Circuits in Quantum Algorithms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Circuits in Quantum Algorithms\n",
    "\n",
    "Qiskit Circuit session, July 22nd, 2020"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What's a quantum algorithm?\n",
    "\n",
    "Algorithms that run some part on a quantum computer. Here running on a quantum computer means running a circuit.\n",
    "\n",
    "![](quantum_algo.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Today we'll focus on the circuit part, using Qiskit's circuit library.\n",
    "\n",
    "![](quantum_algo_focus.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recap: The circuit library\n",
    "\n",
    "The circuit library is a collection of valuable families of circuits. These circuits are are easily accessible, tested building blocks that work natively with the rest of Qiskit.\n",
    "\n",
    "Interesting?\n",
    "For algorithms, eduction and complexity analysis\n",
    "\n",
    "Further material:\n",
    "* `qiskit.circuit.library` \n",
    "* qiskit.org/documentation/apidoc/circuit_library.html\n",
    "* Interactive overview: http://qisk.it/circuits\n",
    "* See also previous session with Ali Javadi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 742.777x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import QFT\n",
    "\n",
    "QFT(3).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Seen they might have a couple of options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 742.777x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QFT(4, approximation_degree=2, do_swaps=False).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Seen that they are normal circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Non-local gates: 4\n",
      "Operations: OrderedDict([('h', 3), ('cu1', 3), ('swap', 1)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 742.777x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qft = QFT(3)\n",
    "print('Non-local gates:', qft.num_nonlocal_gates())\n",
    "print('Operations:', qft.count_ops())\n",
    "qft.inverse().draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "It's easy to stack them together. Remember the `compose` method:\n",
    "```\n",
    "QuantumCircuit.compose(circuit, qubits=None, inplace=False) \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 923.377x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import QuantumCircuit\n",
    "from qiskit.circuit.library import Diagonal\n",
    "\n",
    "circuit = QuantumCircuit(3)\n",
    "circuit.compose(Diagonal([1, 1, -1, -1]), [1, 2], inplace=True)\n",
    "circuit.barrier()  # barrier for visualization purposes\n",
    "circuit.compose(QFT(3), inplace=True)\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Overview\n",
    "\n",
    "Let's have a look what circuits are in the circuit library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![overview](overview.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Workflow\n",
    "\n",
    "How do we as users, researchers or developers want to use these circuits?\n",
    "\n",
    "![](quantum_algo_circlib.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: Variational Quantum Classifier\n",
    "\n",
    "Supervised learning with quantum enhanced feature spaces, Havlicek et al. [arXiv:1804.11326](https://arxiv.org/abs/1804.11326)\n",
    "\n",
    "![](quantum_algo_vqc.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oGx6kWwbyYQdj3XtjvFvb69YhQj068y0mcKaz2ax65r5zlbF4SMmyuc8lKuPHG/Xgvzr53J2YAFfUCQ/S3GkXKfXb60uWffXqpdr57fW6yoeLX4wJ3Mdms+ruG9z7N7u2Xys1j3RvUQ2ojqaNa2nQJdFubXP0De0VEOBXJR6v85u/TnZ2tlJSUtS1a9dSyydPnqz09HQVFBQoKytL6enpat26tUEpfUfO5t+1aWxPbXq0t3a9PabUusKsPUoZf5E2je2po6t/kNPplD3niPbMnSin3S577rFy2/xrSF3tnvOYJCnj4ylaO7Spdr8/vmT97vfHa/WN9eS0F7vt92jbsq4eu72z29qb8cj5qlvb2DsFVfbaSNKut8do82MXaNdb90mSirMP69i6JB1bl6Ti7MOSpL2fTlfu9r88lvHA4tlKHhWnY8lLy82Un7FVG+7vot3vj1fujjXau2CaT2QtzNqjDWO6atV1ISX7YUVZjXTNxS31jwvPcktbNptFM5/oxcAWQIl6df6ePuCGAa0VFspl//B/Z0WGl/z78gvO4rJHF5hlPCBJ990cr4RY98yZVDc8SC88dL5b2qoJxgSey+ovY4LnHzpP9dw0Nu3Ypr7uv7mjW9oyM7/55AgPD5fdbtc999xjdBS/ENS4pWKf/lHtnv1FxUf2Ky/177vO7f3kWTW9abLaTvpOGfOelrO4SJnfzlT2puXK+Hiy7DmHy20ztGUnNbv1GUlSxKW3K/qB/5Va3+zmpxUa3cXtv8v4EV2qvJbZkvBOlXfGuO6SVvrXlcZP/lvZa5O7bZUc+dmKe+ZnOYoLlbNlhbI3/qKspPeUtWSOstf/JKfDoZyNyxQWc7ZHc0Ze87Bqd+xTbqaQqDY6a/gMSVJYdGflbPpVTqfT8KwBtRsodvJi1YrrXrKuoqxGslgsevOJXmraqPK5eFzZryeP7qZuHSLcGQ8AAJiAmcYDQYE2zZlyocLDKi/ou3Ls9MaEnmrWxPizvxgTeC6rv4wJmjaupZlP9Kp0G1f26VqhAZoz5UJuiOUCvymAoXoC60fKGhQiSbIEBErWvztD3s51qtWup2yh4bKF1pazKF86ZXrR7dOHKHf7auWlrtO25waVbb9ek+Ozj3pBUKBNX716mc7tePqD/H9ceJbem9rHJ86Sqey1yd78m2p3uUSSVKdzP+Vs+rXM4/NS1yg46vhlnMfWJWn1jfW1eVyi1t3eUlunXFXtPIdXfKn0WQ/L6XBoy8T+KsxMK7XelUzBTdsqr5xvdLyd1RoUooDwyu/wWVFWb2vauJZ+eGtAlUWwyjxyW4IeHc5NQQAAQFlmGg9Ix2/28dUrl1ZZBKuIxSK9Pr6nbhjgG1cLMSZgTCBJgy+L+f+rOU7v8bVCA/TlK5fq7PZ8Ie4KCmAml5u6VkVHMhXa4qTr5h32kkKQLayuirMPqdFlIxTerqeiBk+QrVY9nXX7DKXPelC7Zj2os27/j0Hp/9agbrCWvH257h5Svev/AwOsemp0V336Yj+FBPvWJSDlvTb2nMOyhdWR9P+vTc5hhbfvrYaJt6hh31sVHn+h8vdsUVDjVpKk8PgLVavteYqbkqTw+D5qcedr1c5R79yBKjq8TztfHaG6516hoEYtSq0vL9OpgpvEKD99k+FZXXEiqy9oH1NPf3xwpS6/oHm1Hle/TpDef6aPnr3/XJ8o6gIAAN9llvGAJF14TpT++OAqndexene6Oyuylr59o7/uHNzeQ8lOH2MCxgQjrmun72cOqPbNHs7tGKHf/3elEs+N8lAy8/GtigDcqvjYQe2aebdixn5ceoX177qnPfeoAsLryxZWR02HTJQk2cJqyxZWW8FNYiSrVUENfeNOErXCAvXyYz00ZECMnv9vsj5P2im7vfzTVkOCbbqhf4we+lcnxbepvPpvhIpeG1tYXdlzj0qS7HlHFVCrngLC66l2p8Ry2ynYt11BkTGSpMIDuxTUsFmp9UWH9mr79BtKLQusF6mYhz8staxR/5HaMmmAWtz5apnnKC9TRYzO6o+aNamlL1+5VAt+SNVLH2zQT3/urXDbBnWDNfyaWI25paOianDmGAAAODOYbTwgHf8CcdmcgZr1WYpe+XCj1qYcrHDb5k1qaeSgON17Y7zqhBs7D3B5GBMwJjjh4u5Nlbzgn3rpfxs0c/4m7dqbU+G2CbENNPqG9rrt6lgmva8mCmAm5bQXa8eLN6v5sOkKrB9Zal1oywRlb/pVoa0SZM87WlLJP1lu6lrZ847JWVSg/PTNCmke563oVerZpYl6dmmivQdy9eua/fpzwwHtP5gvq9Wipo3C1K1DQ/Xs0kT1T5oE2JdU9tqEt+uhzG9nqkHvwTq25gc1vGhomceHNG2rg1tWSJLy09YrtEW8nHa7LNayb36B9SMVNyWp8jwOhzI+mqymNzx5fD6IG56sdqaCfdvV4IIbyiz3dlZXVJTVSBaLRddeEq1rL4nW1rSj+n3dfv21MUtHsgsVYLOq9Vl11K1DQ3VPaKzQEN62AQBA1cw8HggIsOqO69rp9mvjlLzlkFasP6C1KQeVk1ekoECb2kXXVbcOETqvYyOfLRAwJmBMcKratYI0bkQXPXJbgv5IztSfGw5oc+oRFRTaVSs0UJ3a1te5HRupU9v6XAVymhhJmdShZfOUu2WF0v87VpLU7JZndPCnD9RixMuK/OdYpc64VY7CPDUdMqnMY512u9LffVDRY96Ts7hQO1+/U20mfFVqmwPfv6PMRa+p+NhB2bMPGVJ5j4wI0zUXt9I1F7fy+nPXRHmvTXCTaB34/h1FDR4na2CINj92gUKju6hW7HllHh/aqrPy506UJOWlrVd4XA85iwtUdGS/ig5mKLBB9U6B3f/lS6rX/Ro16j9S2569Tnlp60utD2vdtcpM+XtSyp3w1NtZncVF2jJpgPJ2rNGWiZep2c1TVSuu9F1+KsrqK9q0qKM2Leropn+0MToKAADwY2fCeMBisahTbAN1ctMdIr2JMQFjgooEBFhLTvqAe1mcRt/6wMcVPz5JzuQNhjy3pWMHBUx1vZo9Ypm0KstzeZLvaqf63a8pufPLqXa/P16Hls9X/MvrZbHZ1LWh9GblN7U4I3jiddn76XTV6Xyxx+6kcmjZfO395Fk1v+151e7Yp8z6/IytSn3hZtXvNUi1O/fT0VXfKPLaR/w2K/uq+5y4S41z7XCDkwDu44/7tT9mBqpi5H5t1JiguuMBybNjguqOBySOs05gTODbWdlP3csb79eJiYmSpKSkJJcfwxlgcFnH1yqfJLDZzU+r2c1PeynNmS3ymoc82n79Xtepfq/rKlwfEtVG7f79W8n/h0V3rnBbf8oKAACAijEe8C3+dJztT1lhXhTAqmCJbuk3zx1X10NBTpOv5TEKfwffx2sEAAAqY9SY4HSe19eOa3wtj1H4O/g2Xp8zAwWwKtjuGGp0BJc92NHoBCgPrwsAAIB/Y0yAmuJ1AYznm7fEAAAAAAAAANyEAhgAAAAAAABMjQIYAAAAAAAATI0CGAAAAAAAAEyNAhgAAAAAAABMjQIYAAAAAAAATI0CGAAAAAAAAEyNAhgAAAAAAABMjQIYAAAAAAAATI0CGAAAAAAAAEyNAhgAAAAAAABMjQIYAAAAAAAATI0CGAAAAAAAAEwtwOgAvs7+1mw5d+w05Lkt0S1lu2Ooy9s/nyxtPuK5PNUVV1d6sKPRKQDgOF97j0RZfG6cOeiPvo2+WJZRY4Lqjgck3+tf7E8AfAUFsCo4d+yUM3mD0TFcsvmItCrL6BQA4Jt4jwR8B/0R/oYxAQD4Py6BBAAAAAAAgKlRAAMAAAAAAICpcQkkAKBGsnOL9Oua/Vq5/kDJsrEv/KGz2zVUj86N1apZbQPTAacn82Celq/Zrz83/L1fP/Hqn+rWIUK9ujRRRP0QA9OVz253aEXyAa08KfO9z/6qjm3q69z4CHVp11AWi8XAhED15eUXl/mMeWj67+ry/58xrc+qY2A6AMAJu/Zm69c1+7Vq49/XYE95c7W6dYhQzy6NVSc8yMB0x1EAAwCclp17jmn6f5P134VbdCynqNS6f89eV/Lvft2baswtHXX5BWd5OyJQbX9uOKDps9fpkx9SVVTsKLVu8szVkqTAAKuuu6SVHvpXJ3XtEGFAytJycov0yocb9PrHm7RzT3apdS9/8PecRe1j6mn0De11x7VxCgq0eTsmUC179ufohTnJevezFB06Wlhq3fNzkkv+fWG3SN13U7yuubglBV4AMMAPv+3WC3OS9c2ydDmdpdeNf+VPSVKt0ADdPLCNHh7aydAvLrgEEgBQLU6nU69/tFHx1yzQK3M3lCl+neqH3/boH6O/0+CHflTmwTwvpQSqJ7+gWGNf+EPn3bhQH36zvUzx62RFxQ7NXbRd5964UI/OWKGCQrsXk5b208oMJVz3qR6dsbJM8etUG7cf1t1Tf9V5Ny7Ums3MkA3f5HQ6NWfhFsVfs0DPz0kuU/w61U9/7tW1DyzWlfd8rz37c7yUEgBw6GiB/jVuqS4Z8Y0W/VK2+HWynLxizZy3SZ3+uUAz3kuWw1HJxh7EGWAosXlconI2/SpLQKBktSm4SYyiBo9X/Z7XGh0NgI9wOJy6c/IyvfXJ5mo/dt53O/TnhgNa/NYALousAd6r3e9YTqEG3v29fvpzb7Ue53A49dy7a/X7ukx98fIlCg8L9FDC8s1ZuEXDnvi52geRazYfVPebv9CnL/ZT/97NPZTuzEB/dC+n06mHn/+j1Blervryp10678aF+uGtAWoXXc/94c4Q7NMAXLFnf44uvmORNu04Uq3H5RXYNebfv2vlhgOaPflCBQR495wszgBDKVHXT9DZH2Wry/tZanDhEG3/9/XK351idCwAPuKRF1ecVvHrhO3px9RvxCIdOlrgxlRnHt6r3cdud+ia+xdXu/h1sqQVGbr2gcVe/Tbzi6Q0DZ3w02k/Z36BXdeM+UG/rdnv5mRnHvqj+0x5a/VpFb9O2L0/V/3uWKSMzFw3pjrzsE8DqEx2bpEuGflNtYtfJ/vfV9t09zO/ujGVayiAoVwWW4AaDbhLctiVt3Nd1Q8AYHo//r5H0/9b+fuBc+1wOdcOr3SbbbuO6f7nfnNntDMW79U1N+P99Vr8+55Kt3Flv/5u+W69/MF6d0arUObBPA1/8udKLzVwJXN+gV23jl+q3LxiNyc8M9Efa2ZFcqaefO2vSrdxZb/evT9Xd05eJmdlHQQuYZ8GUJ6xL/yhDdsOV7qNK+/XM+dt0hdJaW5MVjWfLoA5HA5Nnz5dbdu2VUhIiDp37qylS5cqLi5OI0aMMDqeqTmKCpX59auyBAQqNLqz0XEAGMxud2jEU7+4rb05X2xV0ooMt7V3puK9umb27M8pmZzVHR77z0rtPeD5M08e/c9KZR7Kd0tbW3Ye1XPvrnVLW2c6+uPpczqdGvHUL247i3JhUpoWenlQZUbs0wBOtSI5U69/vMlt7d05eZkKi7w3l6pPF8CGDx+uyZMna+TIkVq0aJEGDx6sIUOGaPv27erWrZvR8crVb/kSTU3Z4PJyX5Mxb4pW31hP64Y31+HfP1fMI58oJKqN0bEAGOzrn9O1bdcxt7b5kpfOljEj3qvd461PNiu/wH0HXXkFdr294PQvEXbFgUP5+t9XW93a5hvzNho6kb+/oz/W3M9/7tXqTQfd2uZL/zP2M8afxwTs0wAqcvLdpd1hT2auFvyQ6tY2K+Ozk+DPnTtXs2fPVlJSkvr06SNJ6tu3r1atWqUFCxaoa9euBic0p6hB4xQ1eLzRMQD4mFmfu3/uj8+XpCnrcL4a1gtxe9tmx3u1e8z6fIv72/xsi8aPONvt7Z7w4TfbVVBY8R0qT8f+g/la9MsuXX1RK7e2e6agP9acJ/rij39kaOeeY2rZlJuuVBf7NIDy5OQW6ePvtru93Vmfb9ENA1q7vd3y+OwZYFOnTlX//v1Lil8ntGnTRoGBgUpISNChQ4c0cOBAxcbGqnPnzrr00ku1dat7vxUFAEi/rc10e5sOh1Mr1x9we7uAK/YeyNXOPdlub3d7+jFlHsxze7sn/LbWM5PWe6KPA67y1H79+zr2awBwl9WbD7r9Szjp+Hu1t+Zt9MkCWHp6upKTkzVo0KAy69LS0hQfH6/g4GBZLBbdf//9SklJ0Zo1azRw4EANGzbMgMQAYF77s/I8dket1ZuzPNIuUBV3X251sjUpnmt79SbP9BlPtQtUJb+gWJtTT/9OYpXxZD8HgDONp47bjxwrVOpu938pWR6fvAQyPT1dkhQZGVlqeV5enpYuXaoBAwZIkurVq6d+/fqVrO/Zs6emTZvm0nNYLBaXtvu+R6L6RDR2adsTnt2yUS9uKz0HSLa9WBdFNKlWO0lJSbrEMtHl7WOfXqLanRKr9RyetDQpSZbefY2OAaCmghpLcVNLLarqri4VrbckvFPq/x99fJIeHf5pzfK5yNfeI1GWVz836p4jtbiz1CJ37deXXHaVdNR9k+uXEjdNCmrgUq7K1p2a+dsffpLFMqDm+VxEf/RtXu2LtnCpw4xSi9zVF5+Z9qKeuf+DGsU7wagxQXXHA5Lv9S/GBIBJNBogRV5bapG73q9j2sZL+btqls8FPlkAi4iIkCSlpKTo8ssvL1k+bdo0ZWRkVDgB/owZM3T11Vd7I2KlHm3bXo/Hdii1rN/yJQalcV3clCSjIwDwRU4PTo7tdP9p1GbHe7WbeHLf82SfkYfa9mhm86I/uoFH+6KxnzH+OCZgnwZQIb89dvqbTxbAYmJilJCQoKlTp6pBgwZq1qyZ5s+fr6+//lqSyi2ATZo0SVu3btWPP/7o0nO4eo1p8eOT5Ew25k4tiYmJclbjQ3LEMmmVD13B0CcxUZu9dC0vAM8pLLKrTo/3St0l7tRvbU448S1PRetP9d+3/q1br/ysxhld4WvvkSjLm58bazZnqcugz0otc9d+ve7PxerYtkHVG56GS0Ys0g+/7Sm1rLxc1c089MZ/aNbk52oe0EX0R9/mzb7odDrV8IL3dehoYckyd/XFl6aP1z03zq15SBk3JqjueEDyvf7FmAAwhwU/pOraBxaXWuaO92ur1aIjB1MVHhZY85BVPZfHn+E0WK1WzZs3T/Hx8Ro1apSGDRumiIgIjR49WjabTQkJCaW2f/rpp/Xll1/qm2++UVhYmEGpAcCcggJtSoit75G2u3WI8Ei7QFU6xNRXcJDN7e2GhtjULrqe29s9wVN9hr4Io1gsFvZrAPAD3To09Ei77aLreqX4JfloAUySYmNjtWTJEuXk5CgtLU2TJ0/WunXr1KFDB4WGhpZsN2nSJH3xxRf6/vvvVa9ePeMCA4CJXdGnhdvbjGleW+1j6rm9XcAVgYFWDejd3O3tDuh1lgICPHd45Ym+aLFIl1/g/r8F4CpP7NdNGobqnHgKYADgLi2iwtWprfu/FB944Vlub7MiPlsAK8/KlStLXf64fv16TZw4UVlZWUpMTFSXLl3UpUsX4wJK+qFn3zLX+le2HAD8we3/jFOAzbWbh7hq1OD2slrd2yZQHXdd397tbY6+wf1tnqxnl8ZKiHXv5ZUDejdXTPM6bm0TqI5br2ijsBD3zsxyx7VxCgp0/1mermJMAMBsLBaL24+dLBbpzkGePXY6md8UwLKzs5WSkqKuXbuWLIuPj5fT6dTWrVu1evXqkh8AgHtFNQrTvTfFu629FlG1NOK6OLe1dzpyNv+uTWN7atOjvbXr7TFl1u96e4w2P3aBdr11nySpOPuwjq1L0rF1SSrOPixJ2vvpdOVu/8tjGQ8snq3kUXE6lry03Ez5GVu14f4u2v3+eOXuWKO9C6b5RNby/rYVZTVSv+5N1ffcKPe2d5772iuPxWLRlHvKvxnQ6bDZLJp0V9eqN/Qgf+uLhVl7tGFMV626LkROe7Ek+mJN1asTrEduS6h6Qxc1qh+i+9z4mQUAOO5fV7ZVbMu6bmvvjmvjFN28ttvaq4rfFMDCw8Nlt9t1zz33GB3FL1R2MFmYtUcp4y/SprE9dXT1D3I6nbLnHNGeuRPltNtlzz1Wbpt/Damr3XMekyTtfG2kNj3SS5se7a3c1LWSpP1fvaI1/4pUfsZWz/5yAAzx9N3d3PaB986kC1QnPMgtbZ2uoMYtFfv0j2r37C8qPrJfeanrStblblslR3624p75WY7iQuVsWaHsjb8oK+k9ZS2Zo+z1P8npcChn4zKFxZzt0ZyR1zys2h37lJspJKqNzho+Q5IUFt1ZOZt+ldPpNDxreX/birIayWKx6J1JF6hWaM3PPKldK1BvT+wti8XzZzUO7NNCt17Rxi1tPTIsQefEN3JLW6fL3/piQO0Gip28WLXiupesoy/W3GPDO+vsdu6ZX+b18T0VUT/ELW35M8YDANwtNCRAsyZfIHcc7rSIqqV/P3BezRuqBr8pgKF6KjuY3PvJs2p602S1nfSdMuY9LWdxkTK/nansTcuV8fFk2XMOl9tmaMtOanbrM5KkyGsfVbvnlqnVvbOU8eEkSVLjf9ytul37e/x3A2CM0JAAffHyJWrSMLTCbSwJ71R5t5cXHz5f/bo3c3e8agusHylr0PEBkiUgULL+falM9ubfVLvLJZKkOp37KWfTr2Uen5e6RsFRx4sQx9YlafWN9bV5XKLW3d5SW6dcVe08h1d8qfRZD8vpcGjLxP4qzEwrtd6VTMFN2yqvnDNLvJ21sr9tVVm9Lbp5bc1//mIFBVZ8SFTVfh0UaNX85y9Sy6be+wbz9fG91PvsJhWud6Uv/vPiVoaf/SX5X1+0BoUoILzyOVDoi9UXGGjVZ//ppxZRtSrcxpX9euKos3XtJdHujueXGA8A8ISeXZpo5oRelW5T1ft1/TpB+vLlS73+hTgFMJOq7IAnb+c61WrXU7bQcNlCa8tZlC+pdAl3+/Qhyt2+Wnmp67TtuUFl2g9ucvzAwmILlKWcgykA5hTbqq5+mvUPdWhdr9qPDQm26c0neun+Wzq6P1gN5KauVdGRTIW2+HtOFnvOYdnCjs+JZAurq+Kcwwpv31sNE29Rw763Kjz+QuXv2aKgxq0kSeHxF6pW2/MUNyVJ4fF91OLO16qdo965A1V0eJ92vjpCdc+9QkGNSk8KXV6mUwU3iVF++ibDs55Q3t/21Ky+oH/v5vr61cvUuEH1zxhp0jBU37x+mS7t6d1J5MNCA/TN65fpnxe3Oq3HjxzUTh9O6+vRCfury1/6oivoi6enRVS4fp49UF3bV/9MsMAAq154+Hw9Ocr4oq6vYDwAwFPuuK6d3n+mz2mdRd+2ZR39NOsf6uTmOU1d4d7ZJuFzyj3gcdhLLtGwhdVVcfYhNbpshBwFOYoaPEGOglyddfsM7Xj+RslqU6t7Z1fY/u73HlPjgfd6+LcA4EtiW9XVqo+u1lNv/KUX30tWXoG9ysf0PTdKb0zopdhW7pszwB2Kjx3Urpl3K2bsx6WW28Lqyp57VJJkzzuqgFr1FBBeT7U7JZbbTsG+7QqKjJEkFR7YpaCGpc9wKzq0V9un31BqWWC9SMU8/GGpZY36j9SWSQPU4s5XyzxHeZkqYnRWqeK/ra+6uHtTrf/0Wt0/7TfNXbRdDkfll4RZrRbddHlrvTj2fDWsZ8ylVrXCAjX/hYs09+vteuiFP5SRmVvlY1qfVVsvP9pDAy7w3h2XXOFPfbE6fCGrv/XFFlHh+u39K/XcrDV67t21ys4trvIxPTo31swJvQwZTPkDxgMAPOGmf7RRz85NdNeU5fpmWXqV2wcHWTX6hg6aPLqbwtww/cTpoABmYhUe8Fj//rbXnntUAeH1ZQuro6ZDJkqSbGG1ZQurreAmMZLVqqCGTcttf9/CGQo9q4PCO/T21K8AwEcFB9k05d5z9NDQTpqzcIu+WbZbKzcc0IFD+ZKOXxKWENtAPTs31vB/xrn9rnXu4LQXa8eLN6v5sOkKrB9Zal14ux7K/HamGvQerGNrflDDi4aWeXxI07Y6uGW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      "text/plain": [
       "<Figure size 1591.6x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library.data_preparation import ZZFeatureMap  # can also drop .data_preparation\n",
    "\n",
    "data_preparation = ZZFeatureMap(3)\n",
    "data_preparation.draw(output='mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 562.032x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library.n_local import RealAmplitudes  # can also drop .n_local\n",
    "\n",
    "classifier = RealAmplitudes(2)\n",
    "classifier.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.aqua.algorithms import VQC\n",
    "from qiskit.aqua.components.optimizers import SPSA\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "from qiskit.ml.datasets import ad_hoc_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, training_data, test_data, _ = ad_hoc_data(10, 10, 2, 0.2)\n",
    "\n",
    "markers = ['o', '^']\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.title('Training (full) and test (hollow) data')\n",
    "for marker, (label, data) in zip(markers, training_data.items()):\n",
    "    plt.scatter(data[:,0], data[:,1], color='tab:blue', label=label, s=60, marker=marker)\n",
    "for marker, (label, data) in zip(markers, test_data.items()):\n",
    "    plt.scatter(data[:,0], data[:,1], facecolor='', edgecolor='tab:blue', s=60, marker=marker)\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "optimizer = SPSA(maxiter=100)\n",
    "vqc = VQC(optimizer, data_preparation, classifier, training_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 0.3044436195870143\n"
     ]
    }
   ],
   "source": [
    "from qiskit import Aer\n",
    "from qiskit.aqua import QuantumInstance\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "result = vqc.run(backend)\n",
    "print('Loss:', result['training_loss'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 19 / 20\n"
     ]
    }
   ],
   "source": [
    "points_a = test_data['A']\n",
    "points_b = test_data['B']\n",
    "_, predicted_a = vqc.predict(points_a)\n",
    "_, predicted_b = vqc.predict(points_b)\n",
    "\n",
    "print('Score:', sum(predicted_a == 0) + sum(predicted_b == 1), '/', (len(predicted_a) + len(predicted_b)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13109add0>"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.title('Correctly predicted')\n",
    "plt.scatter(points_a[:,0], points_a[:,1], s=60, marker='o',\n",
    "            color=['tab:green' if label == 0 else 'tab:red' for label in predicted_a])\n",
    "plt.scatter(points_b[:,0], points_b[:,1], s=60, marker='^',\n",
    "            color=['tab:green' if label == 1 else 'tab:red' for label in predicted_b])\n",
    "for marker, (label, data) in zip(markers, training_data.items()):\n",
    "    plt.scatter(data[:,0], data[:,1], color='tab:blue', label=label, s=60, marker=marker)\n",
    "\n",
    "train = mpatches.Patch(color='tab:blue', label='training data')\n",
    "correct = mpatches.Patch(color='tab:green', label='correctly labeled')\n",
    "wrong = mpatches.Patch(color='tab:red', label='wrongly labeled')\n",
    "plt.legend(handles=[train, correct, wrong])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Circuits in Algorithms\n",
    "\n",
    "![](algo_overview.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notebook link: github.com/Cryoris/notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* QSVM, VQC: Supervised learning with quantum enhanced feature spaces, Havlicek et al. [arXiv:1804.11326](https://arxiv.org/abs/1804.11326)\n",
    "* VQE: Moll\n",
    "* Variational QTE: Ardle\n",
    "* QGAN: Zoufal\n",
    "* QBM: Zoufal\n",
    "* QAOA: Farhi\n",
    "* QSBO: Gacon\n",
    "* QPE: Textbook\n",
    "* QAE: , Woerner\n",
    "* HHL: .."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Building a quantum algorithm\n",
    "\n",
    "Let's see how easy it is to build the quantum phase estimation (QPE) algorithm. Provided with $U$ and $|u\\rangle$, we want to find $\\varphi$.\n",
    "\n",
    "$$\n",
    "U|u\\rangle = e^{2\\pi i \\varphi}|u\\rangle\n",
    "$$\n",
    "\n",
    "This example:\n",
    "$$\n",
    "U = X \\otimes X \\cong \n",
    "\\begin{pmatrix} \n",
    "0 & 0 & 0 & 1 \\\\\n",
    "0 & 0 & 1 & 0 \\\\\n",
    "0 & 1 & 0 & 0 \\\\\n",
    "1 & 0 & 0 & 0\n",
    "\\end{pmatrix}\n",
    "\\text{ and }\n",
    "|u\\rangle = \\frac{|00\\rangle - |11\\rangle}{\\sqrt{2}} \n",
    "\\cong\n",
    "\\frac{1}{\\sqrt{2}} \n",
    "\\begin{pmatrix}\n",
    "1 \\\\ 0 \\\\ 0 \\\\ - 1\n",
    "\\end{pmatrix}\n",
    "\\text{ with }\n",
    "e^{2\\pi i\\varphi} = - 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x131127390>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitary = QuantumCircuit(2, name='U')\n",
    "unitary.x(0)\n",
    "unitary.x(1)\n",
    "\n",
    "# (|00> - |11>) / sqrt(2)\n",
    "bell1 = QuantumCircuit(2, name='|u>')\n",
    "bell1.x(0)\n",
    "bell1.h(0)\n",
    "bell1.cx(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before applying the unitary:\n",
      " Statevector([ 0.70710678+0.j,  0.        +0.j,  0.        +0.j,\n",
      "             -0.70710678+0.j],\n",
      "            dims=(2, 2))\n",
      "After:\n",
      " Statevector([-0.70710678+0.j,  0.        +0.j,  0.        +0.j,\n",
      "              0.70710678+0.j],\n",
      "            dims=(2, 2))\n",
      "Factor of -1?\n",
      " True\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "before = Statevector.from_instruction(bell1)\n",
    "after = before.evolve(unitary)\n",
    "print('Before applying the unitary:\\n', before)\n",
    "print('After:\\n', after)\n",
    "print('Factor of -1?\\n', all(after.data * -1 == before.data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The circuit we want to use is the following (see also [Nielsen]):\n",
    "\n",
    "![](qpe_circ.png)\n",
    "\n",
    "[Nielsen]: Quantum Computation and Quantum Information, Michael A. Nielsen & Isaac L. Chuang. [Online](http://mmrc.amss.cas.cn/tlb/201702/W020170224608149940643.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1314bcc10>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import QuantumRegister, ClassicalRegister\n",
    "\n",
    "num_eval_qubits = 3\n",
    "\n",
    "qr_eval = QuantumRegister(num_eval_qubits, 'eval')\n",
    "qr_unitary = QuantumRegister(unitary.num_qubits, 'state')\n",
    "cr = ClassicalRegister(num_eval_qubits, 'bits')\n",
    "\n",
    "circuit = QuantumCircuit(qr_eval, qr_unitary, cr)\n",
    "\n",
    "# start with eigenstate\n",
    "circuit.append(bell1, qr_unitary[:])\n",
    "\n",
    "# hadamards\n",
    "circuit.h(qr_eval)\n",
    "\n",
    "# controlled powers\n",
    "for i in range(num_eval_qubits):\n",
    "    controlled_power = unitary.power(2 ** i).control()\n",
    "    circuit.compose(controlled_power, qubits=[i] + qr_unitary[:], inplace=True)\n",
    "    \n",
    "# inverse qft \n",
    "iqft = QFT(num_eval_qubits, do_swaps=False).inverse()\n",
    "circuit.append(iqft, qr_eval[:]) # could also use compose but append wraps it so it's nicer to read\n",
    "\n",
    "circuit.measure(qr_eval, cr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.348x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import Aer, execute\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "counts = execute(circuit, backend, shots=1024).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'001': 1024}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Binary fraction: \n",
    "$$\n",
    "    0.b_0 b_1 \\dots = \\frac{b_0}{2^1} + \\frac{b_1}{2^2} + \\cdots\n",
    "$$\n",
    "Means \n",
    "$$\n",
    "    |001\\rangle \\rightarrow 0.100 = \\frac{1}{2} + \\frac{0}{4} + \\frac{0}{8} = \\frac{1}{2} = \\varphi\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Thus we have the eigenvalue\n",
    "$$\n",
    "    \\lambda = e^{2\\pi i \\varphi} = e^{\\pi i} = -1\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Could also just do this with the `PhaseEstimation` circuit from the library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 653.095x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import PhaseEstimation\n",
    "\n",
    "pec = PhaseEstimation(3, unitary)\n",
    "pec.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 802.977x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(5, 3)\n",
    "\n",
