$-th atom is in the Rydberg state, otherwise $x_i=0$. When two neighboring atoms occupy ground and Rydberg states respectively, they form a domain wall, and the above cost function counts the number of domain walls in the atomic chain. For an ideal AFM order, each domain wall contributes $-\\frac{1}{4}$ to the cost function, and for the nine-atom chain, the cost function is evaluated to be $H_\\text{cost}=-2$. \n",
    "\n",
    "The cost function can be specified as follows.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "58f53617-7690-4d3d-b833-145b20f834b7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Initialize the cost function\n",
    "H_cost = 0\n",
    "for i in range(len(coords) - 2):\n",
    "    # Add the contribution from each domain wall\n",
    "    H_cost += qml.prod(\n",
    "        qml.Projector([1], wires=[i]) - 1 / 2, qml.Projector([1], wires=[i + 1]) - 1 / 2\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90aa2743-5735-446f-b566-e4b4e41b65e8",
   "metadata": {},
   "source": [
    "Here we use the [Projector](https://docs.pennylane.ai/en/stable/code/api/pennylane.Projector.html) in PennyLane to represent the Boolean variables. For example, `qml.Projector([0], wires=[1])` represents $x_1=0$  and `qml.Projector([1], wires=[2])` represents $x_2=1$. The product between the Boolean variables is realized with [qml.prod](https://docs.pennylane.ai/en/stable/code/api/pennylane.prod.html).\n",
    "\n",
    "## Variational analog Hamiltonian simulation program with PennyLane\n",
    "\n",
    "With the cost Hamiltonian defined, we can create a variational AHS program, which evolves the Rydberg system followed by measuring the cost function $H_\\text{cost}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "94cb8760-1ee5-4ed3-8f3d-cd64f6103e12",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Define the PennyLane local simulator\n",
    "dev = qml.device(\"default.qubit.jax\", wires=range(len(coords)))\n",
    "\n",
    "\n",
    "# Define the qnode that evolves the Rydberg system, followed by calculating the cost function\n",
    "@qml.qnode(dev, interface=\"jax\")\n",
    "def program_cost(detuning_param, amplitude_param=amplitude_param, ts=ts):\n",
    "    qml.evolve(H_ryd)([amplitude_param, detuning_param], ts)\n",
    "    return qml.expval(H_cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21ef2d41-070c-471e-88c0-f760039176e6",
   "metadata": {},
   "source": [
    "We note again that `program_cost` is a parametrized AHS program that has only one positional argument, the parameters for the detuning, and outputs the cost function $H_\\text{cost}$. With the JAX interface, we can optimize the detuning to minimize the cost function. We use `detuning_param` defined above as the initial parameter for the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "86837d12-ecfa-4619-aa60-3daf97c34b5c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The initial parameter for detuning = [13.262911924324612, 1.45]\n",
      "The initial cost value             = -1.4220786805245207\n"
     ]
    }
   ],
   "source": [
    "theta = detuning_param.copy()\n",
    "initial_cost = program_cost(theta)\n",
    "print(f\"The initial parameter for detuning = {theta}\")\n",
    "print(f\"The initial cost value             = {initial_cost}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86b4867e-f89c-4ea1-b300-0cb68d101b73",
   "metadata": {},
   "source": [
    "We see that the initial cost function is evaluated to be approximately $-1.422$, which is larger than $-2$, the expected value for the ideal AFM order. This is consistent with our finding that the corresponding state is not an ideal AFM order. To minimize the cost function $H_\\text{cost}$, we first introduce a JAX function that calculates the expectation value and its gradient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "31608fa5-7aa9-483d-a86e-35226c2df28f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "value_and_grad = jax.jit(jax.value_and_grad(program_cost))\n",
    "\n",
    "# Compile the value_and_grad function\n",
    "_, _ = value_and_grad(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98964114-0922-41ff-89d0-2ca34b8d6101",
   "metadata": {},
   "source": [
    "Next, we define the learning rate schedule, followed by using the `nadam` implementation in [optax](https://optax.readthedocs.io/en/latest/) for optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b97cc48b-86ad-4b33-80d1-9d771afcf34e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import optax\n",