    "# start with eigenstate\n",
    "circuit.append(bell1, [3, 4])\n",
    "\n",
    "# phase estimation\n",
    "circuit.compose(PhaseEstimation(3, unitary), inplace=True)\n",
    "\n",
    "# measure\n",
    "circuit.measure([0, 1, 2], [0, 1, 2])\n",
    "\n",
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Parameterized quantum circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Max-cut problem\n",
    "\n",
    "Goal: Find the largest possible cut in a given graph.\n",
    "\n",
    "Further references: [Qiskit textbook](https://qiskit.org/textbook/ch-applications/qaoa.html) or [James Weaver's Medium article](https://medium.com/qiskit/the-variational-quantum-eigensolver-43f7718c2747) or [Moll].\n",
    "\n",
    "[Moll]: Quantum optimization using variational algorithms\n",
    "on near-term quantum devices, Moll et al. [arXiv:1710.01022](https://arxiv.org/pdf/1710.01022.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "\n",
    "graph = nx.Graph()\n",
    "graph.add_nodes_from([0, 1, 2, 3])\n",
    "elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]\n",
    "graph.add_weighted_edges_from(elist)\n",
    "\n",
    "nx.draw(graph, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](maxcut_line.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Maximum cut at labels 0101 (or 1010, since symmetric problem)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Objective function must be encoded in a Hamiltonian (see Ref. [Moll]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.aqua.operators import Z, I\n",
    "ising = (I ^ I ^ Z ^ Z) + (I ^ Z ^ I ^ Z) + (Z ^ I ^ I ^ Z) + (I ^ Z ^ Z ^ I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Which Ansatz? Ideally, we have full access to the subspace of possible solutions. Here, we e.g. don't need complex amplitudes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1344.78x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import RealAmplitudes\n",
    "\n",
    "ansatz = RealAmplitudes(num_qubits=4)\n",
    "ansatz.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Why is it called `RealAmplitudes`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Statevector([0.35223618+0.j, 0.19504538+0.j, 0.3413613 +0.j,\n",
       "             0.00225788+0.j, 0.07074963+0.j, 0.11899706+0.j,\n",
       "             0.33085966+0.j, 0.24249931+0.j, 0.23170059+0.j,\n",
       "             0.26273251+0.j, 0.41993687+0.j, 0.02834874+0.j,\n",
       "             0.09823054+0.j, 0.10132007+0.j, 0.34313451+0.j,\n",
       "             0.31047391+0.j],\n",
       "            dims=(2, 2, 2, 2))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "bound_ansatz = ansatz.assign_parameters(np.random.random(ansatz.num_parameters))\n",
    "Statevector.from_instruction(bound_ansatz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's run the algorithm!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimal energy at: {'0010': 1, '0101': 1, '1010': 741, '1100': 202, '1110': 79}\n"
     ]
    }
   ],
   "source": [
    "from qiskit.aqua.algorithms import VQE\n",
    "from qiskit.aqua.components.optimizers import SPSA\n",
    "\n",
    "optimizer = SPSA()  # choosing Simultaneous Perturbation Stochastic Approximation optimizer\n",
    "ansatz = RealAmplitudes(4, reps=4)  # ansatz on 4 qubits\n",
    "\n",
    "vqe = VQE(ising, ansatz, optimizer)\n",
    "result = vqe.run(Aer.get_backend('qasm_simulator'))\n",
    "print('Minimal energy at:', result.eigenstate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "plot_histogram(result.eigenstate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can also choose others, but they have more parameters and are more difficult to optimize since they have more parameters!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1585.58x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import EfficientSU2\n",
    "\n",
    "ansatz = EfficientSU2(4)\n",
    "ansatz.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqe = VQE(ising, ansatz, optimizer)\n",
    "result = vqe.run(Aer.get_backend('qasm_simulator'))\n",
    "plot_histogram(result.eigenstate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Creating your own Ansatz: The `TwoLocal` circuit\n",
    "\n",
    "Template for hardware efficient, quantum-native circuits.\n",
    "\n",
    "    TwoLocal(num_qubits, rotation_blocks, entanglement_blocks, reps, entanglement)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1344.78x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import TwoLocal\n",
    "\n",
    "two = TwoLocal(4, 'ry', 'cx')\n",
    "two.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Qn7CwCKY9fzHdOvblnMQLLEpak7fc/3PNiVO2U/9+Eddd1Pjv9wkGb7/nYf3G8dhbN7Dk2zcJDQnjwZvesyip96yVVUd54NUR5Oxcx/2vXsXtI2awsyiHrLx0Xln4ewDGj3ic5C6pVsQXE/jTkV6JgwgPi+TuFy6lVVQcv7x4mq0yL18/p9YO2/F1W4LDn45YvY/0J7Od9jfiTBqI2FDXjik8d9c3x7/eWrCWd5c+QXxcj+OzV0wZVfMmsh2FW3l10f1ckjLa1Kwn8yX3MbOmrATskdtpvP2eW0TG8MT/fFzjOVb9nr1lDQ0J48mJS2o8p1fiIIb1G1tjmXrSePnTEYCJP5tZ42szO+It87B+Y0/rMNjzdVuCw9+OHGPFPtLfzHbZ34gzuTweT20ftitBlPEuFOdb87NjEmDgr/x7rlW5zyTzmZj6tvH3rBvN/9lO/F07tddNjVW9dmo/nLgtNjVN8bUa1GtpHHSPiIiIiIiImE6XZlmgZVtn/myrclv5+7KKE3/XTu21mMOp/XDitijmUa+d8XPFvjQQsUDSMKsT+MepuZ3Iib9rJ2YW8zi1H07NLeZwaj+cmlsaH12aJSIiIiIiptNARERERERETKeBiIiIiIiImE4DERERERERMZ0GIiIiIiIiYjoNRERERERExHQaiIiIiIiIiOk0EBEREREREdNpICIiIiIiIqbTQEREREREREyngYiIiIiIiJhOAxERERERETGdBiIiIiIiImK6UKsDNEVbPoeDe6z52S3bQtIw/55rVe4zySzmcWKvnZhZzOXE1z31WrxRrxtGvQ4eDUQscHAPFOdbnaLhnJpbzOHEfjgxs5jLiR1xYmYxlxM74sTM4p0uzRIREREREdNpICIiIiIiIqbTpVkiP/F4IG8f5OyFHftOLH8/HRJiIakDxDS3Lp+IP6qqIXsP/FgIBcUnls9fC51+6nXzZtblE/FHRSVs2Ql5RSeWvb4COrSCxDbQsz2EhliXT0R8o4GIzd0wvSOlh/bjdofgdoeQnJjKtNGv0Damk9XR6uS0zB4PpG+DZZuhYP/p31+RZfztAs5NgCvONXZ04h+n9eMYp+U+WgXLN8PKLCg+dPr3P//e+DssBAaeDVeeC62jzM3YmDitH8c4LXfpYfgkE77JgcNHa35vXS6s++nfLSIgtRtc1hsiwkyP2Wg4rR/HODV3U6RLs2ys8MAO9pXs5Pmpa/jw/0p58/4cisv28OrC+6yOVienZd5fBi98Du98Vfsg5GQeYEM+PLMYPlwLlVWmRGxUnNaPY5yWO7cIZi6CBd/VPgg52dEq+GorPLHA+NvjMSdjY+K0fhzjtNzrcuHxBfDFltMHIacqPQyfboQ/L4CsXebka2yc1o9jnJq7qdJAxMa25KXTPCKaxLbnABAd1Ybu8f0pLrVo/jofOCnz7gPwzMcN30l5gM++h9e+MA7ixHdO6sfJnJT7+x3wt09hd0nDnldRCe99bVyypcFIwzipHydzUu6lm4xLr8oqGva8/Yfghc8gPSc4uRozJ/XjZE7N3VRpIGJjW/LSSUo4H5fLRVVVJembF7N83XsM6zfO6mh1ckrm0sPw/GdQUu7/OjYVGGdSdNDmO6f041ROyZ1bBP9YcWZn65ZuOnHZlvjGKf04lVNyf5MD/13j//M9GK/VmwoCFqlJcEo/TuXU3E2V7hGxsS156WRuX8l1D8dQfqSUiLDm3D36NdL6jLE6Wp2cknluOhzwMgiZdaPx99S3637M2h+N+0YGdAlYtEbNKf04lRNyH60yDra8DUJ86fWiddCrI3RsHbh8jZkT+lEbJ+TeX2ZMGFIfXzrtAd5dDfddA83DAxavUXNCP2rj1NxNla3PiFRXVzNz5kx69OhBREQEffr0Yfny5SQlJTFhwgSr4wXdD/kZPDBuNvOmF/POg3nEtUogd89mq2PVywmZt+yE73IDt74PMuBIZeDW568d+2HxBpi/Br78AcqPWJ3odE7oR22ckPuLzbDrQGDWVeWB9zMCs64z4fEYl04u/M64L2vtj/a8N8sJ/aiNE3LPX2tcNhgIB8rh48zArOtMVFYZXf5wrdHtrF32PLPuhH7Uxqm5mypbD0TGjx/P9OnTmThxIh999BFjxoxh7Nix5OTkMGDAAKvjBdWOwq0cLN9Pj4T+ALSJ7sD1aXezYPWLVFdXA+DxeLjr2VQKCrMpPFDAtOcvZte+7bbOnLntS56YffPx5zz+zo1szv3G1JzHZsEKlLKKwA5sGqr0MDy/BP6yCBavh883wZxv4I8fGDOB2YUTOw3O6HV1Naz8IbDrzN7jfQKHYNpZbNyY/Pxnxk3Hn30P/1wJf/qPcR+MXajXwXPgkHGDeiB9nR24gY0/vt9hdPifK41Of7rR6PjjC4zO24V6LWax7UBk9uzZvPHGG8yfP5977rmHoUOH8uCDD5KamkplZSX9+/e3OmJQbclLp2XzWNq17nx82ZDeoyg+uJvM7SsBcLlc3D5iBi9++DuemH0jU3/5Mu1ju1iU2LfMPRMGkFNgTLC4IWcFYaHhnJN4gWkZD1XAxiAcxFh1I+TRKmPWrx921/69ed/Cii3m56qNEzsNzuh19l7jEpZAS98W+HX6Yn8ZPLcE9h48/XuHKuDV5bC1ls5bQb0OnjU/QnWAzxQcPgob8wO7Tl9t3W1091AtN9zvPWh0PhjbsT/UazGLbQciM2bMYPjw4aSlpdVY3r17d8LCwkhJSQHgj3/8Iz179sTtdjN37lwrogZFVl463Tv2q7GsVVQcyV2GsGL9if9n1w4pZG5bwVXn307ndr3MjlmDL5mbhUUQGd6CkrIiXv/4IcaPeNzUjHn7gnMKPLco8DtMX6zZblySVd+PXrjOHpeOObHT4Ixe5xYGab1F3h8TDJ9vMs401ratejCWL/jO9Fi1Uq+DJ1j9+9GiXi/4zuhuba/XHo/R+c83mR6rVuq1mMWWN6vn5+eTmZnJtGnTTvtebm4uvXv3JjzcuNts+PDh3Hrrrdx+++1mxwyq3177dK3Ln5m84vi/yytKeeytG5g86m8sTn+NKwbcXOtzzOJLZoBeiYOZ9f5EUpOvpXXLdmZEOy5Yp74rKo13stq0CM7667I62/igxfoGIoePQmY+9O9iUqg6OLHT4IxeFwSp11ZcKlJVDd9k1/8YD7C9EPaUQNtoU2LVSb0OnmBdGmhFr3eXGJ315ptsuK4/hFj8NrF6LWax5RmR/HzjvGn79u1rLC8vL2f58uU1LssaMmQIXbt2DVoWl8sV8D/Lly8741xHKiuY/tYYxl32IJcPuIkOsV1ZueE/Xp+3fPkyS3MDJHcZwvZdmfz8ort8evyZZD71z30PPHza+mfdWPsfX79/TFKv84LSl/r+rN+cW+8g5JgJd/w+6FnOtB/+dhr870igOg3W9vrfc+edtv5A9PrgoaOmdzoqOtbna/gHDrm80fbaDq/VYG2vt+acfoNIIF6rv1j5tem9Pn/I5T79/ioqISo6Vr1uxL1uKn98ZcszInFxcQBkZWVx9dVXH1/+5JNPsnPnzkZ/o7ovmoWGM2P8ouNf3z3mNQvTNMy67GVMHvU3QkPCTP/ZVZXBm0qqqsr8aaoqDh2gRWw1Llf97ylUlAdoOqUgcnKnweJeB6l7VZUN/PS4AKisKKO6uhK32/vu6Yh6HXTqdWD42tXq6koqK2xyo0g91GsJFFsORLp27UpKSgozZswgNjaW+Ph45s6dy6JFRunNHIh4gnBDQca7UGzRzXJpaZfiecG//9OZ5t5bnM9z8+4gsV0yA5Ou9Pl5Z5L5VOvz4B9f1FxW19zzvsxNf0yIG/bmbSE05MzyNdQnmcZnPtTH7YJVC16iZeRLQc3ixF4HIrMder1ondGFkwWi1107tAjKa6A3//gCNuTXfz9X6ygo2JqO2/c33vxiVa+tfK0Ge/T65aXw/SkfQlhbbxvSaYBfXnMJc6ab2+tqD0yfZ3zSe11cLujbOZTKo8EfKKnX1vVaarLlQMTtdjNnzhwmTpzIpEmTaNOmDbfccgtTpkzhgQceOH6jujjLWTEJPHrr6ZeQmKlTbHDW2yEG0wchAKndjE/CPnyk7vtEBneDlpGmxmpS7NDrhCD1Oljr9WZoL2MgUp8rehP0QUhTZpdenzoQCYRg7Qfq43bBFefCv73MEjvU+vu9GzU79FpqsuU9IgA9e/Zk6dKllJWVkZuby/Tp09mwYQPJyclERuqoSvzTOio4O6E+nQK/Tl+0jIRJwyCyWc3lxy7PPDcBfjHQ/FxirqT2EB6Et5X6JAZ+nb44+yy4acjpA41jX17RG1K7mx5LTJYShNdVtwt6JwR+vb5I7W50F050+Ri3C24eYnRfpCmx7UCkNhkZGaddlvXwww+TkJDAV199xcSJE0lISCA728uUK9KkXdQzsOsLcRtnHayS2AYeGgU/P2nT6JsIky+D8ZdYc6ZGzBUeBhcEeM6ONi0gqUNg19kQA7rAw6PgynNPLEvtDvdeDdf0PTHYlsYrIRbOjgvsOs9NgJjmgV2nr1wuo7v3Xl1zIH1Fb6PrVs9sKGIFxwxESktLycrKOu2DDKdPn05+fj4VFRUUFRWRn59Pt24WHhUGyNYda7nv5Su5428X8Oan/8ttTyaxLns5AIUHCpg0qz9X/yGCqipjepkdhVuZ+HRfXl/8kJWx6829a992Rj/ajrtfuJT7XjauzbQi94Au0LF14NY3rJf1lz41bwZp55z4+paLoGd7+x2s1dePqqpK/u+tX3HPi0N5ZcHvAWt73dBtcNuuTP7fc0OY9vzF/OW92/B4PKbmv7w3RAbwvstr+1l/6VPrKLi6z4mvxwyC+ABuu2eiof1I37yYu1+4lLtfuJQb/rcDX2bOs6Tf9eXelPs1/++5IUz9+0W8MH9anf8XM3P/rN/pZw/8FeqGa/p4f1ywxbc2unzMNX2NrttBQ/thh/16QzPbbV/T1DlmINKiRQuqqqq48847rY4SdJVVR3l10f08cssHjLvsIdzuEEan3UufbsaHO0Y3j+XJCZ/RK3Hw8efEx3Vn8qhZVkUGvOcGGNDjCp6atIw/T/gEsCZ3aAiMGwwhAdi7dYiBq8478/U0Bd76sTLzP3Tt2IeZv11KRWU52QXrLOu1P9tgp7OS+Osdq47PV5+Vn2Fq/lbN4ZfnB2Zd/Ttbd1mWE/jTj/PPGc5Tk5bx1KRltI1JpH+Py03vt7fc7WI685eJnzNrykqKS/ewbecGy/c3XdvCJed4f5wvru4D7VoFZl2NkT/9AGv36/5kttO+Rhw0EGlKvs36hJSuaUSGt6BNdAfmrfhrje83C4ugZXObvC14Em+5Ab7LXsq05y/m/S+esSDhCQmx8OuL6n/Hd+rb9c/C0joKJlyqS5985a0fO/fl0LWDMRFFt459+X77KitiAv5tgydPAxkWGs5Zrcy/cWjg2d4Hxt563fUs+NXgur8vZ/YavbMoh5iW7YgMN/nTT/GeOza6Pc3CIgAIcYfhdofYYn9zbb/67xfx1mkwLoXSjeD186cfYO1+3Z/MdtrXiE1nzWrq1mcvZ83WJXyb9Qklh4oYd7kzThV6yx0b3YHX78uiWUg4f3xjFP26X0bXjtbNgNYnEX6TBu98BaUNnC3x7DhjIGOX0+lO4K0fnc5KYn32cgb1uoZ1W5fSuX1vi5L6vw2u2jif1z96gPi4HkRHtQlyytqNSIGocJi/BiqrG/bcAV3ghkHQTHuGep3Ja/TKDR9w4bk/D2K6uvmaO6dgPQfK9tK5XbLJCWsX4jYuN533LazIathzj81WNfw8+12qajf+9ONIZYWl+3V/MufvzbLNvkZ0RsSWikoKmH7bAp6atIzzk4bj8TTwaMIi3nI3Cw0nslkUISGhDO41ku27M+tYk3mS4+H+kcaNviE+bA0twuG6/nDnFRqENJS3fgxO/hkVleXc+9JlhIWG07pFO4uS+r8NDul9La/ck0lcTAKrv18Q5JR1uyTJuCHW15vNz2oJt18CN1+oQYgvzuQ1+qtNHzIk+dogpqubL7lLDu3juXl3cPdoe31AXYjbuPRwymW+3+N3dhxMvcoYnGsQ4p0//bB6v+5PZjvta0RnRGwpKjKGg4eKaLyj3ZsAACAASURBVBYaTv7eLDq3601VdaXVsbzylvvQ4YM0j2gJwMbtXzLqInvc79MiAsalws/6Qvo2yNkL+fvgUIWx84qNgoQ2cE4HY5peXYrlH2/9CHGHcMd1zwLwzNwJDEy6yqqofm2DRyoraBYaDkDz8GjCw6ydwaBdK2Nq590lkJEDuUWwoxgqjhoHdW2jjamsUzpBj/bW35juJP6+Ru8r2UVYSDPLzpZ5y11VVckTs29iwsiZxEa3tySjNz3aw70jYHshrP0R8vbB7gNwtMoYRHeIMXo9oIt1n4PjVP70w+r9uj+Z7bSvEQ1EbOmaQRN4as54oqPiuGPUs2zYtqLG9yurjvLAqyPI2bmO+1+9ittHzKBX4qA61mYeb7k3bFvBPz9+mLDQcM49+2JbZD5Zy0gYlgzDrA7SSHnrR+GBHTz+zo24XW4uH/Br4lrFW5TUv21wf8ku5q54GoD4uB4M6On7p/YGU7toY1YeCRx/X6NXbfwvqb1HWZTae+7l6+eQlZfOKwuNmYTGj3icnp0G2m5/43IZn7ehz9wILH/6cbB8v6X7dX8yt22daJt9jWggYktdO6bw3F0nPn51a8Fa3l36BPFxPejTLY3QkDCenLikxnN2FG7l1UX3c0nKaLPjHuct96BeVzOo19U1nmOH3GIOb/2IaxXPU5OW1XiOVf3wZxsEGHJuzYNM9btx8rcfI1Mn1vja7H54yz2s31iG9Rt72vPsuL+RwPO3H1bu1/3NbJd9jYDL4/F4rA7R1GS8C8X51vzsmAQY+Cv/nmtV7jPJ3NQcmzlm1o3m/2wn9tqJmZuipthrJ75Wg3rdEOp1w6jXjZPOiFigZVtn/myrclv5+xLfObHXTsws5nLi6556Ld6o18752Y2dBiIWSHLoTQhOzS3mcGI/nJhZzOXEjjgxs5jLiR1xYmbxTtP3ioiIiIiI6TQQERERERER02kgIiIiIiIiptNARERERERETKeBiIiIiIiImE4DERERERERMZ0GIiIiIiIiYjoNRERERERExHQaiIiIiIiIiOk0EBEREREREdNpICIiIiIiIqbTQEREREREREyngYiIiIiIiJgu1OoATdGWz+HgHmt+dsu2kDTMv+dalftMMovUR9tiw2hbdAb1umHUa2dwYq+dmNlsGohY4OAeKM63OkXDOTW3SF2c2mmn5hZzOLUfTs0t5nBiP5yY2Wy6NEtEREREREyngYiIiIiIiJhOAxGRRuJA+Yl/5+2DI5XWZREJBI8HCg+e+HpnMVRVW5dHJBCqqo0uH1N40Oi6SFOke0REHKxgP6z8ATLzoeSkgchTH4HbBfGt4YKuMPBsiGxmXU4RX3k88MNu+PIHyNoF5UdOfO/PCyEsBLrEQWp3SOkEoSHWZRXxVWUVrM+Dr7bC9kI4WnXie4/NN16fe7aHC3tAj3bgclmXVcRMGojY3A3TO1J6aD9udwhudwjJialMG/0KbWM6WR2tTk7M7DSlh+H9DFj7Y92PqfYYZ0by9sHCdfDzAcagRDs4/zix107LvLsE3v0KthXW/ZijVcZA5Yfd0KYF/GqwceAm/nFaR8B5mX/YDe+uhqLSuh9TfgTW5Rp/usTB2FRoF21exsbGaR0BZ2YOBF2aZWOFB3awr2Qnz09dw4f/V8qb9+dQXLaHVxfeZ3W0Ojkxs9PkFhnvDNc3CDnV4aMwezW8saLmO3HiGyf22mmZ12yHvyyqfxByqqJS+PsSWLROl7b4w2kdAWdl9niMbv59Sf2DkFNtLzS2hTXbgxatUXNSR45xYuZA0UDExrbkpdM8IprEtucAEB3Vhu7x/SkutWhSah84MbOT5O2D5z+Dg4f9e/66PHj9C11n31BO7LWTMq/ZDm9+aVy+4o9PMmHBdwGN1CQ4qSPHOCnzgu+MbvqjssrYJr7dHtBITYKTOnKMEzMHigYiNrYlL52khPNxuVxUVVWSvnkxy9e9x7B+46yOVicnZnaKiqPGGY3DR+t+zKwbjT/1+b4APvVz59hUObHXTsm8pwTeWQ31ndDwpdeffW/cKyW+c0pHTuaUzJn5Rifr463XHowz2XtLAhqt0XNKR07mxMyBYut7RKqrq3n66ad56aWXyMvLIykpib/97W9MmDCBtLQ0Xn75ZasjBtWWvHQyt6/kuodjKD9SSkRYc+4e/RppfcZYHa1OTszsFAvXNez0fn0+yTRu9O3YOjDrOxNV1XCoAsJCISLM6jS1c2KvnZDZ4zEOtPw9E3Kq976Gbm3tMTHD0So4fATCw6CZTfe0TujIqZyQ+dARo4uBUFllbCN3XmGP+/sqKuHIUWMbs+tEEU7oyKmcmDlQbPryaBg/fjwffPABDz/8MAMGDGDVqlWMHTuWvXv38rvf/c7qeEH3Q34GD4ybzUXn/Zyikp38/qXLyN2z2epY9XJiZicoPWzMIhQo1R74fBPcNCRw62yog4dh6ffGLDLlP53l6d4WhvaC3gnW5aqNE3vthMzZe2Db3sCt7+Bh+DoHLj0ncOtsqF0H4PPvjcvNKquN2etSOsGwZEhsY12u2jihI6dyQuZvsv2/fLY2OXshZw90s3BShq27jV5/X2B83SzEmPxkWDLEtrAuV22c0JFTOTFzoNj20qzZs2fzxhtvMH/+fO655x6GDh3Kgw8+SGpqKpWVlfTv39/qiEG1o3ArB8v30yPB+H+2ie7A9Wl3s2D1i1RXGxf4ezwe7no2lYLCbAoPFDDt+YvZtW+7rTNnbvuSJ2bffPw5j79zI5tzv7Ekr5N8kxP4+zrW/mgMcKxQfAie/sgYDJWfdKlZ9h54ZTks2WhNrtpoWwyeQA6uj68zy7ob17fthacXQ3qOMQgBY9C/LhdmfQwbbXTpmHodHB5PcHq9Mgjr9NXX2fDcEti088SyI1XG//Opj4zBt12o185j24HIjBkzGD58OGlpaTWWd+/enbCwMFJSUti/fz8jR46kZ8+e9OnThyuvvJKtW7dalDiwtuSl07J5LO1adz6+bEjvURQf3E3m9pUAuFwubh8xgxc//B1PzL6Rqb98mfaxXSxK7FvmngkDyClYB8CGnBWEhYZzTuIFluR1ki27Ar/OqurAvhvdEO98ZQxGTnXs+HHBd8bMMXagbTE4PB7jc0ICbe/B2rsVbJVV8Npy45KsU8dBHoz/7xsroazC/Gy1Ua+Do/iQ0cFAy9plzQC78CC8+9NlZqf+fA9w6KgxAYpdZq1Tr53HlgOR/Px8MjMzGT169Gnfy83NpXfv3oSHh+NyuZg6dSpZWVmsW7eOkSNHctttt1mQOPCy8tLp3rFfjWWtouJI7jKEFevnHl/WtUMKmdtWcNX5t9O5XS+zY9bgS+ZmYRFEhregpKyI1z9+iPEjHrciqqN4PJC/LzjrzgvSeuuz+8BPO9V6HuMCVm4xK1H9tC0GR/Gh4B2UW9HrdXlQWlH3AZkHY5CSnmNqrDqp18ERrO6VVcD+suCsuz5f/lD/IMPjMT7/J9smkzup187j8njsMo49YfXq1aSmprJw4UKuvvrq48vLy8vp1q0bI0aM4LXXXjvteRkZGVx33XXk5wfu/LcrCHeHzfztUvp0u/SM11NeUcqf3riOKwfeyuL015j526Ven7Muexn3vDjUr58XqNwvzv8de4pz6dU5ldFpd3t9/JlkbgxCwsK54/Wa11B5m0GoLlPfrvn1xuX/YMkr4/1M5p9zh03gsttf8vq4suKdvHpHx6Bm0bZo3bbYoUcqY/60qsayQPV66T/vYP2nf/czmX+G3f4ivS/9DW533XfwVldXsf27hXz49KigZlGvret1yhVTGHrLczWWBarX7z2Syq6tq/1M5p9fTc+gbZf+Xo+FVn/wCF9/8GhQszix14HKDM47dvJ1eGHLMyJxcXEAZGVl1Vj+5JNPsnPnTgYMGFDr82bNmsV1110X9Hx2cKSygulvjWHcZQ9y+YCb6BDblZUb/mN1LJ8kdxnC9l2Z/Pyiu6yO4hDBmyolGANtb+o7UDuZy8fHWU3bor+C2OsgrrvOn+kO8en6FPU6+KzsdTC753KZf8jmdod43U94PB712gSN9djJlmdEqqur6devHzt37mTmzJnEx8czd+5cFi1aRG5uLqtXr2bQoEE1nvPoo4/y0Ucf8fnnn9O8eXOLkvsm410otuimxZgEGPgr/54bqNzP/ucOUpOvZWDSlT49/kwyNwYeD9z/b2PaRG+OvfN26jtpdRnWC641ed6HHwvhmY/rf4zLBb06wIQgv5mjbdG6bXFvCfzfh749tqG9/vWF0L+LX7H89mUWzEn3/rgrz4Wr+wQ3i3ptXa/XbId/fenbYxva6wd+Bm2j/Yrlt/e+htVb67+UFuD2S4zZ4YLJib0OZObGeuxkyzMibrebOXPm0Lt3byZNmsRtt91GXFwcU6ZMISQkhJSUlBqPf+yxx1iwYAGLFy+2/SCkKdtbnM+f3riO5hHRPm9IYhyUJ8QGZ93BWm99EttAfOv63w/3eOCinqZFanLssC22aQnhQZpAvpMFvR5wtjGlaX1cLhjSw5w8TZEdeh2s19TwUIhrGZx112dID+/380VHQu94sxI1PXbodTDZ9nNEevbsydKlNa/bu/nmm0lOTiYyMvL4skcffZRFixbx6aefEhMTY3ZMaYCzYhJ49NZ5VsdwpG5tA38zoAvo2jaw6/Tp57pg7GB49lNjCsjazskO6ga9gnt7SJNmh23R7TJ6fexzCQIlOsIY5JgtIgzGpsK/jEluahy8uX76+hcDIEbvlQWNHXod19LoYEmAp0bv2tbYZszWKRau6A2fbjzR42NcgNttfB5ViC3f1m4c7NDrYHJUdTIyMmrcH7Jx40YeeeQRioqKuPTSS+nbty99+/a1MKFIcAzqFvgr6pPjrTsoSoiFqVdB8imDjehIGNUfbhhkj08RluAa3D3w60ztYc0BG0C/zjBx2OkfXNiuFdx6EVycZE0uMY/bFZxeDwnCOn11dR/jNTk2quby7u2MT3zv2d6aXNI42PaMyKlKS0vJyspi8uTJx5f17t3b57vynWbrjrW8svA+yg4XM6jXSD5f+zZTf/kyfbqlsSn3a16cPw2Xy01Sp/OZdO0z7Cjcyv/+63oGJ4/ktuGP2TI3wKcZ/+KTb/9JdXUVfxj3NhVHy22R2+7atIA+ifBdbuDWeam1MxbSIQb+51JjGtdHfrpX8E/X2eedtfq6XHiggIdfH8mPu7/nw8dKCQkxXkpfmD+NrPwMusf3Z8qov5q+XfqTGeD9L55hxYb3mTVlpamZe8cb17zvKQnM+sJDrT1gAzing/FnTwnM+OkemPuusc/AuqEdOXzkENPfHM3hI2VERbTioZv/zd7iPNv0urb9odX7yAt7wLLNcMSH+/p80TbaeOPIKi4XpHY33hD73TvGsodHGfslO2hoP8AexyL15d62K5NZcyfgdofQsU137hnzD1wul+X7mGCwyS7fuxYtWlBVVcWdd95pdZSgq6w6yquL7ueRWz5g3GUP4XaHMDrt3uMH8+1iOvOXiZ8za8pKikv3sG3nBuLjujN51Cxb5y48sIP1Ocv5y8TPeGrSMuJaxdsit1P8YiA0bxaYdaV2hx7tArOuM3XyWRm7DEK8dTm6eSxPTviMXomDjz/nh/w1lFeU8szkFVRWHmFLXrqp/fYnMxizyGQXfHf8azMzh7iNy/QCdYx+bT9oZZNLn06+qdgugxB/OpK+ZTHnJA7iqUnLSEq8gIzNi23V69r2h1bvI1s1N7oYCC6MbcQOr40nn2m0yyDEn37Y4VjEW+5OZyXx1ztW8czkFQBk5WdYvo8JFhtUW071bdYnpHRNIzK8BW2iOzBvxV9rfD82uj3NwiIACHGH+TwdarB5y52x5WOqqqu496XLeG7enVRVV1mU1JmiI+HGIfVfdjL1be8zsHRsbVz+JHXz1uVmYRG0bN66xrJNuasZ0PMKAPr3uJzvf/zKtLzgX2aAxd+8xhUDbzEr5mnOPsv7LFK+9LpvonFZltTNn450bNONw0eMT9IrKy8mOuqU686CzJ/9oR32kUN6GJ2sjy+9vrqPsY1I7fzphx2ORbzlDg0JO/7vsNBwzmrVyfJ9TLA45tKspmR99nLWbF3Ct1mfUHKoiHGXP1Tr43IK1nOgbC+d2yWbnLB23nLvL91NZdUR/jLxM15ZeB+rNv6Xi8/7hUVpnal3PNxykTE9ZFV1w5/fKRYmDjVurJW6+boNnqy0vJgOsV0BiIpoxfbdG4MdswZ/MldWHWVd9jKuHTKZf378RxNS1u7y3lDlgcXr/Xt+30Tjhlmr7g1xCn86Eh/Xg00/fsVvZvYmpkVbfnP1n01IesKZ7A+t3Ee6XUYnwf9LaoenGNuG1M2ffqza+F/Lj0V8yb1q43xe/+gB4uN6EB3VxvJ9TLBoIGJDRSUFTL9tAXGtOvLygnvxeE4/4iw5tI/n5t3BQzf924KEtfOWOyqiFSldjdOOfbsPIys/w4qYjtcnEe6Jhne+grx9vj3HBQxLNnZsYfY4gWZrvmyDp4qKaMWhCuNmh7KKElpEmjuLnz+Zl3z7JsP6jTMhXf1cLhh+HnSJg3dXG/cN+SI81Di7l9rdPpc/2Zk/Hfk0458MTv4ZYy69lznLZvLZmre4YuCvTUhr8Hd/aId9ZGiI8cZRz63w3zW+fRYUGJer/mqwca+R1M+fftjhWMSX3EN6X8uQ3tfy3Lw7Wf39Asv3McGiS7NsKCoyhoOHiigpKyJ/bxZRETXLVlVVyROzb2LCyJnERttnugpvuZM7DyFnp/GWZ3bBd3SIPduKmI1Chxhj1qlbLzZmLqlLRBhc3BPuGwk/66dBiK+8dbk2yZ1TWfvDZwCs/WHJafdiBJs/mfP2buHDr17gD68M58fdG5m38lkTktbtnA7wh5Fw/fnQoVXdj2sVaQyqH7jWuARGgxDf+NMRDx5aNjc+HCM6Ko6ywweCHbMGf/aHdtpHHvvsmAeuNTrbKrLux3ZoZXT/DyM1CPGVP/2ww7GIt9xHKiuO/7t5eDThYZGW72OCRWdEbOiaQRN4as54oqPiuGPUs2zYtqLG95evn0NWXjqvLPw9AONHPE5yl1QrotbgLXf3+L6Eh0Vy9wuX0ioqjl9ePM2ipI1DiNu4JKVvIpQfgfz9UHjQuGQrIsz40MB20cY879Iw3rpcWXWUB14dQc7Oddz/6lXcPmIGvRIHERYWwbTnL6Zbx76ck3iB7TP/zzUnLrOZ+veLuO4i6ycDCQ8zPszyop5QUm6c9TtwyPi8mRYRxtTPsVEafPjDn44M6zeOx966gSXfvkloSBgP3vSerTLXtj/ctX+77faRrSKNs35XnQv7yoxelx02etyqOSTGQst6BilSO3+Pl6w+FvGWO2PzYuaueBowLo8c0PNK3G63pfuYYNFAxIa6dkzhubu+Of711oK1vLv0CeLjetCnWxrD+o1lWL+xNZ6zo3Arry66n0tSRpsd9zhvuQEm/mxmjefYIXdjENnMmAXLLjNhOZ23LoeGhPHkxCWnPW/KqJo3HJrZb38zHzNrykrTM3ujT2wOLH878sT/fFzjazv1urb9YXKXVFvuI8EYeLRpYZ9Zp5zOn36A9cci3nIPOXcUQ84dddrzrNzHBIvL01g/iMPGMt6F4nxrfnZMAgz8lX/PtSr3mWQWZzg2c8ysG839udoWG0bbYsOo1w2jXtufVZ0GZ/baiZnNpos2RERERETEdLo0ywIt2zrzZ1uV28rflzRu2had8XOlYdRrZ/xcaRgn9tqJmc2mgYgFkoZZncA/Ts0tUhendtqpucUcTu2HU3OLOZzYDydmNpsuzRIREREREdNpICIiIiIiIqbTQEREREREREyngYiIiIiIiJhOAxERERERETGdBiIiIiIiImI6DURERERERMR0GoiIiIiIiIjpNBARERERERHTaSAiIiIiIiKm00BERERERERMp4GIiIiIiIiYTgMRERERERExXajVAZqiLZ/DwT3W/OyWbSFpmH/PtSr3mWQWqY+2xYbRtugM6nXDqNfO4MReOzGz2TQQscDBPVCcb3WKhnNqbpG6OLXTTs0t5nBqP5yaW8zhxH44MbPZdGmWiIiIiIiYTgMRERERERExnS7NEhHTHa2CjfmwrRAK9p9Y/s+V0CkWkuOhfSvr8on4o6wCNuRBbhHsPHBi+ezVRq/P6wStIq3LJ+KPolLIzIe8fSeWPfspdIyBxDZGryPCrMsnzqaBiM3dML0jpYf243aH4HaHkJyYyrTRr9A2ppPV0erkxMxijopKWJIJq7YaB22nWvuj8Wf+WujRDkakQNe25uesjRN77cTMTnTgECxcB2t+hMqq07//dbbx54MMSOkEI/tCXEvzc9bGiR1xYmYn2rEfFq2D73eA55TvZe8x/gCEp8OgbjD8PGgebnrMWjmxI07MHAi6NMvGCg/sYF/JTp6fuoYP/6+UN+/PobhsD68uvM/qaHVyYmYxx7a98JeF8OnG2gchp/pht/Gu23++rf3gzkxO7LUTMzvRt9vhiQXwTY73nlZ74Ltc+PNCWLEFPKce3ZnMiR1xYmanqfbA4g3w1EewsZZByKkqKuGLLfDEQthUYErEejmxI07MHCgaiNjYlrx0mkdEk9j2HACio9rQPb4/xaUWzQXnAydmluDbVAB/XwKFpQ17ngdYvhle+8LawYgTe+3EzE6zdBO8+SWUH23Y845WwfsZxpk/KwcjTuyIEzM7SXU1vPMVLF5vDEgaoqQcXl4KGduCk81XTuyIEzMHigYiNrYlL52khPNxuVxUVVWSvnkxy9e9x7B+46yOVicnZpbgKtj/00Ci2v91bCqAd78OXKaGcmKvnZjZSdZsh/+uObN1LN0Ey7cEJI5fnNgRJ2Z2kgXrzmwg4QHeXgVZuwIWqcGc2BEnZg4U3SNiY1vy0sncvpLrHo6h/EgpEWHNuXv0a6T1GWN1tDo5MbMET1U1vP2V97MZs240/p76dt2PydhmXF+fYsHlsk7stRMzO8WBcpiT7v1xvvR6wVro1QHaWTA5gxM74sTMTpGzB5Z+X/9jfOm0B2OChvuuseYmdid2xImZA8XWZ0Sqq6uZOXMmPXr0ICIigj59+rB8+XKSkpKYMGGC1fGC7of8DB4YN5t504t558E84lolkLtns9Wx6uXEzBI8q7caNzwGygcZxuDGbE7stRMzO8Xi9VB+JDDrqqw+8zMr/nJiR5yY2Qk8HuN+vEBdKbi/zDjjZwUndsSJmQPF1gOR8ePHM336dCZOnMhHH33EmDFjGDt2LDk5OQwYMMDqeEG1o3ArB8v30yOhPwBtojtwfdrdLFj9ItXVxpGYx+PhrmdTKSjMpvBAAdOev5hd+7bbOnPmti95YvbNx5/z+Ds3sjn3G0vySnB5PLAyK7DrLD5k3DxpJm2LcrJDRwJ/DfymAmOKVDOp13KyH4tqTs8bCF/9YP4bR+q189h2IDJ79mzeeOMN5s+fzz333MPQoUN58MEHSU1NpbKykv79+1sdMai25KXTsnks7Vp3Pr5sSO9RFB/cTeb2lQC4XC5uHzGDFz/8HU/MvpGpv3yZ9rFdLErsW+aeCQPIKVgHwIacFYSFhnNO4gWW5JXg2llc87MUAuXb7YFfZ320LcrJMvONm80DyYNxz4mZ1Gs5WTD6V3LYmP3QTOq189h2IDJjxgyGDx9OWlpajeXdu3cnLCyMlJQUAK677jpSUlLo168fF1xwAUuWLLEibsBl5aXTvWO/GstaRcWR3GUIK9bPPb6sa4cUMret4Krzb6dzu15mx6zBl8zNwiKIDG9BSVkRr3/8EONHPG5FVDFBboDfXTsmryg4662LtkU5WW6Q+hfod6O9Ua/lZEHrtV6vvWrqvbblzer5+flkZmYybdq0076Xm5tL7969CQ83PjXnjTfeICYmBoC1a9dy6aWXsm/fPkJCQkzNHGi/vfbpWpc/M3nF8X+XV5Ty2Fs3MHnU31ic/hpXDLi51ueYxZfMAL0SBzPr/YmkJl9L65btzIgmFthVHJz17isz5q0PN+nVS9uinGxXEM7yBXO9dVGv5WTB6t/OIO0H6qJeO49tByIA7du3r7G8vLyc5cuXM2LEiOPLjg1CAA4cOIDL5cITwInZXS5XwNZ1zMzfLqVPt0vPaB1HKiuY/tYYxl32IH27D2Vd9lJWbvgPF53383qft3z5Ms4fO9SvnxmI3ADJXYbwzeJFPHDjbJ8efyaZxTpDb32elMsn1Vh2bMaVutT1/VNnaIlpHcfh0jN/q03borbFhrrhkdW07z6oxjJ/en1qp7NzcnG5Op/+QD+o1+p1Q93xxhFCQk9McRWo1+o578/jlovr74yvnNjrQHUanNdrX4/FbTkQiYuLAyArK4urr776+PInn3ySnTt3nnaj+pQpU/joo484cOAA77//PqGhtvxvBVSz0HBmjF90/Ou7x7xmYZqGWZe9jMmj/kZoiAXz+olpqo4eduS6G0rbYtNSGaTuVR4tD8p6/aVeNy1VRw/XGIgEinodOI211y5PIE8fBEh1dTX9+vVj586dzJw5k/j4eObOncuiRYvIzc1l9erVDBo06LTnLV++nGnTpvHFF1/QokULC5L7JuNdKM635mfHJMDAX/n33DPNvbc4n+fm3UFiu2TGj5jh8/POJLNY56ut8J6PH0Loy9z0x8Q0h0cC8wabtkVtiw32729g1Q++PbYhvT43AX6T5v1xvlCv1euGenqxb/eJNKTTACNS4Krz/M91Mif2OhCZG3uvbXnqwO12M2fOHCZOnMikSZNo06YNt9xyC1OmTOGBBx44fqP6qdLS0nC73Xz55ZdcddVVJqcWb86KSeDRW+dZHUNM0ik2OOtNbBOc9TYl2hb9lxgLq4K0Xjkz6rX/EmODc8N6sPYDTUlj77UtByIAPXv2ZOnSpTWW3XzzzSQnJxMZGQlAk4RjkAAACHVJREFUaWkpRUVFdO5sXFe7du1asrOz6dXL2hkQRAQ6toazWsLeg4Fdb9/EwK5PpCHOTYDQdOODCAOpT2BuDxHxS7/OsNLHM32+igqHHu29P06aNtsORGqTkZHB4MGDj39dVlbGDTfcQGlpKaGhoURERPDWW2+RmKgjFRGruV1wYU+Y923g1tkyAlI6BW59Ig3VIgL6dg7shxr