    "\n",
    "n_epochs = 10\n",
    "\n",
    "# The following block creates a constant schedule of the learning rate\n",
    "# that increases from 0.1 to 0.5 after 10 epochs\n",
    "schedule0 = optax.constant_schedule(1e-1)\n",
    "schedule1 = optax.constant_schedule(5e-1)\n",
    "schedule = optax.join_schedules([schedule0, schedule1], [10])\n",
    "optimizer = optax.nadam(learning_rate=schedule)\n",
    "opt_state = optimizer.init(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa179767-fb9c-4b97-831e-d1387b38bd58",
   "metadata": {},
   "source": [
    "Now we are ready to run the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d24a0108-5242-4a30-bd38-98315f289a7a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch  expectation\n",
      "0     -1.4220786805245293\n",
      "1     -1.4440255545399934\n",
      "2     -1.4682669156813517\n",
      "3     -1.494929936649468\n",
      "4     -1.52414541861693\n",
      "5     -1.5561124234490418\n",
      "6     -1.590274680470023\n",
      "7     -1.6261105967628833\n",
      "8     -1.6618436930215126\n",
      "9     -1.695197967500683\n",
      "The final parameter for detuning = [12.268508609205842, 0.4353973115231312]\n"
     ]
    }
   ],
   "source": [
    "energy = np.zeros(n_epochs + 1)\n",
    "energy[0] = program_cost(theta)\n",
    "gradients = np.zeros(n_epochs)\n",
    "\n",
    "## Optimization loop\n",
    "print(\"epoch  expectation\")\n",
    "for n in range(n_epochs):\n",
    "    val, grad_program = value_and_grad(theta)\n",
    "    updates, opt_state = optimizer.update(grad_program, opt_state)\n",
    "    theta = optax.apply_updates(theta, updates)\n",
    "\n",
    "    energy[n + 1] = val\n",
    "    gradients[n] = np.mean(np.abs(grad_program))\n",
    "\n",
    "    print(n, \"   \", val)\n",
    "\n",
    "print(f\"The final parameter for detuning = {[float(i) for i in theta]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2660f7bd-8862-449c-9893-d98f14146511",
   "metadata": {},
   "source": [
    "We see that the expectation $H_\\text{cost}$ is indeed gradually decreasing as expected. In order to reach the expected valued $-2$, we encourage the interested readers to try larger number of epochs or different optimization schedules. By construction, a larger absolute value of $H_\\text{cost}$ corresponds to a sharper alternating pattern for the Rydberg probability. To confirm that, we calculate the Rydberg probability with the optimized detuning, followed by comparing the Rydberg probability before and after the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "79639ebd-043f-4d49-a432-764627b39fbe",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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mFJvRLfL8H066xpDKTNfvyYv87ly5cgUDBgzAG2+8gS+//FLrvXv37sHX1xfW1taYNWsWGjduDJVKhcTEREyaNIljg5Ew3FRCT548AQDNCauNGzfGvn370KlTpzINGg0aNIBarUZKSorWiaqZmZm4d+8eGjRo8I99NG7cGPfv34efn1+Ztg88PVG5UaNGmvaCggJcuXKlWJ83btwo9lfGhQsXAEBzUpy+Qa08zZs3Dz///DO2b9+OFi1aFHt/69atCAoKwoIFCzRtjx49wr1797SWM2RfGjRogFOnTkGtVmv9tVs0la3Pf0uSpg0bNsDOzg5Lly4t9t727duxY8cOREdHlziGlPQ9LPqdtbCwKNPvf2kM/T6npKQU6+PChQtaJ8uaemx4+PAh3nnnHdja2uKnn34qNisVHx+P27dvY/v27VonJj8721ZE3315dox9XnJyMurUqVNsNlzqeM5NJfP48WP8+uuvUCgUmiDSr18/FBYWYvbs2cWWf/LkSbH/s3xez549AaDYFU2RkZEAgF69ev1jXf369UNCQgL27t1b7L179+5pApkufn5+UCgUWLRokdZfBatWrUJ2dnax7T958gTff/+95ueCggJ8//33qFu3Ljw9PQFA84v6T/teXvbt24epU6diypQp6Nu3r85l5HJ5sb+CFi9eXOzcB0P2pWfPnsjIyEBMTIym7cmTJ1i8eDGsrKzg6+tr2I6QJDx8+BDbt29H79698d577xV7hYSEIDc3Fzt37iyxj2rVqgEo/j20s7NDt27d8P333yM9Pb3Yejdv3ixz3YZ+n3/++Wet83uOHj2KI0eOoEePHpo2U48Nn3zyCS5cuIAdO3Zone9WpGjG5NmxoaCgAN99912xZatXr67XYSpHR0d4eHhg3bp1Wvt95swZ/Prrr5r/D3iZcObGxP773/9q/krJysrCxo0bkZKSgsmTJ2sOc/j6+mLkyJGIiIhAUlIS3nzzTVhYWCAlJQVbtmzBt99+i/fee6/EbbRp0wZBQUFYvny5Zkr06NGjWLduHfr27as5+bA0n3/+OXbu3InevXtj0KBB8PT0RF5eHk6fPo2tW7ciNTW12PHpInXr1kVYWBhmzpyJt956CwEBATh//jy+++47tGvXrthl705OTvjqq6+QmpqKZs2aISYmBklJSVi+fLnm8uXGjRvD1tYW0dHRqFGjBqpXrw5vb2+9j/W/qMDAQNStWxdNmzbFjz/+qPXeG2+8AXt7e/Tu3Rs//PADbGxs4ObmhoSEBOzbt09zqXgRDw8PyOVyfPXVV8jOzoZSqcRrr72m8xyrESNG4Pvvv8egQYNw4sQJuLq6YuvWrfjjjz8QFRWFGjVqlOt+U+W0c+dO5ObmIiAgQOf7HTp00NzQr3///jqXsbS0hJubG2JiYtCsWTPUqlUL7u7ucHd3x9KlS9G5c2e0atUKw4cPR6NGjZCZmYmEhARcu3YNf/75Z5nqNvT73KRJE3Tu3BnBwcHIz89HVFQUateurXW4vOgPoDFjxsDf3x9yuRwffPBBmeoz1K5du7B+/Xq8++67OHXqFE6dOqV5z8rKCn379kXHjh1Rs2ZNBAUFYcyYMZDJZPjhhx90Hg7y9PRETEwMQkND0a5dO1hZWaFPnz46tz1//nz06NEDPj4+GDp0qOZScBsbG8k8jsIgJrpK66Wn61JwlUolPDw8xLJly4RarS62zvLly4Wnp6ewtLQUNWrUEK1atRITJ04UN27c0Cyj61JwIZ7exG/mzJmiYcOGwsLCQri4uJR6Ez9dcnNzRVhYmGjSpIlQKBSiTp06omPHjuKbb77RXKJdmiVLlogWLVoICwsLYW9vL4KDg/W6iV+DBg3EkiVLivX373//W7i5uQlzc3O9b+L3rKIbbm3ZskWrXdcNFp+/JPv5/3bPvoou6b57964YPHiwqFOnjrCyshL+/v4iOTlZNGjQQOtyUiGEWLFihWjUqJGQy+V63cSvqF+FQiFatWpV7FLUkva5qPaqfot90tanTx+hUqlKvQnboEGDhIWFhbh165bOS8GFEOLQoUPC09NTKBSKYt+TS5cuiYEDBwoHBwdhYWEhnJ2dRe/evcXWrVs1y5R0c9LSGPp9XrBggXBxcRFKpVJ06dJF/Pnnn1rLPnnyRIwePVrUrVtXyGQyvW7i9/znUNI4WjQ+PV9XUb0l3eIDz93E748//hAdOnQQlpaWwsnJSUycOFHs3bu32C0h7t+/Lz788ENha2ur10389u3bJzp16iQsLS2FtbW16NOnT4k38Xt+n4tqf/Ymo1WZTAiJnD1EktCtWzfcunULZ86cMXUpRFRJpKamomHDhpg/fz4mTJhg6nKoCuA5N0RERCQpDDdEREQkKQw3REREJCk854aIiIgkhTM3REREJCkMN0RERCQpL91N/NRqNW7cuIEaNWqY/DbdRC8rIQRyc3Ph5ORU7Pb0lRXHDiLTMmTceOnCzY0bN4o9BZqITOPq1auoV6+eqcvQC8cOospBn3HjpQs3Rbfzvnr1qiQe605UFeXk5MDFxaVKPS6CYweRaRkybrx04aZoOtna2poDFJGJVaXDOxw7iCoHfcaNqnGwm4iIiEhPDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3RFTl/Pbbb+jTpw+cnJwgk8nw888//+M68fHxePXVV6FUKtGkSROsXbu23OskItNguCGiKicvLw9t2rTB0qVL9Vr+ypUr6NWrF7p3746kpCSMGzcOw4YNw969e8u5UiIyhZfu8QtEVPX16NEDPXr00Hv56OhoNGzYEAsWLAAAtGzZEgcPHsTChQvh7+9fXmUSkYlw5oaIJC8hIQF+fn5abf7+/khISChxnfz8fOTk5Gi9iKhqYLghIsnLyMiAvb29Vpu9vT1ycnLw8OFDnetERETAxsZG83JxcamIUonICBhuiIh0CAsLQ3Z2tuZ19epVU5dERHriOTdEJHkODg7IzMzUasvMzIS1tTUsLS11rqNUKqFUKiuiPCIyMoabf+A6eZdR+kmd18so/RCR4Xx8fLB7926tttjYWPj4+JTL9ow1bgAcO6jyqszfcx6WIqIq5/79+0hKSkJSUhKAp5d6JyUlIS0tDcDTQ0oDBw7ULP/JJ5/g8uXLmDhxIpKTk/Hdd99h8+bNGD9+vCnKJ6JyxnBDRFXO8ePH0bZtW7Rt2xYAEBoairZt22L69OkAgPT0dE3QAYCGDRti165diI2NRZs2bbBgwQKsXLmSl4ETSRQPSxFRlTv82q1bNwghSnxf192Hu3XrhpMnT5ZjVURUWTDcEBGRRlULukS68LAUERERSQpnboiIiEyIs2XGx3BDRERVXmW+LJkqHg9LERERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpJg83CxduhSurq5QqVTw9vbG0aNHS10+KioKzZs3h6WlJVxcXDB+/Hg8evSogqolIiKiys6k4SYmJgahoaEIDw9HYmIi2rRpA39/f2RlZelcfuPGjZg8eTLCw8Nx7tw5rFq1CjExMfjiiy8quHIiIiKqrEwabiIjIzF8+HAMHjwYbm5uiI6ORrVq1bB69Wqdyx86dAidOnXChx9+CFdXV7z55psIDAz8x9keIiIienmYLNwUFBTgxIkT8PPz+18xZmbw8/NDQkKCznU6duyIEydOaMLM5cuXsXv3bvTs2bPE7eTn5yMnJ0frRURERNJlbqoN37p1C4WFhbC3t9dqt7e3R3Jyss51PvzwQ9y6dQudO3eGEAJPnjzBJ598UuphqYiICMycOdOotRMREVHlZfITig0RHx+PuXPn4rvvvkNiYiK2b9+OXbt2Yfbs2SWuExYWhuzsbM3r6tWrFVgxERERVTSTzdzUqVMHcrkcmZmZWu2ZmZlwcHDQuc60adPw8ccfY9iwYQCAVq1aIS8vDyNGjMCUKVNgZlY8qymVSiiVSuPvABEREVVKJpu5USgU8PT0RFxcnKZNrVYjLi4OPj4+Otd58OBBsQAjl8sBAEKI8iuWiIiIqgyTzdwAQGhoKIKCguDl5YX27dsjKioKeXl5GDx4MABg4MCBcHZ2RkREBACgT58+iIyMRNu2beHt7Y2LFy9i2rRp6NOnjybkEBER0cvNpOGmf//+uHnzJqZPn46MjAx4eHhgz549mpOM09LStGZqpk6dCplMhqlTp+L69euoW7cu+vTpgzlz5phqF4iIiKiSMWm4AYCQkBCEhITofC8+Pl7rZ3Nzc4SHhyM8PLwCKiMiIqKqqEpdLUVERET0TxhuiIiISFIYboiIiEhSGG6IiIhIUhhuiIiISFIYboiIiEhSGG6IiIhIUhhuiIiISFIYboiIiEhSGG6IiIhIUhhuiIiISFIYboiIiEhSGG6IqEpaunQpXF1doVKp4O3tjaNHj5a6fFRUFJo3bw5LS0u4uLhg/PjxePToUQVVS0QVieGGiKqcmJgYhIaGIjw8HImJiWjTpg38/f2RlZWlc/mNGzdi8uTJCA8Px7lz57Bq1SrExMTgiy++qODKiagiMNwQUZUTGRmJ4cOHY/DgwXBzc0N0dDSqVauG1atX61z+0KFD6NSpEz788EO4urrizTffRGBg4D/O9hBR1cRwQ0RVSkFBAU6cOAE/Pz9Nm5mZGfz8/JCQkKBznY4dO+LEiROaMHP58mXs3r0bPXv2LHE7+fn5yMnJ0XoRUdVgbuoCiIgMcevWLRQWFsLe3l6r3d7eHsnJyTrX+fDDD3Hr1i107twZQgg8efIEn3zySamHpSIiIjBz5kyj1k5EFYMzN0QkefHx8Zg7dy6+++47JCYmYvv27di1axdmz55d4jphYWHIzs7WvK5evVqBFRPRi+DMDRFVKXXq1IFcLkdmZqZWe2ZmJhwcHHSuM23aNHz88ccYNmwYAKBVq1bIy8vDiBEjMGXKFJiZFf87T6lUQqlUGn8HiKjcceaGiKoUhUIBT09PxMXFadrUajXi4uLg4+Ojc50HDx4UCzByuRwAIIQov2KJyCQ4c0NEVU5oaCiCgoLg5eWF9u3bIyoqCnl5eRg8eDAAYODAgXB2dkZERAQAoE+fPoiMjETbtm3h7e2NixcvYtq0aejTp48m5BCRdDDcEFGV079/f9y8eRPTp09HRkYGPDw8sGfPHs1JxmlpaVozNVOnToVMJsPUqVNx/fp11K1bF3369MGcOXNMtQtEVI4YboioSgoJCUFISIjO9+Lj47V+Njc3R3h4OMLDwyugMiIyNZ5zQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSYm7qAoikwnXyLqP1lTqvl9H6IiJ62XDmhoiIiCSFMzcSxVkEIiJ6WXHmhoiIiCSF4YaIiIgkheGGiIiIJIXhhoiIiCSF4YaIiIgkheGGiIiIJIXhhoiIiCSF4YaIiIgkxeBwExQUhN9++608aiEiIiJ6YQaHm+zsbPj5+aFp06aYO3curl+/Xh51EREREZWJweHm559/xvXr1xEcHIyYmBi4urqiR48e2Lp1Kx4/flweNRIRERHprUzn3NStWxehoaH4888/ceTIETRp0gQff/wxnJycMH78eKSkpBi7TiIiIiK9vNAJxenp6YiNjUVsbCzkcjl69uyJ06dPw83NDQsXLjRWjURERER6MzjcPH78GNu2bUPv3r3RoEEDbNmyBePGjcONGzewbt067Nu3D5s3b8asWbPKo14iIiKiUpkbuoKjoyPUajUCAwNx9OhReHh4FFume/fusLW1NUJ5RERERIYxONwsXLgQ77//PlQqVYnL2Nra4sqVKy9UGBEREVFZGHxY6sCBAzqvisrLy8OQIUOMUhQRERFRWRkcbtatW4eHDx8Wa3/48CHWr19vlKKIiIiIykrvw1I5OTkQQkAIgdzcXK3DUoWFhdi9ezfs7OzKpUgiIiIifekdbmxtbSGTySCTydCsWbNi78tkMsycOdOoxREREREZSu9wc+DAAQgh8Nprr2Hbtm2oVauW5j2FQoEGDRrAycmpXIokIiIi0pfe4cbX1xcAcOXKFdSvXx8ymazciiIiIiIqK73CzalTp+Du7g4zMzNkZ2fj9OnTJS7bunVroxVHREREZCi9wo2HhwcyMjJgZ2cHDw8PyGQyCCGKLSeTyVBYWGj0IomIiIj0pVe4uXLlCurWrav5NxEREVFlpVe4adCggc5/E5UH18m7jNJP6rxeRumHiIiqFr3Czc6dO/XuMCAgwKACli5divnz5yMjIwNt2rTB4sWL0b59+xKXv3fvHqZMmYLt27fjzp07aNCgAaKiotCzZ0+DtktERETSpFe46du3r16dGXrOTUxMDEJDQxEdHQ1vb29ERUXB398f58+f13lDwIKCArzxxhuws7PD1q1b4ezsjL///psP6SQiIiINvcKNWq0ul41HRkZi+PDhGDx4MAAgOjoau3btwurVqzF58uRiy69evRp37tzBoUOHYGFhAQBwdXUtl9qIiIioajL42VLGUlBQgBMnTsDPz+9/xZiZwc/PDwkJCTrX2blzJ3x8fDBq1CjY29vD3d0dc+fOLXW2KD8/Hzk5OVovIiIiki69Zm4WLVqEESNGQKVSYdGiRaUuO2bMGL02fOvWLRQWFsLe3l6r3d7eHsnJyTrXuXz5Mvbv348BAwZg9+7duHjxIj799FM8fvwY4eHhOteJiIjgYyGIiIheInqFm4ULF2LAgAFQqVRYuHBhicvJZDK9w01ZqNVq2NnZYfny5ZDL5fD09MT169cxf/78EsNNWFgYQkNDNT/n5OTAxcWl3GokIiIi09L7Pje6/v0i6tSpA7lcjszMTK32zMxMODg46FzH0dERFhYWkMvlmraWLVsiIyMDBQUFUCgUxdZRKpVQKpVGqZmIiIgqvxc650YIofNOxfpQKBTw9PREXFycpk2tViMuLg4+Pj461+nUqRMuXryodYLzhQsX4OjoqDPYEBER0cunTOFm1apVcHd3h0qlgkqlgru7O1auXGlwP6GhoVixYgXWrVuHc+fOITg4GHl5eZqrpwYOHIiwsDDN8sHBwbhz5w7Gjh2LCxcuYNeuXZg7dy5GjRpVlt0gIiIiCdL7qeBFpk+fjsjISIwePVozw5KQkIDx48cjLS0Ns2bN0ruv/v374+bNm5g+fToyMjLg4eGBPXv2aE4yTktLg5nZ//KXi4sL9u7di/Hjx6N169ZwdnbG2LFjMWnSJEN3g4iIiCTK4HCzbNkyrFixAoGBgZq2gIAAtG7dGqNHjzYo3ABASEgIQkJCdL4XHx9frM3HxweHDx82aBtERET08jD4sNTjx4/h5eVVrN3T0xNPnjwxSlFEREREZWVwuPn444+xbNmyYu3Lly/HgAEDjFIUERERUVnpdVjq2fvEyGQyrFy5Er/++is6dOgAADhy5AjS0tIwcODA8qmSiIiISE96hZuTJ09q/ezp6QkAuHTpEoCn96ypU6cOzp49a+TyiIiIiAyjV7g5cOBAeddBREREZBQme3AmERERUXkoU7g5fvw4Jk6ciA8++ADvvPOO1ouIqCIsXboUrq6uUKlU8Pb2xtGjR0td/t69exg1ahQcHR2hVCrRrFkz7N69u4KqJaKKZHC42bRpEzp27Ihz585hx44dePz4Mc6ePYv9+/fDxsamPGokItISExOD0NBQhIeHIzExEW3atIG/vz+ysrJ0Ll9QUIA33ngDqamp2Lp1K86fP48VK1bA2dm5gisnoopg8E385s6di4ULF2LUqFGoUaMGvv32WzRs2BAjR46Eo6NjedRIRKQlMjISw4cP1zyqJTo6Grt27cLq1asxefLkYsuvXr0ad+7cwaFDh2BhYQEAcHV1rciSiagCGTxzc+nSJfTq1QvA04df5uXlQSaTYfz48Vi+fLnRCyQielZBQQFOnDgBPz8/TZuZmRn8/PyQkJCgc52dO3fCx8cHo0aNgr29Pdzd3TF37lwUFhaWuJ38/Hzk5ORovYioajA43NSsWRO5ubkAAGdnZ5w5cwbA0+PZDx48MG51RETPuXXrFgoLCzXPoCtib2+PjIwMnetcvnwZW7duRWFhIXbv3o1p06ZhwYIF+PLLL0vcTkREBGxsbDQvFxcXo+4HEZUfg8NN165dERsbCwB4//33MXbsWAwfPhyBgYF4/fXXjV4gEdGLUqvVsLOzw/Lly+Hp6Yn+/ftjypQpiI6OLnGdsLAwZGdna15Xr16twIqJ6EUYfM7NkiVL8OjRIwDAlClTYGFhgUOHDuHdd9/F1KlTjV4gEdGz6tSpA7lcjszMTK32zMxMODg46FzH0dERFhYWkMvlmraWLVsiIyMDBQUFUCgUxdZRKpVQKpXGLZ6IKoTB4aZWrVqaf5uZmek8eY+IqLwoFAp4enoiLi4Offv2BfB0ZiYuLg4hISE61+nUqRM2btwItVoNM7OnE9YXLlyAo6OjzmBDRFWbweEGAAoLC7Fjxw6cO3cOAODm5oZ//etfMDcvU3dERAYJDQ1FUFAQvLy80L59e0RFRSEvL09z9dTAgQPh7OyMiIgIAEBwcDCWLFmCsWPHYvTo0UhJScHcuXMxZswYU+4GEZUTg9PI2bNnERAQgIyMDDRv3hwA8NVXX6Fu3br4z3/+A3d3d6MXSUT0rP79++PmzZuYPn06MjIy4OHhgT179mhOMk5LS9PM0ACAi4sL9u7di/Hjx6N169ZwdnbG2LFjMWnSJFPtAhGVI4PDzbBhw/DKK6/g+PHjqFmzJgDg7t27GDRoEEaMGIFDhw4ZvUgioueFhISUeBgqPj6+WJuPjw8OHz5czlURUWVgcLhJSkrSCjbA08vD58yZg3bt2hm1OCIiIiJDGXwpeLNmzYpdpQAAWVlZaNKkiVGKIiIiIiorvcLNs3fojIiIwJgxY7B161Zcu3YN165dw9atWzFu3Dh89dVX5V0vERERUan0Oixla2sLmUym+VkIgX79+mnahBAAgD59+pR6O3MiIiKi8qZXuDlw4EB510FERERkFHqFG19f3/Kug4iIiMgoynTXvXv37mHVqlWam/i98sorGDJkCGxsbIxaHBEREZGhDL5a6vjx42jcuDEWLlyIO3fu4M6dO4iMjETjxo2RmJhYHjUSERER6c3gmZvx48cjICAAK1as0Dxu4cmTJxg2bBjGjRuH3377zehFEhEREenL4HBz/PhxrWADAObm5pg4cSK8vLyMWhwRERGRoQw+LGVtbY20tLRi7VevXkWNGjWMUhQRERFRWRkcbvr374+hQ4ciJiYGV69exdWrV7Fp0yYMGzYMgYGB5VEjERERkd4MPiz1zTffQCaTYeDAgXjy5AkAwMLCAsHBwZg3b57RCyQiIiIyhEHhprCwEIcPH8aMGTMQERGBS5cuAQAaN26MatWqlUuBRERERIYwKNzI5XK8+eabOHfuHBo2bIhWrVqVV11EREREZWLwOTfu7u64fPlyedRCRERE9MIMDjdffvklJkyYgF9++QXp6elaTwzPyckpjxqJiIiI9GbwCcU9e/YEAAQEBBR7UrhMJuNTwYmIiMikDA43fEI4ERERVWYGhxs+IZyIiIgqszI9Ffzu3btaTwV3c3PD4MGDUatWLaMWR0RERGQog08o/u233+Dq6opFixbh7t27uHv3LhYtWoSGDRvyoZlERERkcgbP3IwaNQr9+/fHsmXLIJfLATy9ud+nn36KUaNG4fTp00YvkoiIiEhfBs/cXLx4EZ999pkm2ABPb+4XGhqKixcvGrU4IiIiIkMZHG5effVVzbk2zzp37hzatGljlKKIiIiIysrgw1JjxozB2LFjcfHiRXTo0AEAcPjwYSxduhTz5s3DqVOnNMu2bt3aeJUSERER6cHgcBMYGAgAmDhxos73ZDIZb+hHREREJmNwuLly5Up51EFERERkFAaHmwYNGpRHHURERERGYfAJxURERESVGcMNERERSQrDDREREUkKww0RERFJSpnCzb1797By5UqEhYXhzp07AIDExERcv37dqMURERERGcrgq6VOnToFPz8/2NjYIDU1FcOHD0etWrWwfft2pKWlYf369eVRJxEREZFeDJ65CQ0NxaBBg5CSkgKVSqVp79mzJ58KTkRERCZncLg5duwYRo4cWazd2dkZGRkZRimKiIiIqKwMDjdKpRI5OTnF2i9cuIC6desapSgiIiKisjI43AQEBGDWrFl4/PgxAEAmkyEtLQ2TJk3Cu+++a/QCiYiIiAxhcLhZsGAB7t+/Dzs7Ozx8+BC+vr5o0qQJatSogTlz5pRHjURERER6M/hqKRsbG8TGxuLgwYM4deoU7t+/j1dffRV+fn7lUR8RERGRQQwON0U6d+6Mzp07G7MWIiIiohdmcLhZtGiRznaZTAaVSoUmTZqga9eukMvlL1wcERERkaEMDjcLFy7EzZs38eDBA9SsWRMAcPfuXVSrVg1WVlbIyspCo0aNcODAAbi4uBi9YCIiIqLSGHxC8dy5c9GuXTukpKTg9u3buH37Ni5cuABvb298++23SEtLg4ODA8aPH18e9RIRERGVyuCZm6lTp2Lbtm1o3Lixpq1Jkyb45ptv8O677+Ly5cv4+uuveVk4ERERmYTBMzfp6el48uRJsfYnT55o7lDs5OSE3NzcF6+OiIiIyEAGh5vu3btj5MiROHnypKbt5MmTCA4OxmuvvQYAOH36NBo2bGi8KomIiIj0ZHC4WbVqFWrVqgVPT08olUoolUp4eXmhVq1aWLVqFQDAysoKCxYs0LvPpUuXwtXVFSqVCt7e3jh69Khe623atAkymQx9+/Y1dDeIiIhIogw+58bBwQGxsbFITk7GhQsXAADNmzdH8+bNNct0795d7/5iYmIQGhqK6OhoeHt7IyoqCv7+/jh//jzs7OxKXC81NRUTJkxAly5dDN0FIiIikjCDZ26KtGjRAgEBAQgICNAKNoaKjIzE8OHDMXjwYLi5uSE6OhrVqlXD6tWrS1ynsLAQAwYMwMyZM9GoUaMyb5uIiIikp0x3KL527Rp27tyJtLQ0FBQUaL0XGRmpdz8FBQU4ceIEwsLCNG1mZmbw8/NDQkJCievNmjULdnZ2GDp0KH7//XfDd4CIiIgky+BwExcXh4CAADRq1AjJyclwd3dHamoqhBB49dVXDerr1q1bKCwshL29vVa7vb09kpOTda5z8OBBrFq1CklJSXptIz8/H/n5+Zqfc3JyDKqRiIiIqhaDD0uFhYVhwoQJOH36NFQqFbZt24arV6/C19cX77//fnnUqJGbm4uPP/4YK1asQJ06dfRaJyIiAjY2NpoX75pMREQkbQaHm3PnzmHgwIEAAHNzczx8+BBWVlaYNWsWvvrqK4P6qlOnDuRyOTIzM7XaMzMz4eDgUGz5S5cuITU1FX369IG5uTnMzc2xfv167Ny5E+bm5rh06VKxdcLCwpCdna15Xb161aAaiYiIqGoxONxUr15dc56No6OjVqC4deuWQX0pFAp4enoiLi5O06ZWqxEXFwcfH59iy7do0QKnT59GUlKS5hUQEIDu3bsjKSlJ56yMUqmEtbW11ouIiIiky+Bzbjp06ICDBw+iZcuW6NmzJz777DOcPn0a27dvR4cOHQwuIDQ0FEFBQfDy8kL79u0RFRWFvLw8DB48GAAwcOBAODs7IyIiAiqVCu7u7lrr29raAkCxdiIiIno5GRxuIiMjcf/+fQDAzJkzcf/+fcTExKBp06YGXSlVpH///rh58yamT5+OjIwMeHh4YM+ePZqTjNPS0mBmVuYr1omIiOglY1C4KSwsxLVr19C6dWsATw9RRUdHv3ARISEhCAkJ0flefHx8qeuuXbv2hbdPRERE0mHQlIhcLsebb76Ju3fvllc9RERERC/E4OM97u7uuHz5cnnUQkSkNz6TjohKYnC4+fLLLzFhwgT88ssvSE9PR05OjtaLiKi8FT2TLjw8HImJiWjTpg38/f2RlZVV6np8Jh3Ry8HgcNOzZ0/8+eefCAgIQL169VCzZk3UrFkTtra2qFmzZnnUSESkhc+kI6LSGHy11IEDB8qjDiIivVTUM+n46BaiqsvgcOPr61sedRAR6aUinkkHPH10y8yZM1+kVCIykTLdQOb333/HRx99hI4dO+L69esAgB9++AEHDx40anFERC+qLM+kA/joFqKqzOCZm23btuHjjz/GgAEDkJiYqJm2zc7Oxty5c7F7926jF0lEVORFnklXRK1WA3j6fLzz58+jcePGxdZTKpVQKpVGrp6IKkKZrpaKjo7GihUrYGFhoWnv1KkTEhMTjVocEdHzKuKZdERUtRk8c3P+/Hl07dq1WLuNjQ3u3btnjJqIiErFZ9IRUWkMDjcODg64ePEiXF1dtdoPHjzIyyuJqELwmXREVBqDw83w4cMxduxYrF69GjKZDDdu3EBCQgImTJiAadOmlUeNRETF8Jl0RFQSg8PN5MmToVar8frrr+PBgwfo2rUrlEolJkyYgNGjR5dHjURERER6MzjcyGQyTJkyBZ9//jkuXryI+/fvw83NDVZWVuVRHxEREZFBDD4o/eOPP+LBgwdQKBRwc3ND+/btGWyIiIio0jA43IwfPx52dnb48MMPsXv3bhQWFpZHXURERERlYnC4SU9Px6ZNmyCTydCvXz84Ojpi1KhROHToUHnUR0RERGQQg8ONubk5evfujQ0bNiArKwsLFy5EamoqunfvrvMun0REREQVyeATip9VrVo1+Pv74+7du/j7779x7tw5Y9VFREREVCZlusvVgwcPsGHDBvTs2RPOzs6IiorC22+/jbNnzxq7PiIiIiKDGDxz88EHH+CXX35BtWrV0K9fP0ybNk3n81yIiIiITMHgcCOXy7F582b4+/tDLpdrvXfmzBk+q4WIiIhMyuBws2HDBq2fc3Nz8dNPP2HlypU4ceIELw0nIiIikyrzk+V+++03BAUFwdHREd988w1ee+01HD582Ji1ERERERnMoJmbjIwMrF27FqtWrUJOTg769euH/Px8/Pzzz3BzcyuvGomIiIj0pvfMTZ8+fdC8eXOcOnUKUVFRuHHjBhYvXlyetREREREZTO+Zm//+978YM2YMgoOD0bRp0/KsiYiIiKjM9J65OXjwIHJzc+Hp6Qlvb28sWbIEt27dKs/aiIiIiAymd7jp0KEDVqxYgfT0dIwcORKbNm2Ck5MT1Go1YmNjkZubW551EhEREenF4KulqlevjiFDhuDgwYM4ffo0PvvsM8ybNw92dnYICAgojxqJiIiI9FbmS8EBoHnz5vj6669x7do1/PTTT8aqiYiIiKjMXijcFJHL5ejbty927txpjO6IiIiIyuyFngpOLyfXybuM1lfqvF5G64uIiAgw0swNERERUWXBcENERESSwnBDREREksJzbuilwvOFiIikjzM3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQplSLcLF26FK6urlCpVPD29sbRo0dLXHbFihXo0qULatasiZo1a8LPz6/U5YmIiOjlYvJwExMTg9DQUISHhyMxMRFt2rSBv78/srKydC4fHx+PwMBAHDhwAAkJCXBxccGbb76J69evV3DlREREVBmZPNxERkZi+PDhGDx4MNzc3BAdHY1q1aph9erVOpffsGEDPv30U3h4eKBFixZYuXIl1Go14uLiKrhyIiIiqoxMGm4KCgpw4sQJ+Pn5adrMzMzg5+eHhIQEvfp48OABHj9+jFq1aul8Pz8/Hzk5OVovIiIiki6Thptbt26hsLAQ9vb2Wu329vbIyMjQq49JkybByclJKyA9KyIiAjY2NpqXi4vLC9dNRERElZfJD0u9iHnz5mHTpk3YsWMHVCqVzmXCwsKQnZ2teV29erWCqyQiIqKKZNJwU6dOHcjlcmRmZmq1Z2ZmwsHBodR1v/nmG8ybNw+//vorWrduXeJySqUS1tbWWi8iqvp4lSURlcSk4UahUMDT01PrZOCik4N9fHxKXO/rr7/G7NmzsWfPHnh5eVVEqURUifAqSyIqjckPS4WGhmLFihVYt24dzp07h+DgYOTl5WHw4MEAgIEDByIsLEyz/FdffYVp06Zh9erVcHV1RUZGBjIyMnD//n1T7QIRVTBeZUlEpTE3dQH9+/fHzZs3MX36dGRkZMDDwwN79uzRnGSclpYGM7P/ZbBly5ahoKAA7733nlY/4eHhmDFjRkWWTkQmUHSV5bN/9Bj7Kkvg6ZWW+fn5mp95pSVR1WHycAMAISEhCAkJ0flefHy81s+pqanlXxARVVqlXWWZnJysVx//dJUl8PRKy5kzZ75QrURkGiY/LEVEVJH0ucoS4JWWRFVZpZi5ISLSlzGusty3b1+pV1kCT6+0VCqVL1wvEVU8ztwQUZXCqyyJ6J9w5oaIqpzQ0FAEBQXBy8sL7du3R1RUVLGrLJ2dnREREQHg6VWW06dPx8aNGzVXWQKAlZUVrKysTLYfRFQ+GG6IqMrhVZZEVBqGGyKqkniVJRGVhOfcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkmJu6ACLSj+vkXUbpJ3VeL6P0Q0RUWXHmhoiIiCSF4YaIiIgkheGGiIiIJIXn3JgQz6EgIiIyPs7cEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpJibugAiIqLKznXyLqP0kzqvl1H6odJx5oaIiIgkhTM3RERUIYw1+wFwBoRKx5kbIiIikpRKEW6WLl0KV1dXqFQqeHt74+jRo6Uuv2XLFrRo0QIqlQqtWrXC7t27K6hSIqosOG4QUUlMHm5iYmIQGhqK8PBwJCYmok2bNvD390dWVpbO5Q8dOoTAwEAMHToUJ0+eRN++fdG3b1+cOXOmgisnIlPhuEFEpTH5OTeRkZEYPnw4Bg8eDACIjo7Grl27sHr1akyePLnY8t9++y3eeustfP755wCA2bNnIzY2FkuWLEF0dHSF1k5EpvEyjxs8b4UM8bJ+X0w6c1NQUIATJ07Az89P02ZmZgY/Pz8kJCToXCchIUFreQDw9/cvcXkikhaOG0T0T0w6c3Pr1i0UFhbC3t5eq93e3h7Jyck618nIyNC5fEZGhs7l8/PzkZ+fr/k5OzsbAJCTk6NXjer8B3ot9090ba8q9K2r//Ls25j983OpHH2XtpwQwuBtVMS4AbzY2MHvGX//pNa3rv7L+zMvaRl9xg2TH5YqbxEREZg5c2axdhcXlwqtwyaqavZd3v1X1b7Lu/+Xpe/c3FzY2NiUSy0vimNH5e27vPtn3xXfvyF96zNumDTc1KlTB3K5HJmZmVrtmZmZcHBw0LmOg4ODQcuHhYUhNDRU87NarcadO3dQu3ZtyGSyF9yDp0nSxcUFV69ehbW19Qv3V1Gqat0AazcFY9cthEBubi6cnJwMXrcixg2gfMeOqvo9AFi7KVTVugHj1m7IuGHScKNQKODp6Ym4uDj07dsXwNMBJC4uDiEhITrX8fHxQVxcHMaNG6dpi42NhY+Pj87llUollEqlVputra0xytdibW1d5b50QNWtG2DtpmDMuss6Y1MR4wZQMWNHVf0eAKzdFKpq3YDxatd33DD5YanQ0FAEBQXBy8sL7du3R1RUFPLy8jRXQQwcOBDOzs6IiIgAAIwdOxa+vr5YsGABevXqhU2bNuH48eNYvny5KXeDiCoQxw0iKo3Jw03//v1x8+ZNTJ8+HRkZGfDw8MCePXs0J/+lpaXBzOx/F3V17NgRGzduxNSpU/HFF1+gadOm+Pnnn+Hu7m6qXSCiCsZxg4hKJeiFPHr0SISHh4tHjx6ZuhSDVNW6hWDtplBV666sqvLnydorXlWtWwjT1S4TogzXYhIRERFVUiZ//AIRERGRMTHcEBERkaQw3BAREZGkMNwQERGRpDDcvIClS5fC1dUVKpUK3t7eOHr0qKlL+kcRERFo164datSoATs7O/Tt2xfnz583dVkGmzdvHmQymdZN2Sqz69ev46OPPkLt2rVhaWmJVq1a4fjx46Yu6x8VFhZi2rRpaNiwISwtLdG4cWPMnj27TM+Eov/h2GE6HDvKX6UYNyr02iwJ2bRpk1AoFGL16tXi7NmzYvjw4cLW1lZkZmaaurRS+fv7izVr1ogzZ86IpKQk0bNnT1G/fn1x//59U5emt6NHjwpXV1fRunVrMXbsWFOX84/u3LkjGjRoIAYNGiSOHDkiLl++LPbu3SsuXrxo6tL+0Zw5c0Tt2rXFL7/8Iq5cuSK2bNkirKysxLfffmvq0qosjh2mw7GjYlSGcYPhpozat28vRo0apfm5sLBQODk5iYiICBNWZbisrCwBQPzf//2fqUvRS25urmjatKmIjY0Vvr6+VWKAmjRpkujcubOpyyiTXr16iSFDhmi1vfPOO2LAgAEmqqjq49hhGhw7Kk5lGDd4WKoMCgoKcOLECfj5+WnazMzM4Ofnh4SEBBNWZrjs7GwAQK1atUxciX5GjRqFXr16aX32ld3OnTvh5eWF999/H3Z2dmjbti1WrFhh6rL00rFjR8TFxeHChQsAgD///BMHDx5Ejx49TFxZ1cSxw3Q4dlScyjBumPzxC1XRrVu3UFhYqLnVexF7e3skJyebqCrDqdVqjBs3Dp06daoSt6HftGkTEhMTcezYMVOXYpDLly9j2bJlCA0NxRdffIFjx45hzJgxUCgUCAoKMnV5pZo8eTJycnLQokULyOVyFBYWYs6cORgwYICpS6uSOHaYBseOilUZxg2Gm5fYqFGjcObMGRw8eNDUpfyjq1evYuzYsYiNjYVKpTJ1OQZRq9Xw8vLC3LlzAQBt27bFmTNnEB0dXakHKADYvHkzNmzYgI0bN+KVV15BUlISxo0bBycnp0pfO5Ufjh0Vo6qOHZVi3KiwA2ASkp+fL+RyudixY4dW+8CBA0VAQIBpijLQqFGjRL169cTly5dNXYpeduzYIQAIuVyueQEQMplMyOVy8eTJE1OXWKL69euLoUOHarV99913wsnJyUQV6a9evXpiyZIlWm2zZ88WzZs3N1FFVRvHjorHsaPiVYZxg+fclIFCoYCnpyfi4uI0bWq1GnFxcfDx8TFhZf9MCIGQkBDs2LED+/fvR8OGDU1dkl5ef/11nD59GklJSZqXl5cXBgwYgKSkJMjlclOXWKJOnToVu2T2woULaNCggYkq0t+DBw+0nq4NAHK5HGq12kQVVW0cOyoex46KVynGjQqLURKzadMmoVQqxdq1a8Vff/0lRowYIWxtbUVGRoapSytVcHCwsLGxEfHx8SI9PV3zevDggalLM1hVueLh6NGjwtzcXMyZM0ekpKSIDRs2iGrVqokff/zR1KX9o6CgIOHs7Ky5pHP79u2iTp06YuLEiaYurcri2GF6HDvKV2UYNxhuXsDixYtF/fr1hUKhEO3btxeHDx82dUn/CIDO15o1a0xdmsGqygAlhBD/+c9/hLu7u1AqlaJFixZi+fLlpi5JLzk5OWLs2LGifv36QqVSiUaNGokpU6aI/Px8U5dWpXHsMC2OHeWrMowbMiF4q1EiIiKSDp5zQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcEOlkslk+PnnnwEAqampkMlkSEpKMmlNpUlOTkaHDh2gUqng4eFh6nKIXkocN8jUGG4katCgQejbt69R+3RxcUF6ejrc3d2N2q8xhYeHo3r16jh//rzW83sMURUGY6LywHGD44ZUmJu6AKo65HI5HBwcTF1GqS5duoRevXpV+gfLEb0sOG6QKXDm5iXRrVs3jBkzBhMnTkStWrXg4OCAGTNmaC2TkpKCrl27QqVSwc3NDbGxsVrv6/rL5OzZs+jduzesra1Ro0YNdOnSBZcuXdK8v3LlSrRs2RIqlQotWrTAd999p3mvoKAAISEhcHR0hEqlQoMGDRAREVHiPqjVasyaNQv16tWDUqmEh4cH9uzZo3lfJpPhxIkTmDVrFmQyWbH9K7Jnzx507twZtra2qF27Nnr37q1Vc9HTjtu2bQuZTIZu3brptf2iz2fz5s3o0qULLC0t0a5dO1y4cAHHjh2Dl5cXrKys0KNHD9y8eVOzXnx8PNq3b4/q1avD1tYWnTp1wt9//13i50BUUThu/A/HjSqmwp5iRRUqKChI/Otf/9L87OvrK6ytrcWMGTPEhQsXxLp164RMJhO//vqrEEKIwsJC4e7uLl5//XWRlJQk/u///k+0bdtWABA7duwQQghx5coVAUCcPHlSCCHEtWvXRK1atcQ777wjjh07Js6fPy9Wr14tkpOThRBC/Pjjj8LR0VFs27ZNXL58WWzbtk3UqlVLrF27VgghxPz584WLi4v47bffRGpqqvj999/Fxo0bS9ynyMhIYW1tLX766SeRnJwsJk6cKCwsLMSFCxeEEEKkp6eLV155RXz22WciPT1d5Obm6uxn69atYtu2bSIlJUWcPHlS9OnTR7Rq1UoUFhYKIZ4+iReA2Ldvn0hPTxe3b9/Wa/tFn0+LFi3Enj17xF9//SU6dOggPD09Rbdu3cTBgwdFYmKiaNKkifjkk0+EEEI8fvxY2NjYiAkTJoiLFy+Kv/76S6xdu1b8/fffhv4nJ3phHDc4bkgFw41E6RqkOnfurLVMu3btxKRJk4QQQuzdu1eYm5uL69eva97/73//W+ogFRYWJho2bCgKCgp01tC4ceNig87s2bOFj4+PEEKI0aNHi9dee02o1Wq99snJyUnMmTOn2D58+umnmp/btGkjwsPD9eqvyM2bNwUAcfr0aSFE8f3Ud/tF661cuVLz/k8//SQAiLi4OE1bRESEaN68uRBCiNu3bwsAIj4+3qCaicoDxw39cdyo3HhY6iXSunVrrZ8dHR2RlZUFADh37hxcXFzg5OSked/Hx6fU/pKSktClSxdYWFgUey8vLw+XLl3C0KFDYWVlpXl9+eWXmqncQYMGISkpCc2bN8eYMWPw66+/lritnJwc3LhxA506ddJq79SpE86dO1f6jj8nJSUFgYGBaNSoEaytreHq6goASEtLM8r2n/2c7e3tAQCtWrXSaiv63GvVqoVBgwbB398fffr0wbfffov09HSD9oeoPHHceIrjRtXCcPMSeX4wkclkUKvVZe7P0tKyxPfu378PAFixYgWSkpI0rzNnzuDw4cMAgFdffRVXrlzB7Nmz8fDhQ/Tr1w/vvfdemevRV58+fXDnzh2sWLECR44cwZEjRwA8PZZvDM9+zjKZTGfbs5/7mjVrkJCQgI4dOyImJgbNmjXTfEZEpsZx4ymOG1ULww0BAFq2bImrV69qpf9/+kVp3bo1fv/9dzx+/LjYe/b29nBycsLly5fRpEkTrVfRiXcAYG1tjf79+2PFihWIiYnBtm3bcOfOnWL9WVtbw8nJCX/88YdW+x9//AE3Nze99/P27ds4f/48pk6ditdffx0tW7bE3bt3tZZRKBQAgMLCQqNvvyRt27ZFWFgYDh06BHd3d2zcuPGF+yQqbxw3/ofjRuXCS8EJAODn54dmzZohKCgI8+fPR05ODqZMmVLqOiEhIVi8eDE++OADhIWFwcbGBocPH0b79u3RvHlzzJw5E2PGjIGNjQ3eeust5Ofn4/jx47h79y5CQ0MRGRkJR0dHtG3bFmZmZtiyZQscHBxga2urc3uff/45wsPD0bhxY3h4eGDNmjVISkrChg0b9N7PmjVronbt2li+fDkcHR2RlpaGyZMnay1jZ2cHS0tL7NmzB/Xq1YNKpYKNjY1Rtv+8K1euYPny5QgICICTkxPOnz+PlJQUDBw4sMx9ElUUjhv/w3GjcmG4IQCAmZkZduzYgaFDh6J9+/ZwdXXFokWL8NZbb5W4Tu3atbF//358/vnn8PX1hVwuh4eHh+b48rBhw1CtWjXMnz8fn3/+OapXr45WrVph3LhxAIAaNWrg66+/RkpKCuRyOdq1a4fdu3fDzEz3hOKYMWOQnZ2Nzz77DFlZWXBzc8POnTvRtGlTg/Zz06ZNGDNmDNzd3dG8eXMsWrRIc9kmAJibm2PRokWYNWsWpk+fji5duiA+Pt4o239etWrVkJycjHXr1uH27dtwdHTEqFGjMHLkyDL3SVRROG500yzDcaNykQkhhKmLICIiIjIWnnNDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESSwnBDREREksJwQ0RERJLCcENERESS8v+ohW9i+FOOQwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the program with the optimized parameters for the detuning\n",
    "counts_pl_optimized = program_pl(theta)\n",
    "# Calculate the Rydberg density averaged over all the shots\n",
    "prob_pl_optimized = get_prob(counts_pl_optimized)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2)\n",
    "axs[0].bar(range(len(coords)), prob_pl)\n",
    "axs[1].bar(range(len(coords)), prob_pl_optimized)\n",
    "axs[0].set_xlabel(\"Indices of atoms\")\n",
    "axs[1].set_xlabel(\"Indices of atoms\")\n",
    "axs[0].set_ylabel(\"Average probability\")\n",
    "axs[0].set_title(\"Before optimization\")\n",
    "axs[1].set_title(\"After optimization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87125d5d-52ea-4f0f-b932-90f1b1eb76d4",
   "metadata": {},
   "source": [
    "Indeed, the AFM order after optimization exhibits a sharper alternating pattern compared to that before the optimization. We can also compare the detuning before and after the optimization, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "39644be8-0ccd-405f-9e10-962f7ab30010",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "axes[0].plot(vis_time, [ryd_amplitude(amplitude_param, t) for t in vis_time])\n",
    "axes[0].set_xlabel(\"time (μs)\")\n",
    "axes[0].set_ylabel(\"amplitude (MHz)\")\n",
    "axes[1].plot(\n",
    "    vis_time,\n",
    "    [ryd_detuning(detuning_param, t) for t in vis_time],\n",
    "    label=\"detuning before optimization\",\n",
    ")\n",
    "axes[1].plot(\n",
    "    vis_time, [ryd_detuning(theta, t) for t in vis_time], label=\"detuning after optimization\"\n",
    ")\n",
    "axes[1].set_ylabel(\"detuning (MHz)\")\n",
    "axes[1].set_xlabel(\"time (μs)\")\n",
    "axes[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "522375c8-fbf8-43ec-a188-46a96def6daf",
   "metadata": {},
   "source": [
    "The optimized detuning exhibits a smaller slope, particularly in the middle of the evolution, compared to that before the optimization. Hence the optimized AHS program suffers less non-adiabaticity and produces the almost ideal AFM order. \n",
    "\n",
    "## Running on Aquila\n",
    "To illustrate the usefulness of optimizing the AHS program, we now run the two AHS programs, before and after the optimization, on QuEra’s Aquila device and compare the results. This can be done by switching to QuEra’s Aquila device as shown below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "593bf201-440e-4a23-90ce-dc5f0979bfea",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from braket.devices import Devices\n",
    "\n",
    "shots = 100\n",
    "aquila = qml.device(\n",
    "    \"braket.aws.ahs\", device_arn=Devices.QuEra.Aquila, wires=len(coords), shots=shots\n",
    ")\n",
    "\n",
    "program_cost_aquila = qml.QNode(program, aquila)\n",
    "\n",
    "counts_aquila_before = program_cost_aquila(detuning_param)\n",
    "counts_aquila_after = program_cost_aquila(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e46e34ef-a3a5-43c7-8069-26c4fb113c45",
   "metadata": {},
   "source": [
    "Before calculating the Rydberg probability for the results obtained from Aquila, we need to process the counts such that it has consistent format with the counts from PennyLane local simulator. Besides, due to the noise in the real quantum device, certain shot result may contain \n",