2bA/togO3PpGG6toWOrQK7Gc/De4GYc6ewFRM4JiBSGlpKVlZWUyePPn4snbt2rF69WoLUwXP1h1reWXhfZQdLmZQr5F8vvZtpv7yZfp0S2PbrkxmzZ2A2x1CxzbduWfMPygoyuZ//3U9g5NHctvwx2yZO33zYt5d+gQA+Xu3cNcvXqBL+3NtkVuC48Iexqfr7i4JzPpG9YdQk3Zs9XW58EABD78+kh93f8+Hj5USEhJa67IdhVtN7XdDM+/at507nx1EYttehIY0488TPjE9sxNd0wc25BnTSJ8pt8votVka2pGqqkqemH0T+0t3k5RwPv8z8klb9XpT7te8OH8aLpebpE7nM+naZ2y9j7Qrlwt+PhCe/yww62sVCZclB2Zd3jS0H3Y5FmnocV5RyU7L9zHBYNsPNDxVixYtqKqq4s4777Q6StBVVh3l1UX388gtHzDusodwu0MYnXYvfboZdzJ2OiuJv96x6vgc01n5GcTHdWfyqFlWxvaa+/xzhvPUpGU8NWkZbWMS6d/jclvkluAJC4FxqRDiZRbsqW97v/kxpRMM6BKwaPXy1uXo5rE8OeEzeiWeOENb2zIz++1PZoABPa7gqUnL+POET0zP7FSto4yDNm986fXwFIhvHZhc3vjTkZWZ/6Frxz7M/O1SKirLyS5YZ6tet4vpzF8mfs6sKSspLt3Dtp0bbLuPtLue7eGinvU/xpdOA4wZBM3DA5OrPv70ww7HIv4c51m9jwkWxwxEmpJvsz4hpWsakeEtaBPdgXkr/lrj+ydP3RYWGs5ZrexxrYq33MfsLMohpmU7IsPtO7OZBE7nOLj5IuOdX391PQtuHGK8a2cGb11uFhZBy+atvS4zkz+ZAb7LXsq05y/m/S+eMStqozC425nPBpTaHa7oHZg8vvCnIzv35dC1gzFBTLeOffl+ezBu1a+bt8yx0e1pFhYBQIg7DLc7xLb7SCf4+YAzv/z1+vOhd3xg8njjTz+OsfJYxJ/jPKv3McHimEuzmpL12ctZs3UJ32Z9QsmhIsZd/tBpj1m1cT6vf/QA8XE9iI6yxzRCvuQGWLnhAy48N0Dzr4oj9E2EyKHwzldwoIHTyl/Q1dixNTPx1crXLtuJP5ljozvw+n1ZNAsJ549vjKJf98vo2rH2WQnldCNSIDrSuA/qaJXvzwtxGWdCLu9t3uAa/OtIp7OSWJ+9nEG9rmHd1qV0bm/iyAnfM+cUrOdA2V46tzOuB7LjPtIJQtxwy0Ww4DtYtgka8vkOzZvBmAuMe6jM4m8/wNpjEace5wWDzojYUFFJAdNvW8BTk5ZxftJwPJ7Tp2cZ0vtaXrknk7iYBFZ/v8CClKfzJTfAV5s+ZEjytSanE6sldYD7RsLFPX0bVHSKhQmXGpd2mTkIAd+7bCf+ZG4WGk5ksyhCQkIZ3Gsk23dnmpC0cbmwB9x3DfTp5NtZv3M6wN0j4IpzzR2EgH8dGZz8Myoqy7n3pcsICw2ndYt2JiQ9wZfMJYf28dy8O7h79IkPp7PjPtIpQtzGfUt3XWmcjfbl8ed3hftHmjsIAf/7AdYeizj1OC8YdEbEhqIiYzh4qIhmoeHk782ic7veVFWfuCvySGUFzUKNiy+bh0cTHhZpVdQavOUG2Feyi7CQZo16dC91a94Mfnk+XN0HvsuFHwthx344dMTYmcW1gIRY47R+5zjrcvrSZbvxJ/OhwwdpHtESgI3bv2TURY3/HrxgiGsJt10CxYdg7Y+QV2TMPnSk0rhPql0rY2DdN9F4rFX86UiIO4Q7rnsWgGfmTmBgkrmf0eUt87Gb6SeMnElstDFXrF33kU5z9lnGYGRnMazPg7x9sKcEqqohPAziY4zPderX2ZhNzgr+9AOsPxZx6nFeMGggYkPXDJrAU3PGEx0Vxx2jnmXDthU1vp+xeTFzVzwNQHxcDwb0vNKKmKfxlhtg1cb/ktp7lAXpxE4imxnXx6d2tzpJ7bx1ubLqKA+8OoKcneu4/9WruH3EDHrE9z9tWa/EQbbOXFJWxD8/fpiw0HDOPftiU/M2RjHNYaiNP8bKn46c1SqBx9+5EbfLzeUDfk1cK5Mu/vcx8/L1c8jKS+eVhb8HYPyIxyku3WPLfaRTdYgx/tiRP/1I7pJq+bGIP8d5tW2fjeE1WwMRG+raMYXn7vrm+NdbC9by7tIniI/rQZ9uaQw5dxRDzq25Ae0o3Mqri+7nkpTRZsc9zltugJGpE2s8xw65RU7lrcuhIWE8OXHJac87dZmZ/fY386BeV1uWWczlb0eemrSsxtd26vWwfmMZ1m/sac+z4z5SAs/fflh9LOLPcZ4bt6X7mGBxeTyehtyLJAGQ8S4U51vzs2MSYOCv/HuuVbnPJLNIfbQtNoy2RWdQrxtGvXYGJ/baiZnNpjMiFmjZ1pk/26rcVv6+pHHTtuiMnysNo1474+dKwzix107MbDadEREREREREdNp+l4RERERETGdBiIiIiIiImI6DURERERERMR0GoiIiIiIiIjpNBARERERERHTaSAiIiIiIiKm00BERERERERMp4GIiIiIiIiYTgMRERERERExnQYiIiIiIiJiOg1ERERERETEdBqIiIiIiIiI6TQQERERERER02kgIiIiIiIiptNARERERERETKeBiIiIiIiImE4DERERERERMZ0GIiIiIiIiYrr/Dxcm7IxkOdMHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1043.78x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two = TwoLocal(4, ['rx', 'ry'], 'cx', entanglement='linear') # other options: 'full', 'circular', 'sca'\n",
    "two.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Convenient access to standard ansatz circuits, but complex custom circuits are easily constructed, e.g.:\n",
    "* custom single- or two-qubit circuits\n",
    "* custom entanglements\n",
    "* different numbers of repetitions\n",
    "* coupling of parameters\n",
    "* etc.\n",
    "\n",
    "$n$-local version: `qiskit.circuit.library.NLocal`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fxrrdCwVFSkrEukfS83kkTpw9CAA4fuZ3tG76gIgw7YqX31CD9kT3sXgveQw8XL0wYchCHMpNrfJzf5/OcHR0xqTFvdChzUMIaifwTkKSnVR+pGdtwarUfwMAvL380SVAWQ+fUhOpsf7HE/8yfz1xUU8M7cn7q4joNqka4uf9EJwcXTB5SW80cfXCM70mCYrUftjUU4Pm2yYMH7zym/n7nDMH8PWOBfD28jffMZ8wpOrNNqcv5uDjzdMQFRYra6wkP6n8iHxwCCIfHFJlH+aHbSw5Fiu9n7AbAMeaiG6zpIaMezKxyj5aqyFs6onuEBUWg6iwmDq38fbyw8KX98oUkfXU9AAWtdFCfqgFx5qswbpH1TXEGsKmXgB3C5eZU9p7h7u7118gMr2vWsf6Xnz77beqe2S6KA0xP0ThWJM9iap7as1rzufqeW9r6IxGo8BnNRKRNbKysiS3seRx6UFBQfUVUr2Y+KXp7/dHiI2jIeBYkxpJ1T411j2i+sbVb4iIiIiIVI5NPRERERGRyrGpJ9KYxYsXiw6BiEhWrHtEbOqJNCc0NFR0CEREsmLdI2JTT6Q50dHR0hsREWkI6x4Rm3oiIiIiItVjU0+kMd26dRMdAhGRrFj3iNjUE2lOWlqa6BCIiGTFukfEpp6IiIiISPXY1BMRERERqRybeiKNWbVqlegQiIhkxbpHxKaeiIiIiEj12NQTaUxMTIzoEIiIZMW6RwQ4iA6gITq6HSi6IOa93VsAgX1t23fy0T+QUVRUvwFZINzdHe8Fhti0r1rHmkhreCzKh2MtH7WONedz66glr9nUC1B0ASjMFx2F9TKKirDrymXRYVhFrWNNpDU8FuXDsZaPWsea87k28fIbIo1JSEgQHQIRkaxY94jY1BNpzoQJE0SHQEQkK9Y9Ijb1RJoTFRUlOgQiIlmx7hGxqSfSnIKCAtEhEBHJinWPiDfKEpk9O68Nim9cgV5vgF5vQEi7CEyK/QgtPNuKDo2oQeGxKB+ONWlRQ81rnqknAnDx6mlcvnYWiyfux4a3ivH5tBMovH4BH296TXRoVgsJsW25MCIl0NKxqHRaGmvWPaqkpby2Fpt6IgBH89LQ2NkD7VoEAQA8XJvBz7szCosFLYp7D1avXi06BFKAGzftu729qPFY5FiLx7pHlbSU19ZiU08EUxEI9OkGnU6H8vIypGVtQUrGN+jbabjo0Kw2a9Ys0SGQYBeLgHc3AT8esmz74+eBed8BGafsG5cl1HYsnr4CvLUe+CXHsu0P5gFvrgOOnbdvXJZQ21jXhXWPKmkpr63Fa+qJYCoCmSd3Y+gbnii5WQxnx8aYHLsM0eFxokOzWnJyMt58803RYZBA+VeAwhJg80HT9491rH3b4+eB/+4EbpYBR84A4e1kCbFWajsWT1wArpcC3/xq+j7Cr/ZtD+YBK1KBCiNw7Bzg31KeGGujtrGuC+seVdJSXltL0WfqKyoqkJiYCH9/fzg7OyM8PBwpKSkIDAzE2LFjRYdHGnIsPx3Th6/EunmF+GpGHrya+ODUhSzRYRHZ5KF2wIgIQAdTY1/bGfs7G/puDwBxD8sZZc3Udiz2CgSGdDZ9/c2vtZ+xv7Oh7xsMDAyTL8baqG2siSzRkPNa0U39mDFjMG/ePIwbNw7ff/894uLiMGzYMJw4cQJdunQRHZ5sdh9aiydnuJn+THfFo1N1GDy9sfm1t78aITrEuxhLS3HruedRvnpt1ddzc3Er5jlU7EoVFNndTl/MQVHJFfj7mGbmZh6tERM9GRv3LkVFRQUAwGg04pWFEThz8TguXj2DSYt74dzlkwKjJqpb1weAEZG1N/bVG/phPQC94BnBkmMxM/dnLFg50rzP21+NQNap34TEW6lPcN2NffWG/slOgE4nf5x3Yt0Tg/O5fTX0vFbs5TcrV67EihUrsHPnTkRHRwMA+vTpg/3792PNmjXo3Lmz4Ajl07Pj0+jZsRiA6WOlCf/3MD5/PRf3uQv+7LYOOicn6J+NRUXyKuifGgydoyOM586jbPos6F8YCX1UL9Ehmh3NS4N746ZoeV9782uRoUPw/qqxyDy5G2G+UdDpdBg9cD6WbngVN0qvYeIzH6JV0/vFBV2HlJQU0SGQQnR9wPT3l3tuX4pTSWkNPWDZsRjg0wUnzmQAAA6dSIWjgxOC2on/iKFPsOnv7/ZXvRRHiQ09wLonCudz+9JaXltLAWW8ZvPnz8eAAQPMDX0lPz8/ODo6IizM9NnlrFmzEBAQAL1ej1WrVokIVVbZ+fvQvImPogtAJf0TgwAAxp+2wVh4FWXTZ0I/aAAMTz4hOLKqsvPS4NemU5XXmrh6IeT+SKQevJ1Tvq3DkJmbise7jUb7lsFyh2mxw4cPiw6BFKT6GftKSmvoAcuOxUaOznBxcsO165ew/IeZGDPwbRGh1qj6Gfvk35TZ0AOse0rA+bz+aS2vraUzGo1G0UFUl5+fj7Zt22LZsmUYPXp0lZ8NGzYMWVlZOHDgAABgz549aNWqFUaPHo0JEyYgJiamXmPR2aECJ760A+Edetu073vJf8e16xcx98V1Nu2fcXwnpiztY9O+hncXQB9u3YWg5es3omLNWujc3KALCoRhwnir37ci4yDKp06zej/g3sb6TiWlxZi9Yige6/oitqQtQ+JLOyT3uZexrs2kSZMkt0lKSpLcLikpqb5Cqhf/+4WpDP3neYV0PBoU+MgIPP7SZ9DpTB38H6mfYuuHo2E0Vsjy/vV1LALA0vWv4kLhKQS3j0Bs9GTJ7e1xLNal08BXETXiPfP36Rvfwc9fy7dGttbqHiBd+0TVPc7n1uF8bj1r2nSFnJ+pKj8/HwDQqlWrKq+XlJQgJSWlyqU3kZGR8PX1lTU+kbLz0hHg01V0GBbTD3wcuFECNGsG/fiXRIdjk5tlpZj3RRyG95uB/l2eR+umvth9aK30jkQKUnTxFMpv3V4g/er5HNka+voWcn8kTp7LxNM9XxEdSo2uXjiOivJy8/eF57IFRmMb1j3743wuP63ntSLP1Ofk5MDf3x9JSUmYOHGi+fW5c+dizpw5WLRoEcaPr/obYu/eve1ypt4e0r8GCvOt3+/mrb/w1Ex3zBu1Ad2CBtj03p4+QNfnbNoV/dN/xa4rl63ax1hRgbKnY2GY+ir0PR+x6X2j7muKrV2727SvrWNdH+5lrGuTlSV9B39wcDCOHDlS5zZBQUH1FVK9mPil6e/3lXePmCbceVPsA82BkwWAEcCgsLqXu6xP9XksLlw7AREhT6Fr4GMWbW+PY7E2d15Df6dnu9e93GV90lrdA6Rrn6i6x/ncOpzP7UuRN8r6+voiLCwM8+fPR9OmTeHt7Y1Vq1Zh8+bNANCgVr650/GzGSivKIO/j4r++/PygZIS6AL8RUfSYMydO1d0CKQgNa1ys//PqjfPytXY36uCwnx8sG4C2rUMsbihl1P1m2K339FjWrKOPdlObXWP8znZgyIvv9Hr9UhOTkZoaCji4+MxatQoeHl5ISEhAQaDwXyTbEOTnZeOFp7t4OnWXHQoFjNmHwM8PaFr0UJ0KA1GXJz2H7BBlqlt2Uqp5S6VqrmnD+a+uA5jBs4XHcpdalrlppIl69jTvVFb3eN8TvagyDP1ABAQEIAdO6revDBy5EiEhITAxcVFUFRiHTu9T1XX3wGmIqDz56kpOVnyMTRpn9Q69DUtd6mWM/ZKI7VsZW3LXVL9UVvd43xO9qDYpr4m6enp6NGjR5XX3njjDSxfvhwFBQU4dOgQJk6ciJSUFHTo0EFQlPYzJe4T0SFYzZCgzptpiNTs+AXL1qFnY3/vLF2Hno093YnzOdmDIi+/qUlxcTGys7PveujUvHnzkJ+fj9LSUly6dAn5+fmabOjJfnJOH8BrHz5megjIT29i1DuByDhuepDJxatnEP9+Zwx63Rnl5WUATE+sG/fvh7B8y0yRYRPVSq8zXVpjyTr05ktxdIBB8IxQ17FYafWuJExc1BOAMo5Fg940dpasQ1+5jr0Oyh7rc5dPInZuS0xe0huvfWi6d0EJY00kpa68TsvagslLemPykt549s3W+DlznebyWjVn6t3c3FB+xxJhRPWhrPwWPt48DXNeWIMDOduRe+4QYqOnIryD6aFnHo2b4p2x2zDn06fN+3h7+WH8kPex/9hWUWHXqXfv3qJDIMEeaA68OhBo7mbZg6W6PgD4NAVaNbF/bLWROhYB03J0x8/8bv5eCcdiqDcwdRDQ0sOyB0v1CQaC2yh/rLv4P4ppw78wf6+Esa4L6x5J5XW3oAHmlYZe/r/u6OzfHy5OborOa2up5kw9kT3sy/4RYb7RcHFyQzOP1liX+p8qP2/k6Az3xvcJis42S5YsER0CKUBLD+ueFCuyyQSkj0UA2PLbMjza9QUB0dWtVRPrnhSrhrH+/fgOTFrcC6t3KetBdbVh3SNL8hoAzl46AU/3lnBxcpM5QvtTzZl6Ins4eDwF+3O2Yl/2j7h24xKG91f/R3Dx8fGc4Eh1pI7FsvJbyDi+E09FjsenP8wSFKU2SI11U4/WWP5aNhoZnDBrxRB08usH3zbKXnWOdY8snc93H1qDRx58usafqR2bemrQLl07g3mjNsKrSRt8uHGqap+weaedO3eKDoHIalLH4tZ9n6Nvp+GCotMWqbFu5OAEwAkA0CN4ME6ez1R8U8+6R5bO578c2YA5f1sjc3Ty4OU31KC5unii6MYlXLt+CfkF2XB19hQdElGDJHUs5hUcxYZfluD1jwbgz/OHsW73QkGRqp/UWN/4q8j89eGTP6N1My4+QcpnyXx++do5OBoawcO1mYAI7Y9n6qlBe6L7WLyXPAYerl6YMGQhDuWmVvl5WfktTP94IE6czcC0jx/H6IHzEdzOtkdcE1HtpI7FfzzxL/PXExf1xNCeL8sdomZIjfWh3FR8+sMbcHRwwoMP9GLNI1WQymsA2HP4O0SEDhEQnTzY1FOD5tsmDB+88pv5+5wzB/D1jgXw9vJHeIdoOBgc8c64qnfFn76Yg483T0NUWKzc4VpETQ9gIaokdSze6f2E3QCUfywqldRYdw8ehO7Bg6rso/SxZt0jS2rI4IhxVfZRel5bi0090R2iwmIQFRZT5zbeXn5Y+PJemSKy3rfffqu6R6YTVaeFY1EttDDWrHtUnRby2lps6gVwb6HO9w53d6+/QGR6X7WO9b2YPXs2JzdSnIZ4LIrSEMdaVN1T61hzPlfPe1uDTb0AgX1FR2Cb9wJDRIdgNbWONZHW8FiUD8daPmoda87n2sTVb4iIiIiIVI5NPZHGLF68WHQIRESyYt0jYlNPpDmhoaGiQyAikhXrHhGbeiLNiY6Olt6IiEhDWPeI2NQTEREREakem3oiIiIiIpVjU0+kMd26dRMdAhGRrFj3iNjUE2lOWlqa6BCIiGTFukfEpp6IiIiISPXY1BMRERERqRybeiKNWbVqlegQiIhkxbpHxKaeiIiIiEj12NQTaUxMTIzoEIiIZMW6RwQ4iA6gITq6HSi6IOa93VsAgX1t23fy0T+QUVRUvwFZINzdHe8Fhti0r1rHmuTB/CAtYl7LR61jzfncOmrJazb1AhRdAArzRUdhvYyiIuy6cll0GFZR61iTPJgfpEXMa/modaw5n2sTL78h0piEhATRIRARyYp1j4hNPZHmTJgwQXQIRESyYt0jYlNPpDlRUVGiQyAikhXrHhGbeiLNKSgoEB0CEZGsWPeIeKMskdmz89qg+MYV6PUG6PUGhLSLwKTYj9DCs63o0EgBmB+kRcxr0qKGmtc8U08E4OLV07h87SwWT9yPDW8V4/NpJ1B4/QI+3vSa6NCsFhJi23JhVDst5QdRJS3lNeseVdJSXluLTT0RgKN5aWjs7IF2LYIAAB6uzeDn3RmFxYIWxb0Hq1evFh1CrVKygLxLlm1bUQFs/B24esO+MVlCS/lB9cucpyWWbV9yE/huP3Cr3L5xWUJLea3kukfy0lJeW4tNPRFMRSDQpxt0Oh3Ky8uQlrUFKRnfoG+n4aJDs9qsWbNEh1Cjg3nA2n3A4u3SjX1FBfDVXmDrYeCjFKDCKE+MtdFSflD92nLIlKeLtko39iU3gaXbgR1HgNVp8sRXFy3ltScOFdsAAA0xSURBVFLrHslPS3ltLUU39RUVFUhMTIS/vz+cnZ0RHh6OlJQUBAYGYuzYsaLDIw05mpeGzJO7MfQNTwya7ox/fhGHybHLMODh0aJDs1pycrLoEGoU0gYIa2tqbOpq7Csb+vRcoJED8HQXQK+TN9bqtJQfVL+iAoHWnsCFa3U39pUN/Z+XgKauwKMPyhtnTbSU10qteyQ/LeW1tRR9o+yYMWOwZs0avPHGG+jSpQv27NmDYcOGoaCgAK+++qro8GSz+9Ba/OvrkaZvjEb8desGnBxdoNOZfieLDB2C14d/KTDCuxlLS1H2whjoY5+B4Zmnb7+em4uyqa/D8EoC9FG9BEZY1bH8dEwfvhI9Oz6NS9fO4v/9tx9OXcgSHZamOBiAvz0CfPaz6az94u3A+L5A22a3t6ne0I/rA3RoIS7mSswPqo2bM5DQD1i0DThbaGrsE/oDTVxub1O9oU/oDzRzExdzJea1/Dif219DzmvFnqlfuXIlVqxYgfXr12PKlCno06cPZsyYgYiICJSVlaFz586iQ5RNz45PY8NbxdjwVjES43cCAD5/Pdf8mtIKAADonJygfzYWFavXwHjrFgDAeO48yqbPgv6FkYoqAKcv5qCo5Ar8fUw51cyjNWKiJ2Pj3qWoqKgAABiNRryyMAJnLh7HxatnMGlxL5y7fFJg1OpU2djXdsZeiQ0984OkVDb2tZ2xV2JDb0leZ+b+jAUrR5r3efurEcg69ZuQeLWC87l9NfR6rdimfv78+RgwYACio6OrvO7n5wdHR0eEhYXhypUrGDx4MAICAhAeHo7HHnsMOTk5giKWR3b+PjRv4oP73FuKDkWS/olBAADjT9tgLLyKsukzoR80AIYnnxAcWVVH89Lg3rgpWt7X3vxaZOgQFBadR+bJ3QAAnU6H0QPnY+mGV7Fg5QhMfOZDtGp6v6CI65aSkiI6hDrV1NhXUlpDD2gvP8g+amrsKymtoQcsy+sAny44cSYDAHDoRCocHZwQ1O5hIfFKUXrdqwnn8/rX0Ou1Ipv6/Px8ZGZmIjY29q6fnTp1CqGhoXBycoJOp8PEiRORnZ2NjIwMDB48GKNGjRIQsXyy89Ph79NFdBgW0TVyhP65Z1H+bTLKZ86CvnMnGEaOEB3WXbLz0uDXplOV15q4eiHk/kikHlxlfs23dRgyc1PxeLfRaN8yWO4wLXb48GHRIUiq3thXUlpDD2gvP8h+qjf2lZTW0AOW5XUjR2e4OLnh2vVLWP7DTIwZ+LaIUC2ihrpXHefz+tfQ67XOaDQKXlfibnv37kVERAQ2bdqEQYMGmV8vKSlBhw4dMHDgQCxbtuyu/dLT0zF06FDk5+fXWyw6Xf3foZf40g6Ed+ht077j/v0QosJiMKL/TJv2zzi+E1OW9rFpX8O7C6APD7NqH+OtWygb8QJ0wUEwzJ4Jnd763yMrMg6ifOo0