    "`nan`, from which we cannot determine if the atom is in the ground or Rydberg state. Hence, we will discard shot result that contains `nan`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9a65b147-897c-449d-ab96-df414e0c2096",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def process_aquila_counts(counts_aquila):\n",
    "    \"\"\"Process the counts from Aquila before calculating the Rydberg probability\n",
    "\n",
    "    Note 1: For the counts returned from Aquila, a Rydberg state is indicated as\n",
    "            `1.0` instead of `1`. We will convert it to `1` for consistency with\n",
    "            the counts returned from PennyLane local simulator. Similarly, we will\n",
    "            convert `0.0` to `0` for the ground state.\n",
    "\n",
    "    Note 2: For the counts returned from Aquila, certain shot result may contain\n",
    "            'nan' in addition to '1' or '0', due to the noise in the device. For\n",
    "            shot result contains 'nan', we will not include it in the calculation\n",
    "            of Rydberg probability.\n",
    "    \"\"\"\n",
    "    counts_aquila_updated = {}\n",
    "\n",
    "    for key, val in counts_aquila.items():\n",
    "        if \"nan\" not in key:\n",
    "            newkey = [key[i : i + 3] for i in range(0, len(key), 3)]\n",
    "            newkey = \"\".join([\"1\" if a == \"1.0\" else (\"0\" if a == \"0.0\" else a) for a in newkey])\n",
    "            counts_aquila_updated[newkey] = val\n",
    "\n",
    "    return counts_aquila_updated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "efcbe716-e8c6-413d-aa82-d99aa9cf9051",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "counts_aquila_before_updated = process_aquila_counts(counts_aquila_before)\n",
    "counts_aquila_after_updated = process_aquila_counts(counts_aquila_after)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4386c5b0-fd9d-4350-8eec-f02e82a66cf8",
   "metadata": {},
   "source": [
    "We compare the AFM orders obtained from Aquila, before and after the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5e222f50-8ff3-4ba3-abc5-62d7f1e8062d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_aquila_before = get_prob(counts_aquila_before_updated)\n",
    "prob_aquila_after = get_prob(counts_aquila_after_updated)\n",
    "\n",
    "\n",
    "fig, axs = plt.subplots(1, 2)\n",
    "axs[0].bar(range(len(coords)), prob_aquila_before)\n",
    "axs[1].bar(range(len(coords)), prob_aquila_after)\n",
    "axs[0].set_xlabel(\"Indices of atoms\")\n",
    "axs[1].set_xlabel(\"Indices of atoms\")\n",
    "axs[0].set_ylabel(\"Average probability\")\n",
    "axs[0].set_title(\"Before optimization\")\n",
    "axs[1].set_title(\"After optimization\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c17252eb-6f01-4660-b8c6-efe84b9cf3d3",
   "metadata": {},
   "source": [
    "We find that the optimized AHS program indeed yields an AFM order that is much closer to an ideal one, compared to the non-optimized AHS program. This suggests that for AHS programs with small number of atoms, one can optimize it on the local simulator efficiently with the available machineries from PennyLane, before submitting it to the actual hardware. \n",
    "\n",
    "## Conclusion\n",
    "This concludes our demonstration of running and optimizing AHS program on Rydberg device via the PennyLane-Braket plug-in. Following the methods in this post, one can implement incrementally complex parametrizations and optimizations for AHS programs. For instance, with small changes of the code above, one can optimize both the detuning and amplitude for the Rydberg atom device. We also encourage the interested readers to come up with different parametrizations for the driving field, which may be useful to realize other phases of matter with Rydberg atoms.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "03d23db3-3e89-446c-9a7a-09894d6ade73",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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(\"Task Summary\")\n",
    "print(tracker.quantum_tasks_statistics())\n",
    "print(\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",
    ")\n",
    "print(\n",
    "    f\"Estimated cost to run this example: {tracker.qpu_tasks_cost() + tracker.simulator_tasks_cost():.2f} USD\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aaefc2f6-aaad-4069-867a-dfcfa6f3a3af",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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