q/cD7m2s71RSWozZK4bisa4vYkvaMiS+tENyn3sZ69pMmjRJcpukpCTJ7ZKSkuorpHticHDC3xKPwsPLdFblp4/G4I+UT2R7f63lBymDR/P78fyCTDg6uQIAVs7qhgsn0mV7//rKawBYuv5VXCg8heD2EYiNniy5vb3y2pKaJqLucT63Dudz61nTpivyTL2XlxcAIDs7u8rr77zzDs6ePYsuXWr+zfb999/H0KFD7R6fKDdv/YU/zx9GgE9X0aFYzmAASkuhf7SfTQVACW6WlWLeF3EY3m8G+nd5Hq2b+mL3obWiw1I9nU6PfmM+NDf0ANBreCJa3K+u+2WYH3SnRi4eGJCw0tzQA8Dj4z5DY89WAqOyXcj9kTh5LhNP93xFdCiawvlcDK3Xa0Weqa+oqECnTp1w9uxZJCYmwtvbG6tWrcLmzZtx6tQp7N27F927d6+yz9y5c/H9999j+/btaNy4saDILZP+NVBow4cJR079ilcW9kDy7AvwdGtu03t7+gBdn7NpV/RP/xW7rly2ah/jn6dQ9o+X4PDFCuha2HZNRdR9TbG1a3fpDWtg61jXh3sZ69pkZUnfwR8cHIwjR47UuU1QUFB9hWST6qvc/D0a2J1tWhXHpdHdq+LYi9byg8SqvsrNqF6mPD9bCLTwuHtVHHupz7xeuHYCIkKeQtfAxyza3l55LVX7RNU9zufW4XxuX4r8VUuv1yM5ORmhoaGIj4/HqFGj4OXlhYSEBBgMBoSFVf3I6J///Cc2btyILVu2KL6hvxfZeelo4dnO5gIggjH7GODpaXMBIOvNnTtXdAh1qmnZyoBWda+KQ6R0NS1b2bZZ3aviKFlBYT5mrxiKxs4eFjf0Iim97lXH+ZzsQbHr1AcEBGDHjqrXOY0cORIhISFwcbl9qmPu3LnYvHkzfvrpJ3h6esodpqyOnd6nro/qYCoCOn8/0WE0KHFxcaJDqFVd69Bbso49kRLVtQ69JevYK1FzTx/MfXGd6DAspuS6VxPO52QPim3qa5Keno4ePXqYvz98+DDmzJmDDh06oHfv3ubXf//9dwHR2d+UOPluIKwvhoSXRIfQ4FjyMbQIljxYio09qY0lD5ZSa2OvJkqte7XhfE72oJqmvri4GNnZ2Rg/frz5tdDQUKvuCiaqSc7pA/ho02u4/lchugcPxvYDX2LiMx8ivEM0jpz6FUvXT4JOp0dg226IfyoJpy/m4M3PYtAjZDBGDfin6PBV41C+ZevQV2/sV/4KTBkI6Ot/ISqL1JUfuecy8f6qsdDrDWjTzA9T4j7BmUvHmR8NyPY/LFuHvnpjv+l3YHiEvLHeqa68Pnf5JF5e2B3tWgTDwdAI/xr7I+seqUJdef3XzRuY93ks/rp5Ha7OTTBz5LcoKMzTVF6rpql3c3NDeXm56DBIY8rKb+HjzdMw54U1OJCzHbnnDiE2eirCO5geetbSsz3eHbcdjRyd8fZXI5B79hAeaN0R44e8j/3Htkr863SnsLbAgDDAv6X0OvQOBuCFnsDafUDvIHENvVR+tG0eiP9M2AMAePebUcjOT0dg227Mjwbk8Y6ms/V9QqTXoa9s7DdlAEMELvIkldcA0MX/UUwb/oX5e28vP+Y1KZpUXqcd3YKgdt0x8tFZ+HLbW0jP2oLIB4doKq8VeaMskVz2Zf+IMN9ouDi5oZlHa6xL/U+Vnzf1aIVGjs4AAIPeEXq9QUSYVrnzUjQl0emAAR0tf7CUQQ/EdAO83O0bV12k8sPB4Gj+2tHBCc2btJU7RBLMwQDEPGz5g6XcnIFnuwPOjtLb2otUXgPA78d3YNLiXli9SxnPtJCi1LpH8pHK6zbNOuCvm9cBANdLCuHhqr3rOlVzpp7IHg4eT8H+nK3Yl/0jrt24hOG1PATkxJmDuHq9AO1bhsgcofWWLFkiOgTNsCQ/9hxej+XfT4e3l78mJwnSHqm8burRGstfy0YjgxNmrRiCTn794NvGugcVyY11j6Ty2tvLH0f+/AV/TwyFp1sL/H3QvwRFaj88U08N2qVrZzBv1Ea8F78T3QIHwGisuGubazcu44N1EzA59u6nGCtRfHy86BA0w5L8iAx9Ch9NyYSXpw/2/rFRQJRE1pHK60YOTnBp5AqDwQE9ggfj5PlMQZFajnWPpPL6p/RP0SPkSXw85TC6Bz2Bbfu/qOVfUi829dSgubp4oujGJVy7fgn5Bdlwda66LGp5eRkWrHweYwcnoqmHOp4IuXPnTtEhaIZUftwsKzV/3djJA06OXM6ElE8qr2/8VWT++vDJn9G6WQe5Q7Qa6x5J5bURRrg3bgoA8HD1wvW/rooI0654+Q01aE90H4v3ksfAw9ULE4YsxKHc1Co/TzmYjOy8NHy06f8BAMYMfBsh9wtcsoJkJZUf6VlbsCr13wBMH+12CVD+Q3qIpPL6UG4qPv3hDTg6OOHBB3ohuJ1tTwAlkpNUXvftNBz//OJZbN33ORwMjpjx/DeCIrUfNvXUoPm2CcMHr/xm/j7nzAF8vWMBvL38Ed4hGn07DUPfTsOq7HP6Yg4+3jwNUWGxcodLMpPKj8gHhyDywSFV9mF+kNJJ5XX34EHoHjyoyj7Ma1I6qbx2c/HEgn/8UGUfreU1m3qiO0SFxSAqLKbObby9/LDw5b0yRWQ9NT2ARW20kB9E1Wkhr1n3qDot5LW12NQL4G7hkn5Ke+9wdzFrC97L+6p1rO/Ft99+q7pHpovSEPODtK8h5rWouqfWseZ8rp73tobOyEeyEqlGVlaW5DaWPC49KCiovkIiIrI7qdrHukfE1W+IiIiIiFSPTT0RERERkcqxqSfSmMWLF4sOgYhIVqx7RGzqiTQnNDRUdAhERLJi3SNiU0+kOdHR0aJDICKSFeseEZt6IiIiIiLV4zr1RCpiyZJss2fP5tJtRKQpUjWNdY+I69QTEREREakeL78hIiIiIlI5NvVERERERCrHpp6IiIiISOXY1BMRERERqRybeiIiIiIilWNTT0RERESkcmzqiYiIiIhUjk09EREREZHKsaknIiIiIlI5NvVERERERCr3/wGWJVjrq6K1twAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 983.577x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import Parameter\n",
    "\n",
    "p = Parameter('p')\n",
    "ent = QuantumCircuit(2)\n",
    "ent.swap(0, 1)\n",
    "ent.rx(p, 0)\n",
    "ent.ry(p, 1)\n",
    "\n",
    "single = QuantumCircuit(1)\n",
    "single.t(0)\n",
    "single.y(0)\n",
    "\n",
    "two = TwoLocal(3, [single, 'rx'], ent, entanglement='circular', reps=1, insert_barriers=True)\n",
    "two.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Which Ansatz works well? Active field of research! See e.g. [Sim].\n",
    "\n",
    "Circuit 6 in [Sim] is proposed to work well for one repetition already.\n",
    "\n",
    "![](circuit6.png)\n",
    "\n",
    "[Sim]: Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Sim et al. [arXiv:1905.10876](https://arxiv.org/pdf/1905.10876.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4UZVQK78AlF0qQmlFEXILMtDKt/YOEtltMA6e+AIAcPDEjlrvcRFJL3dOwXF89M0K/Gn1aJw5dxSb97whKKnjdu3aJToCCaBXy/WRdb8kus6Zur5adePj31r6+MPH268pIxqGc8eQITiZfxgAkJX3LToF3tLUMYmahEy9k96+aLVW4eX1v8DUsUsQ+MNjokWfz53JrGKP7Qje+iuh+wdOxdKkKfBvFYTp497AkVO7a73eK6QfvL19MXP5UPTs3BfhXe8QlLQ2vdy/vf+vNX+e8dadePBO47/fmNSkV8tV1mt4ds0YnMw/hDlr7sUTYxYhoutAKfdLouucqeuLpd9j4+5XAQDBQb3Qv/c9IqIrx9ljiI+3H2atGI62rYLw8NCZDXx3InKU3r6YfDgJGTkpWP3JHwEAU8b8BZHdBws9nzuT2ag9NieqEurRORpv/u6/NV9n5h3Ehp0vIzioV80TvxLH1X5j9dnCTKzZOgfDoid4NOuPOZL7utcS9wCQIzfRT+nVspfFG4vjd9TZTsb9kug6Z+t6yK3jan3Nutbn7FjH/8+SWl9zrIlco7cvjoyZiJExE+tsJ/J87mzm64zUY5tsNptNdIjmJnUDUJwr5mcHhNg/BNsZonK7kllLenq6W75PeHi4W74PeZ6q+yKRFta15zS3sd7xwzz6rtme/bmuUjG3rJll7Z1U3ReN1lu7G9+jSqThgw8+EB2BiIiISBnsnchdeOuvAG3aq/mzReUWOV4vvPAC4uLixAWgJuVKbV3/DWhAiOd/NpEW1rXncKyJ6hLRO7G3VuPnNhYnqgKEjRSdwDmq5iZqiCs1ff22LBVunaHmhXXtORxrIjmo2qOqmttTeOsvERERERERSYUTVSINy5cvFx2BiIiISBnsnchdOFEl0hAVFSU6AhEREZEy2DuRu3CiSqQhNjZWfyUiIiIiAsDeidyHE1UiIiIiIiKSCieqREREREREJBVOVIk0DBgwQHQEIiIiImWwdyJ34USVSENKSoroCERERETKYO9E7sKJKhEREREREUmFE1UiIiIiIiKSCieqRBo2btwoOgIRERGRMtg7kbtwokpERERERERS4USVSMP48eNFRyAiIiJSBnsnchcv0QGao+NfAmXnxfzsNu2BsJHObSsqtyuZyXNUrWvyDNYHETU37jjupW5wbrvmdtxT9RzD3lobJ6oClJ0HinNFp2g8VXOTZ7A+SAvrg4iaG3cc93jcdIyq5xhVc3sKb/0l0pCYmCg6AhEREZEy2DuRu3CiSqRh+vTpoiMQERERKYO9E7kLJ6pEGoYNGyY6AhEREZEy2DuRu/A9qpJ7ZGFnlF+6CLPZArPZgsiugzFzwmq0D+giOlqDVMzckIKCAtERDMdI9UFNgzVCRM2NkY57svdOqo61qrldwSuqEissOYsLpflYPuMAPvpzOd6bcxLFFeex5pNnREdrkIqZyXNYH6SHNUJEzQ2Pe56j6lirmttVnKhK7HhOClr6+qNr+3AAgH+rdggN7ofickHP33aAipm1REZGio5gKEarD3I/1ggRNTdGO+7J3DupOtaq5nYVJ6oSO56TgrCQATCZTLBaq5CSvh3Jh/6JkTGTREdrkIqZtWzatEl0BEMxWn2Q+7FGiKi5MdpxT+beSdWxVjW3q/geVYkdz0lB2uk9ePD5AFReLYevd0vMmrAWsX3iREdrkIqZtcybNw8LFiwQHcMwjFYf5H6sESJqbox23JO5d1J1rFXN7Sqpr6hWV1djyZIl6NWrF3x9fdGnTx8kJycjLCwMU6dOFR2vyZ3ITcWzk9Zj88Ji/GNuDoLahiD7fLroWJpUzKwlKSlJdARDMVp9kPsZoUaulANnUoETycDp/wCVJaITGVdliX2MTyTbx/xKuehE+qqtwLkflfSFM4DNJi4PiWeE496Pydw7qTrWquZ2ldQT1SlTpmDhwoWIj4/Htm3bEBcXh4kTJ+LkyZPo37+/6HhN6mxhJsoqL6JXSD8AQDv/ThgfOwsf71uJ6upqAIDNZsPv3hiMvMIsFJbkYebyofj+wmmpM1urrXh61SjMWjEc8a/2xW+X3iYsL3mWijVNnqV6jdiqgYydwO5VwIldwJkUIHM38PVq4Og2wFolOqFxWKvsY/r1avsYn0mxj/nuVfZ/A1u16IT1KzwJ7F4JHPn4xrIDScA37wDlheJykTiqH/dUoupYN+f+WtqJ6vr167Fu3Tps2bIFs2fPxogRIzB37lwMHjwYVVVV6Nevn+iITep4TgratAxEh5u61SwbEjUOxWXnkHZ6DwDAZDLhiTGLsPKjP+Dl9Y9hxsNvo2Ngd0GJHctsMVvwSvwXePax9egY2B0LJm8RFZc8TMWaJs9SvUaO7wSy9wOo5+pY/lEg7RNeOXMHm80+lvlH63vR/m9wfKfHY+m6mAN8+y/gWmXd1y5dBPZvAC6Xej4XiaX6cU8lqo51c+6vpZ2oLlq0CKNHj0ZsbGyt5aGhofD29kZ0dDQA+33wvXv3htlsxsaNG0VEbRIZOSkI7RxTa1nbVkGI7D4Euw/f+Hv26BSNtFO7ce+AJ9CtQ4SnY9biaOb8C6fwxofT8PuHVqJT4C2ejtkoycnJoiMYhoo1TZ6lco1UFgO5B7XXKTgBlH7vmTxGVppvH0stuQft/yYyydyt8aINuHbZfmWYmheVj3sNkbV3UnWsjdhfO0rKhynl5uYiLS0NM2fOrPNadnY2oqKi4OPjAwAYPXo0fv3rX+OJJ57wdMwm9eQDr9a7fNm0G2e6yivleOn9RzBt3OvYnrIWd/d/3FPx6uVI5jPnvsO7n87DrLj/RZuWN3kqmtOOHj2K9u3bi45hCCrWNHmWyjWSV9/VvZ8yAXlHgLadmjyOoeWlATCh3ivXtdY7CvT8mScS6au4AJTk6a+Xlwb0GgGYpb2MQO6m8nGvIbL2TqqOtRH7a0dJO1EFgI4dO9ZaXllZieTkZIwZM6Zm2ZAhQ5o0i8lkcvv3XPLkTvTpOdyl73G16goWvh+HSaPmom/oCBzK2ok9R/6FO2/7ueZ2ycm7MGDiCKd+pjtyz1l9DwLbdMKL79pzvvCrD+HfMlBzG1cya6nvFyE/tWzZMt31li1b5q5ISnO1PpytaaDpakTL56/Yu+SmOEYYkarHPUfNmrAWd/f/JSyWhk+r1VYrNid9jsh7xzS4jmgq1PWfp2zF7b3vgdlsaXAdq7UKK19/D0vulOOX2DG9RmHx1B2661mvAQGtA1FWedEDqRpPhfqoj6jcRjzuydo7qTrW7sgNNL6/FtE3/ZjNwffBSDlRDQoKAgBkZGTgvvvuq1m+ePFi5OfnG/5BSo5o4eWDRVO21nw9K26twDSOW/9crugIJClVa5o8R+YaqbhcApNJ+zKYDTZU8BHALqu4XAKbzuVUk8mEisvyjLWj/+7W6ipcvlrRxGlIJTIf94xG5bE2an9tsjk6pfWg6upqxMTEID8/H0uWLEFwcDA2btyIrVu3Ijs7G/v27cPAgQNrbTN8+HBMnz4d48ePF5TacakbgGJB9RQQAtz+qHPbisrtSmYt6en6j/WOiIjAsWPHNNcJDw93VySlqVrXztqxxP7/u2Z79ueqyuj1UZwHpP5Df73oB4D2vZs2iytUqOvzGcBhB54TcvskIKBz0+dxhM1mf0Kx5sOSTMDNoUCfcR6L1Wgq1Ed9ROU24nFP1t5J1bE2Wm/tblK+C8JsNiMpKQlRUVFISEjA5MmTERQUhMTERFgslpoHKRE1tfnz54uOQEQKaNsJaBussYIJaHkTEBTqsUiGFRRqH0to3MXZNliu9wKbTED3gfrrdRvQ9FmImhp7J3IXKW/9BYDevXtj587az5d//PHHERkZCT8/P0GpqLmJi4sTHYGIFGAy2a+EHdwElJ1DnYf9+LUFYsbzITnuYDbbx/JA0k+e7PvDmLdpb/+3kO1tlMHRwOUy4PS+uq+ZzEDUffJcASZyBXsnchelTpmpqal13p/6/PPPIyQkBN988w3i4+MREhKCrKwsQQnJaCIixD+WnIjU0KIlMGAScNsDQNCPPhkgcgww6Nf2ySq5h19b+5hG/ui5VEG32Md+wGP2fwvZmExA6J3AwF8CwX0A/w6Afyeg+yDgZ78BOvJdJGQQ7J3IXZSZqJaXlyMjIwP9+vWrtXzhwoXIzc3FlStXUFRUhNzcXPTs2VNQSvfJPHsQz7x9D6a/fgfe+3wBJi8Ow6Es++dSFZbkIeG1frjvT76wWqsAAGcLMxH/al+8s/05kbE1c39/4TQmzO+AWSuG45m37wEgT27yDK36sFqr8Of3H8XslSOw+uM/AmB9NBeNPd4dy/4Pfv/mEMx4606s2GJ/sqQstWK2AB16A30furGscxSg8TBgcpLFyz621/V9yD72Gg8DlkKb9kDE3cAdjwN3PGafvPr6i05FntbY4x7Pkc7TGuv6zicy9NmNzWzUHluZiWrr1q1htVrx1FNPiY7S5Kqs17Bm6xy8+KsPMWnUczCbLZgQ+zT69IwFAPi3DMTiqV8gouugmm2Cg0IxbdxroiID0M8NAP173Y2lCbvw16mfAZAjN3mGXn3sSfsXenTugyVP7sSVqkpk5R1ifTQDzhzvOgR0wyvxX+K1xD0oLj+PU/lHWCtEpAxnjns8RzpHb6zrO5+I7rOdyQwYs8dWZqLanOzP+AzRPWLh59Ma7fw7YfPuv9V6vYW3r5Qf5quXGwC+zdqJmcuHYtNXanz26PDhw0VHMAy9+si/cBI9OtkflNazc198d3qviJjkYc4c7wL9O6KFty8AwGL21vw8TSIi2Thz3FPpHClT76Q31vWdT0T32c5kBtTrsR3Bm5EkdDgrGQcyd2B/xmcovVSESXepccleL3egfye880wGWlh8MG/dOMSEjkKPznI/wXnFihWiIxiGXn10uTkMh7OSMTDifhzK3IluHaMa+E5kJK4c707mHUZJRQG6dYhswoRERO7lzHFPpXOkTL2To2Mt0/nEmcxXq64o12M7gldUJVRUmoeFkz/G0oRdGBA2GjZbtehIDtHL3cLLB34tWsFi8cKgiLE4fS5NUFLHJSQkiI5gGHr1MSjyf3ClqhJPrxoFby8f3NS6g6Ck5EnOHu9KL13Am5unY9YEdT6QnYgIcO64p9I5UqbeyZGxlu184kxmFXtsR3CiKqFWfgEou1SE0ooi5BZkoJVvgOhIDtHLfelyWc2fj57+Gp3ayf/Qq127domOYBh69WExWzD9wTfwSvwXMJstuD3sXkFJyZOcOd5ZrVV4ef0vMHXsEgT6d/RASiIi93HmuKfSOVKm3klvrGU8nziTWcUe2xG89VdC9w+ciqVJU+DfKgjTx72BI6d213q9ynoNz64Zg5P5hzBnzb14YswiRHR14JPEm5he7iOnduPdT5+Ht5cPbr1lqBSZyXP06qOw5Cz+8o/HYDaZcVf/XyKobbCgpORJzhzv8otOIiMnBas/sT/5csqYvyCy+2AR8YmIGs2Z497NbUN4jnSC3lgnH06qcz7p3eV2oX22M5nLKi8assfmRFVCPTpH483f/bfm68y8g9iw82UEB/VCn56x8LJ4Y3H8jlrbnC3MxJqtczAseoKn49bQyz0w4j4MjLiv1jYy5CbP0KuPoLbBWJqwq9Y2rA/jc+Z4F9F1IEbGTKy1jLVCRKpw5rgHgOdIJ+iN9ciYiXXOJwCE9tnOZjZij22y2Ww20SGam9QNQHGumJ8dEALc/qhz24rK7UpmLenp6W75PuHh/JR2QN26dtaOJfb/3zXbsz9XVc2tPgA1a4SZSYuqYy0qtxGPe7L2TqqOtdF6a3fjFVUB2rRX82eLyi1yvD744APExcWJC6AQV/6drh+kA0I8/7PJM1gfRNTcqNrvuUpE76TqWDfH3roxOFEVIGyk6ATOUTW3K1544QVOVB3kSn1c/223Cr/dI+ewPoiouWmOfRMgpndSdaxVze0pfOovERERERERSYUTVSIiIiIiIpIKJ6pEGpYvXy46AhEREZEy2DuRu3CiSqQhKipKdAQiIiIiZbB3InfhRJVIQ2xsrOgIRERERMpg70TuwokqERERERERSYUTVSINAwYMEB2BiIiISBnsnchdOFEl0pCSku20e54AAB70SURBVCI6AhEREZEy2DuRu3CiSkRERERERFLhRJWIiIiIiIikwokqkYaNGzeKjkBERESkDPZO5C6cqBIREREREZFUOFEl0jB+/HjREYiIiIiUwd6J3MVLdIDm6PiXQNl5MT+7TXsgbKRz24rK7UpmVXGsiai5cfW4l7rBue143FODO86LrBHjYm/dOKrUNCeqApSdB4pzRadoPFVzq4hjTUTNjavHPR4zjc0d50XWiHGp2jepmttTeOsvkYbExETREYiIiIiUwd6J3IUTVSIN06dPFx2BiIiISBnsnchdOFEl0jBs2DDREYiIiIiUwd6J3IUTVSINBQUFoiMQERERKYO9E7kLH6YkuUcWdkb5pYswmy0wmy2I7DoYMyesRvuALqKjNUjFzKriWBNRc8PjHulhjZAWVetD1dyu4BVViRWWnMWF0nwsn3EAH/25HO/NOYniivNY88kzoqM1SMXMWiIjI0VHaJDRxpqISA+Pe6SHNSIeeyf3UzW3qzhRldjxnBS09PVH1/bhAAD/Vu0QGtwPxeWCPijKASpm1rJp0ybRERpktLEmItLD4x7pYY2Ix97J/VTN7SpOVCV2PCcFYSEDYDKZYLVWISV9O5IP/RMjYyaJjtYgFTNrmTdvnugIDTLaWBMR6eFxj/SwRsRj7+R+quZ2ldTvUa2ursarr76KVatWIScnB2FhYXj99dcxdepUxMbG4u233xYdsUkdz0lB2uk9ePD5AFReLYevd0vMmrAWsX3iREdrkIqZtSQlJWHBggWiY9TLaGNNTa/aCly7DHh5A5YWotM4xmar/WeTSVwWo1NhrHncIz2sEfHYO7mfqrldJfVEdcqUKfjwww/x/PPPo3///ti7dy8mTpyIgoIC/OEPfxAdr8mdyE3Fs5PW487bfo6i0nz8cdUoZJ9PFx1Lk4qZVcWxJkdVlgBnUoC8NKC6yr6sXQ+g2+1AYFex2Rpis9nz5uy/sWzPKiCkL9C1P2DxFpfNaKqtQO4hIOfAjWV71wJd+gEhfQCzRVy2n+Jxj/SwRkiLqvWham5XSXvr7/r167Fu3Tps2bIFs2fPxogRIzB37lwMHjwYVVVV6Nevn+iITepsYSbKKi+iV4j979nOvxPGx87Cx/tWorq6GgBgs9nwuzcGI68wC4UleZi5fCi+v3Ba6szWaiueXjUKs1YMR/yrffHbpbcJy6syFeuDxCgvBP77HpD77Y1JKgAUnQIOfADkHRGXrSE2G/Ddp8CxT4HyohvLr5QDWXuA/R8AVVfF5TOSaitwaDOQ8SVQWXxjeWWxfdmhzfZ1ZMDjHulhjZAWVeujOffX0k5UFy1ahNGjRyM2NrbW8tDQUHh7eyM6OhoXL17E2LFj0bt3b/Tp0wf33HMPMjMzBSV2r+M5KWjTMhAdbupWs2xI1DgUl51D2uk9AACTyYQnxizCyo/+gJfXP4YZD7+NjoHdBSV2LLPFbMEr8V/g2cfWo2NgdyyYvEVUXIckJyeLjlAvFeuDPM9mA458BFy7Ut+L9v999xlwqbie1wXKPwrkp/3wha3u66X5QNZuj0YyrDOp9l9aNKTolH0dGfC4R3pYI3Jg7+ReRuyvHSXlRDU3NxdpaWmYMGFCndeys7MRFRUFHx8fmEwmzJgxAxkZGTh06BDGjh2LyZMnC0jsfhk5KQjtHFNrWdtWQYjsPgS7D2+sWdajUzTSTu3GvQOeQLcOEZ6OWYujmfMvnMIbH07D7x9aiU6Bt3g6ZqMcPXpUdIR6qVgf5HkXc4CKItQ72athA84e8lQifTYbkL0fgM77I/PSeFXVVdXVQO5B/fVyDwK26qbPo4fHPdLDGpEDeyf3MmJ/7SiTzWbTamGE2LdvHwYPHoxPPvkE9913X83yyspK9OzZE2PGjMHatWvrbJeamooHH3wQubm5bstiaoKnSSx5cif69Bzu8vepvFKOF9Y9iHtu/zW2p6zFkid36m5zKGsXZq8c4dTPc0fuM+e+w7ufzsPM8avRpuVNDm3jSmYtM2fO1F1n2bJluustW7bMXZFquGOsPV0frvj8Ffth6O6nJXx6SwNUyPz43S/gl/e8qLmOzWbDibMHkPi32z0TSoefT2tseanMoXX/sHwYjpyS99Kq7DUSHNQL657JcGjdX/+1F84WNu0dS83tuKcikTWtau9kNLL2TqrWh7tyN7a/Fl3Tjk4/pbyiGhQUBADIyKh9Al28eDHy8/PRv3//erd77bXX8OCDDzZ5PhlcrbqChe/HYdKoubir/y/QKbAH9hz5l+hYuuasvgfnLp7Bi+/+HLNWDEfppQuiIxmSqvVB7mU2W3RPBiaTCRaJnpZjNjmexSxRbhU15t+9Mf8uovC4R3pYI6RF5fowan8t5RXV6upqxMTEID8/H0uWLEFwcDA2btyIrVu3Ijs7G/v27cPAgQNrbTN//nxs27YNX375JVq2bCkouWNSNwDF7rvo2ygBIcDtjzq3rajcrmTWkp6u/7S0iIgIHDt2THOd8PBwd0WqYbSx1rNjif3/d832/M92lgqZz2cChzfrr9f5NiDy3qbP4wibDfh6NXC5VHs9kxkY+iTQQuLDvew1Yq0CvloOWHVuofbyAYYmAJYm/pyA5nbcU5HImla1dzIaWXsnVeuDxz1tUl5RNZvNSEpKQlRUFBISEjB58mQEBQUhMTERFosF0dHRtdZ/6aWX8PHHH2P79u3ST1JJLfPnzxcdgchpQT2AFq2g+37PkL4eieMQkwnoEqO3EtAhTO5JqgosXkBwtP56nW9r+kkqERkHeydyF2lPPb1798bOnbXvC3/88ccRGRkJPz+/mmXz58/H1q1b8fnnnyMgIMDTMcng4uKM/UHKZGxmM3Dr/cDBjT88T6me+2e6DwL8O3g6mbYuMUBBVgO/ZTYBPq2BXrH1vEaN1mMwUHQaqCis//VWQfZ1iIgcxd6J3EXKK6oNSU1NrfX+1KNHj+LFF19EUVERhg8fjr59+6JvX4kuDZDyIiLEP+2NyBWBXe2399wUUnu5b1sg4h6g58/E5NJi9gJiHga6DQAsLW4sN5mBThHAHY/ZJ6vkOi8fe32E9LGP+3VmL/uy2x+1r0NE5Cj2TuQu0l5R/any8nJkZGRg2rRpNcuioqIcfmqUajLPHsTqT55BxeViDIwYiy8P/h9mPPw2+vSMxbHs/2DllpkwmcwI6zIACQ8sw9nCTCz4+3gMihyLyaNfkjI3AHye+nd8tv9dVFdb8adJ/4cr1yqlyK0arXG+fPUSFr43AZevVqCVb1s89/gHKCjO4Tg3Y207A/0fASqLga/X2Jf97Df222xlZfG2XzXtMQQoKwBQDbRsB7Tw092UGsnbFwi/GwgdBpT/cGW1dZA8E1St411hSR6ef2cszpz7Dh+9VA6LxQvfXziNp94YiK7tI+BlaYG/Tv1MmnMkuV9j64PnyOansT21DH12YzMDxuyxlbmi2rp1a1itVjz11FOiozS5Kus1rNk6By/+6kNMGvUczGYLJsQ+XTPZ6xDQDa/Ef4nXEveguPw8TuUfQXBQKKaNe03q3IUlZ3H4ZDJeif8CSxN2IahtsBS5VaM3zinHtyO860AsTdiFsK53IDV9O8eZAAB+P3p3hMyT1B+zeAMBne0PfuAktWl5+QABwfb/ZJmk6h3v/FsGYvHULxDRdVCt7fr3uhtLE3bhr1M/AwAeAw3KmfrgObJ5caanFt1nO5PZqD22MhPV5mR/xmeI7hELP5/WaOffCZt3/63W64H+HdHC2xcAYDF7S/MRDXq5U49/Cmu1FU+vGoU3Nz8Fa7VVUFLHDR8+XHSEOvTGuXO7nrh8tQIAUFFZDP9W7UTEJCJymd7xroW3b72fGfht1k7MXD4Um75y/+dckzycqQ+eI5ueTL2TMz216D7bmcwq9tiOUObW3+bkcFYyDmTuwP6Mz1B6qQiT7nqu3vVO5h1GSUUBunWI9HDC+unlvlh+DlXWq3gl/gus/uQZ7D36bwy97SFBaR2zYsUK0RHq0Bvn4KBeOHbmG/xmSRQCWrfHb+77q6CkRESucfR8+GOB/p3wzjMZaGHxwbx14xATOgo9OjvweGNSjjP1wXNk05Opd3KlpxbVZzuTee/RfyvXYzuCV1QlVFSah4WTP8bShF0YEDYaNlt1nXVKL13Am5unY9aEtQIS1k8vdyvftojuYb9toW/oSGSf1/6MLRkkJCSIjlCH3jh/nvouBkX+D9bMPoqB4ffjiwPvC0pKROQaR86HP9XCywd+LVrBYvHCoIixOH0uzQNJSQRn6oPnyKYnU+/kbE8tss92JrOKPbYjOFGVUCu/AJRdKkJpRRFyCzLQyrf2x+5YrVV4ef0vMHXsEgT6dxSUsi693JHdhuBk/mEAQFbet+gUeIuImI2ya9cu0RHq0BtnG2xo0zIQAODfKggVl0tExCQicpne8a4+ly6X1fz56Omv0aldz6aMSAI5Ux88RzY9mXonZ3pq0X22M5lV7LEdwVt/JXT/wKlYmjQF/q2CMH3cGzhyanet15MPJyEjJwWrP/kjAGDKmL8gsrv4D7rTyx0a3Bc+3n6YtWI42rYKwsNDZwpKqja9cR4ZMwkvvf8Idux/D14Wb8z9xT8FJSUico3e8a7Keg3PrhmDk/mHMGfNvXhizCKUVhTh3U+fh7eXD269ZSgiug4UlJ6amjP1wXNk8+JMT/39xdNC+2xn5wFG7LE5UZVQj87RePN3/635OjPvIDbsfBnBQb3Qp2csRsZMxMiYibW2OVuYiTVb52BY9ARPx62hlxsA4v9nSa1tZMitGr1xbu0XgJd/+2mtbTjORKQiveOdl8Ubi+N31NluYMR9tb7mMdCYnK0PniObD2d66sjug4X22c5kBozZY5tsRv0gUomlbgCKc8X87IAQ+we4O0NUblcya0lPT3fL9wkPD3fL9/kxo421nh0/HFvvmu35n+0sFTMD6uZWEce6cZrbcU9FImta1d7JaGTtnVStDx73tPE9qkQaPvjgA9ERiIiIiJTB3onchbf+CtCmvZo/W1RukeP1wgsvIC4uzuM/19m/8/XfygWEePbnEhG5qjmeY8hxqvZOzZGI3knV+uBxTxsnqgKEjRSdwDmq5laRs2N9/bYsFW7nICL6MZ5jSAvrg7SoWh+q5vYU3vpLREREREREUuFElUjD8uXLRUcgIiIiUgZ7J3IXTlSJNERFRYmOQERERKQM9k7kLpyoEmmIjY0VHYGIiIhIGeydyF04USUiIiIiIiKpcKJKREREREREUuFElUjDgAEDREcgIiIiUgZ7J3IXTlSJNKSkpIiOQERERKQM9k7kLpyoEhERERERkVQ4USUiIiIiIiKpcKJKpGHjxo2iIxAREREpg70TuQsnqkRERERERCQVTlSJNIwfP150BCIiIiJlsHcid/ESHaA5Ov4lUHZezM9u0x4IG+nctqJyu5KZyIjcsS+mbmj8Ns1xX+RYkxG5WtfO1DTAuqamw966cVTZFzlRFaDsPFCcKzpF46mam8ho3LEvcl92DMeajMjVumZNk2xU7VFVze0pvPWXSENiYqLoCERERETKYO9E7sKJKpGG6dOni45AREREpAz2TuQunKgSaRg2bJjoCERERETKYO9E7sL3qErukYWdUX7pIsxmC8xmCyK7DsbMCavRPqCL6GgNUjFzQwoKCkRHIHKakfZF2XGsyYhY1+QM2XsnVeta1dyu4BVViRWWnMWF0nwsn3EAH/25HO/NOYniivNY88kzoqM1SMXMREbEfdFzONZkRKxrMiJV61rV3K7iRFVix3NS0NLXH13bhwMA/Fu1Q2hwPxSXC3r+tgNUzKwlMjJSdAQipxhtX5QZx5qMiHVNzpK5d1K1rlXN7SpOVCV2PCcFYSEDYDKZYLVWISV9O5IP/RMjYyaJjtYgFTNr2bRpk+gIRE4x2r4oM441GRHrmpwlc++kal2rmttVfI+qxI7npCDt9B48+HwAKq+Ww9e7JWZNWIvYPnGiozVIxcxa5s2bhwULFoiOQdRoRtsXZcaxJiNiXZOzZO6dVK1rVXO7SuorqtXV1ViyZAl69eoFX19f9OnTB8nJyQgLC8PUqVNFx2tyJ3JT8eyk9di8sBj/mJuDoLYhyD6fLjqWJhUza0lKShIdwSE2G1B06sbXWV8Dl0vF5XHU5TLg5Dc3vi7MAmzV4vI4oroaOH/ixten/wNcqRCXpyFG2xdlxrEmI2Jdk7Nk7p1UrWtVc7tK6onqlClTsHDhQsTHx2Pbtm2Ii4vDxIkTcfLkSfTv3190vCZ1tjATZZUX0SukHwCgnX8njI+dhY/3rUR1tb2Tt9ls+N0bg5FXmIXCkjzMXD4U3184LXVma7UVT68ahVkrhiP+1b747dLbhOU1isoSYN864OCP7rQ59Q2w523gRLJ9Eisbm80+md7zNnDy6xvLv/0X8M07wKWL4rJpKS8A9q4BDv/7xrLM3cCeVcCZFHG5fkrF44eqONZkRKxrMiJV67o599fSTlTXr1+PdevWYcuWLZg9ezZGjBiBuXPnYvDgwaiqqkK/fv1ER2xSx3NS0KZlIDrc1K1m2ZCocSguO4e003sAACaTCU+MWYSVH/0BL69/DDMefhsdA7sLSuxYZovZglfiv8Czj61Hx8DuWDB5i6i4hlB1Fdj/AVBxof7Xz6QAp/Z5NpMjslPtk2nUM4m+VGz/O1277PFYmq6U23NdLqv7mq3a/kuBs4c9n6s+Kh4/VMWxJiNiXZMRqVrXzbm/lnaiumjRIowePRqxsbG1loeGhsLb2xvR0dEAgAcffBDR0dGIiYnBHXfcgR07doiI63YZOSkI7RxTa1nbVkGI7D4Euw9vrFnWo1M00k7txr0DnkC3DhGejlmLo5nzL5zCGx9Ow+8fWolOgbd4OmajJCcni46gKf8ocLkE9U74rjv9H6Dqisci6bJeq327bx024EoZkHfEY5EckvstcK0SmmOd9bX91mDRVDx+qIpjTUbEuiZXyNo7qVrXRuyvHSXlw5Ryc3ORlpaGmTNn1nktOzsbUVFR8PHxAQCsW7cOAQEBAICDBw9i+PDhuHDhAiwWi0czu9uTD7xa7/Jl03bX/LnySjleev8RTBv3OranrMXd/R/3VLx6OZL5zLnv8O6n8zAr7n/RpuVNnormtKNHj6J9+/aiYzQoL01/neoq4Hwm0Dmq6fM4ovAkYL2qv15eGtBtQNPncZQjY321AriYDbTr3uRxNKl4/FAVx5qMiHVNrpC1d1K1ro3YXztK2okqAHTs2LHW8srKSiQnJ2PMmDE1y65PUgGgpKQEJpMJNje+Kc9kMrnte1235Mmd6NNzuEvf42rVFSx8Pw6TRs1F39AROJS1E3uO/At33vZzze2Sk3dhwMQRTv1Md+Ses/oeBLbphBffted84Vcfwr9loOY2rmTWUt8vQn5q2bJluustW7bMXZEa7R9zs3FzQBfd9WZO/yM+2PWKBxLpGzckEdN//qbuevnZRTCZgjyQyDFbX74Cb0sL3fUeffhx7DjwfpNmcXVfFHH8UBXHmoyIdU3OkrV3as69NdD4/lr0vujoXE3KiWpQkL05zcjIwH333VezfPHixcjPz6/zIKXExERs27YNJSUl2LRpE7y8pPxruVULLx8smrK15utZcWsFpnHc+udyRUcwlOLyArTzD4bZrH0Xf0lFoYcS6XMkS3V1NUoqCjyQxnFlFRdwU5sOur+8kmmsG6Lq8UNFHGsyItY1GZHKdW3U/tpkc+flRzeprq5GTEwM8vPzsWTJEgQHB2Pjxo3YunUrsrOzsW/fPgwcOLDOdsnJyZg5cya++uortG7dWkByx6RuAIoF1VNACHD7o85tKyq3K5m1pKfrP9Y7IiICx44d01wnPDzcXZEa7UwqcGKX9jpmCzA0AfD29UgkXVVXgd0r7O9V1dLzTuCWQZ7J5IgTyfpP9vX2A4Y+aR/zpmS0fVFmHGsyItY1OUvW3om9deOosi9K+TAls9mMpKQkREVFISEhAZMnT0ZQUBASExNhsVhqHqT0U7GxsTCbzfj666/rfZ2osebPny86gqbOtwI+rQFoXOTr0l+eSSoAeLUAut2hsYIJaNESCK5/NxemSwzg5QPNsb5lUNNPUomIiGQme+9E6pD2HtnevXtj586dtZY9/vjjiIyMhJ+fHwCgvLwcRUVF6NbN/rjmgwcPIisrCxER4p/QRcYQFxcnOoImb1+gXxxwcCNwuRQ3JlE/3CcR3AcIvVNUuobdMsj+8TM5+39Y8KPcPq2AmIftk1WZ+PoDMeOBbz/84em/PxnrWwYBXYz9qVlERES6ZO+dSB3STlTrk5qaikGDbtwLWFFRgUceeQTl5eXw8vKCr68v3n//fXTt2lVgSjISR25fEa1VIDBkClCQCZw/Yb+l1i8ACL4NaC3Ps4hqMZmAsBFASB/7Z49eughYvICbQ4H2vQCzpEemtp2AO6cC547bn15sq7aPf+dooGWA/vZERERGp0LvRGqQtB2sq7y8HBkZGZg2bVrNsg4dOmDfvn0CUzWdzLMHsfqTZ1BxuRgDI8biy4P/hxkPv40+PWNx6vs0vLZxKsxmCzq3C8XsuP9FXlEWFvx9PAZFjsXk0S9JmTslfTs27HwZAJBbcBy/e2gFune8VYrcqjNbgA5h9v9U0ioQ6D1cdIrGsXjbb7nufKvoJHVp7X+FJXl4/p2xOHPuO3z0UjksFq96l50tzOQ+6YDGjvV1m75aht1HNuG1xD0ca5JOY+ua53VSgVZdH8v+D1ZumQmTyYywLgOQ8MAyKfrsxmY26r4o5XtU69O6dWtYrVY89dRToqM0uSrrNazZOgcv/upDTBr1HMxmCybEPo0+PWMBAF1uDsPfpu+t+fykjNxUBAeFYtq410TG1s09IHw0libswtKEXWgf0BX9et0lRW4iI9Db//xbBmLx1C8Q0fXGXSn1LeM+qc+ZsQbsH32Qlfdtzdcca5KJM3XN8zrJTq+uOwR0wyvxX+K1xD0oLj+PU/lHhPfZzmQ26r6ozES1Odmf8Rmie8TCz6c12vl3wubdf6v1upfFu+bP3l4+uLmt/udoeoJe7uvyi04ioE0H+PnI+2Tm64YPHy46ApFD9Pa/Ft6+dT4EvL5lpM+ZsQaA7f9di7tv/5WnYhI1irN1Dah1XqemJ1PvpFfXgf4d0eKHJ05azN4wmy3C+2xnMl9ntH1RmVt/m5PDWck4kLkD+zM+Q+mlIky667k66+w9ugXvbHsWwUG94N+qnYCUdTmSGwD2HPkQP7tV+8OTZbFixQrREYgc4uj+R65zZqyrrNdwKGsXHhgyDe9+Os8DKYkax5VjiErndWp6MvVOjtb1ybzDKKkoQLcOkQDE9tnOZgaMty/yiqqEikrzsHDyx1iasAsDwkbDZquus86QqAewenYaggJCsO+7jwWkrMuR3ADwzbGPMCTyAQ+nc05CQoLoCEQOcXT/I9c5M9Y79r+HkTGTPJCOyDmuHENUOq9T05Opd3KkrksvXcCbm6dj1oS1NctE9tnOZgaMty9yoiqhVn4BKLtUhNKKIuQWZKCVb+3HiV6tulLz55Y+/vDx9vN0xHrp5QaAC6Xfw9vSQpqrwHp27dolOgKRQxzZ/8g9nBnrnILj+OibFfjT6tE4c+4oNu95wwNJiRzn7DFEtfM6NT2Zeie9urZaq/Dy+l9g6tglCPTvCEB8n+1MZsCY+yJv/ZXQ/QOnYmnSFPi3CsL0cW/gyKndtV5PTd+OjbtfBQAEB/VC/973iIhZh15uANh79N8YHDVOQDoiY9Pb/6qs1/DsmjE4mX8Ic9bciyfGLEKv4H51lkV0HSjob6AOZ8b6t/f/teb1GW/diQfvNP6DAUktztR1RNeBPK+T1PTqOvlwEjJyUrD6kz8CAKaM+QuKy88L7bOdyRzZfbAh90VOVCXUo3M03vzdf2u+zsw7iA07X0ZwUC/06RmLIbeOw5Bbaxfi2cJMrNk6B8OiJ3g6bg293AAwdnB8rW1kyE1kBHr7n5fFG4vjd9TZ7qfLuE/qc3asr3stcQ8AjjXJxdm65nmdZKZX1yNjJmJkzMQ624nss53NbMR90WSz2WyiQzQ3qRuA4lwxPzsgBLj9Uee2FZXblcxa0tPT3fJ9wsPD3fJ9iBxltH1RZhxrMiLWNTlL1t6JvXXjqLIv8oqqAG3aq/mzReUWOV4ffPAB4uLixAUgqkdz3BdF4ViTEbGuqSmJ6J3YW6vxcxuLV1Sp2XLkt4IRERE4duyY5jq8okpERETNAXsn8iQ+9ZeIiIiIiIikwokqERERERERSYUTVSINy5cvFx2BiIiISBnsnchdOFEl0hAVFSU6AhEREZEy2DuRu3CiSqQhNjZWdAQiIiIiZbB3InfhRJWIiIiIiIikws9RpWbLkUejv/DCC3yEOhERERHYO5Fn8XNUiYiIiIiISCq89ZeIiIiIiIikwokqERERERERSYUTVSIiIiIiIpIKJ6pEREREREQkFU5UiYiIiIiISCqcqBIREREREZFUOFElIiIiIiIiqXCiSkRERERERFLhRJWIiIiIiIikwokqERERERERSeX/ASS3jC/tP35zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1224.38x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entanglement = [(3, 2), (3, 1), (3, 0),\n",
    "                (2, 3), (2, 1), (2, 0),\n",
    "                (1, 3), (1, 2), (1, 0),\n",
    "                (0, 3), (0, 2), (0, 1)]\n",
    "two = TwoLocal(4, ['rx', 'rz'], 'crx', entanglement=entanglement, reps=1, insert_barriers=True)\n",
    "two.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "vqe = VQE(ising, two, optimizer)  # then run algorithm..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Any arbitrary circuit is supported as algorithm input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.circuit import QuantumCircuit, ParameterVector\n",
    "\n",
    "ansatz = QuantumCircuit(4)\n",
    "\n",
    "p = ParameterVector('p', 16)\n",
    "p_iter = iter(p)\n",
    "\n",
    "for i in range(4):\n",
    "    ansatz.ry(next(p_iter), i)\n",
    "ansatz.append(QFT(4, approximation_degree=1, do_swaps=False), [0, 1, 2, 3])\n",
    "for i in range(4):\n",
    "    ansatz.ry(next(p_iter), i)   \n",
    "ansatz.append(QFT(4, approximation_degree=1, do_swaps=False).inverse(), [0, 1, 2, 3])\n",
    "for i in range(4):\n",
    "    ansatz.ry(next(p_iter), i)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 441.777x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ansatz.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "vqe = VQE(ising, ansatz, optimizer)  # then run algorithm..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If it turns out to be good, add it to the library! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Summary\n",
    "\n",
    "* Choose the right Ansatz for your application\n",
    "* Qiskit's algorithms run on any custom circuit\n",
    "* Circuit library offers a set of standard ansatz circuits (like `RealAmplitudes`) and tools to build new ones (`TwoLocal`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Chemistry applications\n",
    "\n",
    "The ansatz tries to approximate the ground state of a molecule. `RealAmplitudes` from before is not the right, we want complex amplitudes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Statevector([ 0.77658928-0.18547926j, -0.02534895+0.21396543j,\n",
       "              0.25962842+0.22161376j,  0.06110877+0.4425256j ],\n",
       "            dims=(2, 2))"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import EfficientSU2\n",
    "\n",
    "ansatz = EfficientSU2(2)\n",
    "bound_ansatz = ansatz.assign_parameters(np.random.random(ansatz.num_parameters))\n",
    "Statevector.from_instruction(bound_ansatz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.environ['QISKIT_IN_PARALLEL'] = 'TRUE'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.5598794124645186"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# run H2 molecule\n",
    "from qiskit.aqua.operators import I, Z, X\n",
    "from qiskit.aqua.components.optimizers import L_BFGS_B\n",
    "\n",
    "h2_op = -1.052373245772859 * (I ^ I) + 0.39793742484318045 * (I ^ Z) \\\n",
    "        - 0.39793742484318045 * (Z ^ I) - 0.01128010425623538 * (Z ^ Z) \\\n",
    "        + 0.18093119978423156 * (X ^ X)\n",
    "h2_energy = -1.85727503\n",
    "\n",
    "optimizer = L_BFGS_B()  # Broyden–Fletcher–Goldfarb–Shanno\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "vqe = VQE(h2_op, ansatz, optimizer)\n",
    "res = vqe.run(backend)\n",
    "res.eigenvalue.real"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Another approach: Classically motivated\n",
    "\n",
    "In chemistry, the UCCSD(T) method is considered the \"gold\" standard to compute the ground state energy.\n",
    "This also uses the variational principle with a certain wavefunction ansatz. \n",
    "We can also use this wavefunction here! \n",
    "\n",
    "[Barkoutsos]: Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian\n",
    "and optimized wavefunction expansions, Barkoutsos et al. [arXiv:1805.04340](https://arxiv.org/pdf/1805.04340.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1645.63x505.68 with 1 Axes>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.chemistry.components.variational_forms import UCCSD\n",
    "\n",
    "ucc = UCCSD(4, 2, reps=3)\n",
    "p = ParameterVector('p', ucc.num_parameters)\n",
    "ansatz = ucc.construct_circuit(p).decompose()\n",
    "ansatz.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.869270947305635"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqe = VQE(h2_op, ansatz, optimizer)\n",
    "res = vqe.run(backend)\n",
    "res.eigenvalue.real"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This worked well for this small system... what about larger systems? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit.chemistry.drivers import PySCFDriver\n",
    "from qiskit.chemistry import FermionicOperator\n",
    "from qiskit.aqua.operators import Z2Symmetries\n",
    "\n",
    "H2 = 'H 0.0 0.0 0.0; H 0.0 0.0 0.735'  # molecular coordinates in Angstrom\n",
    "LiH = 'Li 0.0 0.0 0.0; H 0.0 0.0 1.3'\n",
    "\n",
    "def define_chemistry_problem(atom, basis, reduction=True):\n",
    "    molecule = PySCFDriver(atom=atom, basis=basis).run()\n",
    "    num_particles = molecule.num_alpha + molecule.num_beta\n",
    "    num_orbitals = 2 * molecule.num_orbitals\n",
    "\n",
    "    ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)\n",
    "    if reduction:\n",
    "        qubitOp = ferOp.mapping(map_type='parity')\n",
    "        qubitOp = Z2Symmetries.two_qubit_reduction(qubitOp, num_particles)\n",
    "    else:\n",
    "        qubitOp = ferOp.mapping(map_type='jordan_wigner')\n",
    "\n",
    "    return qubitOp.to_opflow(), num_particles, num_orbitals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SummedOp(\n",
      "[-1.052373245772859 * II,\n",
      "0.39793742484318007 * IZ,\n",
      "-0.39793742484318007 * ZI,\n",
      "-0.01128010425623538 * ZZ,\n",
      "0.18093119978423136 * XX])\n"
     ]
    }
   ],
   "source": [
    "qubitOp, num_particles, num_orbitals = define_chemistry_problem(H2, 'sto3g')\n",
    "print(qubitOp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 2)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_orbitals, num_particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SummedOp(\n",
      "[-5.259038246818582 * IIIIIIIIII,\n",
      "1.0235687911585036 * IIIIIIIIIZ,\n",
      "-0.01771856623628656 * IIIIIIIIZX,\n",
      "0.01771856623628656 * IIIIIIIIIX,\n",
      "-0.02654806113115581 * IIIIIIIZXX,\n",
      "-0.02654806113115581 * IIIIIIIIYY,\n",
      "-0.004686977340277227 * IIIIIXXXXX,\n",
      "-0.004686977340277227 * IIIIIYXXXY,\n",
      "-0.1060833226130983 * IIIIIIIIZZ,\n",
      "0.008011661921423425 * IIIIIIIZXZ,\n",
      "-0.008011661921423425 * IIIIIIIIXI,\n",
      "-0.005696482431937478 * IIIIIXXXXZ,\n",
      "-0.005696482431937478 * IIIIIYXXYI,\n",
      "-0.19442319698823987 * IIIIIIIZZI,\n",
      "-0.014333639794327236 * IIIIIXXXZI,\n",
      "-0.014333639794327236 * IIIIIYXYII,\n",
      "-0.22447370517677553 * IIIIIIZZII,\n",
      "-0.22447370517677542 * IIIIIZZIII,\n",
      "-0.41689839336782997 * IIIIIZIIII,\n",
      "1.0235687911585032 * IIIIZIIIII,\n",
      "-0.017718566236286547 * IIIZXIIIII,\n",
      "0.017718566236286547 * IIIIXIIIII,\n",
      "-0.026548061131155848 * IIZXXIIIII,\n",
      "-0.026548061131155848 * IIIYYIIIII,\n",
      "-0.004686977340277227 * XXXXXIIIII,\n",
      "-0.004686977340277227 * YXXXYIIIII,\n",
      "-0.10608332261309833 * IIIZZIIIII,\n",
      "0.008011661921423434 * IIZXZIIIII,\n",
      "-0.008011661921423434 * IIIXIIIIII,\n",
      "-0.005696482431937463 * XXXXZIIIII,\n",
      "-0.005696482431937463 * YXXYIIIIII,\n",
      "-0.19442319698823995 * IIZZIIIIII,\n",
      "-0.014333639794327231 * XXXZIIIIII,\n",
      "-0.014333639794327231 * YXYIIIIIII,\n",
      "-0.2244737051767755 * IZZIIIIIII,\n",
      "-0.22447370517677526 * ZZIIIIIIII,\n",
      "-0.41689839336782997 * ZIIIIIIIII,\n",
      "0.09760890024461519 * IIIIIIIIZI,\n",
      "-0.0011565826096576752 * IIIIIIIZXI,\n",
      "0.0011565826096576752 * IIIIIIIIXZ,\n",
      "0.0027394317537303924 * IIIIIXXXXI,\n",
      "0.0027394317537303924 * IIIIIYXXYZ,\n",
      "0.09375745007789797 * IIIIIIIZZZ,\n",
      "0.0039719139622109816 * IIIIIXXXZZ,\n",
      "0.0039719139622109816 * IIIIIYXYIZ,\n",
      "0.09660936871402734 * IIIIIIZZIZ,\n",
      "0.09660936871402735 * IIIIIZZIIZ,\n",
      "0.08931080489725143 * IIIIIZIIIZ,\n",
      "0.0038756342038197716 * IIIIIIIZYY,\n",
      "0.0038756342038197716 * IIIIIIIIXX,\n",
      "0.002840167738012162 * IIIIIXXXYY,\n",
      "-0.002840167738012162 * IIIIIYXXYX,\n",
      "-0.003402502500304318 * IIIIIIIZIX,\n",
      "0.003402502500304318 * IIIIIIIZZX,\n",
      "-0.0014720039146502784 * IIIIIXXXIX,\n",
      "-0.0004257105377678607 * IIIIIYXYZX,\n",
      "-0.0010462933768824179 * IIIIIXXYIY,\n",
      "-0.0010462933768824179 * IIIIIYXXIY,\n",
      "0.0004257105377678607 * IIIIIXXXZX,\n",
      "0.0014720039146502784 * IIIIIYXYIX,\n",
      "-0.0032374459046439516 * IIIIIIZZZX,\n",
      "0.0032374459046439516 * IIIIIIZZIX,\n",
      "-0.0032374459046439538 * IIIIIZZIZX,\n",
      "0.0032374459046439538 * IIIIIZZIIX,\n",
      "0.0013409649292806234 * IIIIIZIIZX,\n",
      "-0.0013409649292806234 * IIIIIZIIIX,\n",
      "-0.0005313204106595455 * IIIIIXXYYX,\n",
      "-0.0005313204106595455 * IIIIIYXYYY,\n",
      "-0.0037643909963563245 * IIIIIIZIXX,\n",
      "-0.0037643909963563245 * IIIIIIZZYY,\n",
      "-0.0037643909963563254 * IIIIIZZZXX,\n",
      "-0.0037643909963563254 * IIIIIZZIYY,\n",
      "-0.003781269074511558 * IIIIIZIZXX,\n",
      "-0.003781269074511558 * IIIIIZIIYY,\n",
      "-0.001135865796876707 * IIIIIXYYXX,\n",
      "-0.001135865796876707 * IIIIIYYYXY,\n",
      "-0.0011358657968767068 * IIIIIYYXXX,\n",
      "0.0011358657968767068 * IIIIIXYXXY,\n",
      "0.4140579227814105 * IIIIZIIIIZ,\n",
      "-0.03273291354927221 * IIIIZIIIZX,\n",
      "0.03273291354927221 * IIIIZIIIIX,\n",
      "-0.03373687566028914 * IIIIZIIZXX,\n",
      "-0.03373687566028914 * IIIIZIIIYY,\n",
      "0.0031870245795891203 * IIIIZXXXXX,\n",
      "0.0031870245795891203 * IIIIZYXXXY,\n",
      "0.03273291354927221 * IIIIXIIIIZ,\n",
      "-0.03273291354927221 * IIIZXIIIIZ,\n",
      "-0.004726476426781394 * IIIIXIIIZX,\n",
      "0.004726476426781394 * IIIZXIIIZX,\n",
      "0.004726476426781394 * IIIIXIIIIX,\n",
      "-0.004726476426781394 * IIIZXIIIIX,\n",
      "-0.0031025134310981306 * IIIIXIIZXX,\n",
      "0.0031025134310981306 * IIIZXIIZXX,\n",
      "-0.0031025134310981306 * IIIIXIIIYY,\n",
      "0.0031025134310981306 * IIIZXIIIYY,\n",
      "0.0011571650373133004 * IIIIXXXXXX,\n",
      "-0.0011571650373133004 * IIIZXXXXXX,\n",
      "0.0011571650373133004 * IIIIXYXXXY,\n",
      "-0.0011571650373133004 * IIIZXYXXXY,\n",
      "-0.03373687566028914 * IIIYYIIIIZ,\n",
      "-0.03373687566028914 * IIZXXIIIIZ,\n",
      "0.0031025134310981306 * IIIYYIIIZX,\n",
      "0.0031025134310981306 * IIZXXIIIZX,\n",
      "-0.0031025134310981306 * IIIYYIIIIX,\n",
      "-0.0031025134310981306 * IIZXXIIIIX,\n",
      "0.0052639440128288435 * IIIYYIIZXX,\n",
      "0.0052639440128288435 * IIZXXIIZXX,\n",
      "0.0052639440128288435 * IIIYYIIIYY,\n",
      "0.0052639440128288435 * IIZXXIIIYY,\n",
      "0.000485909491003698 * IIIYYXXXXX,\n",
      "0.000485909491003698 * IIZXXXXXXX,\n",
      "0.000485909491003698 * IIIYYYXXXY,\n",
      "0.000485909491003698 * IIZXXYXXXY,\n",
      "0.0024567585594751206 * IIYXYIZXXX,\n",
      "0.0024567585594751206 * IZXXXIZXXX,\n",
      "0.0024567585594751206 * IIYXYIIYXY,\n",
      "0.0024567585594751206 * IZXXXIIYXY,\n",
      "0.0024567585594751215 * IYXXYZXXXX,\n",
      "0.0024567585594751215 * ZXXXXZXXXX,\n",
      "0.0024567585594751215 * IYXXYIYXXY,\n",
      "0.0024567585594751215 * ZXXXXIYXXY,\n",
      "0.0031870245795891203 * YXXXYIIIIZ,\n",
      "0.0031870245795891203 * XXXXXIIIIZ,\n",
      "-0.0011571650373133004 * YXXXYIIIZX,\n",
      "-0.0011571650373133004 * XXXXXIIIZX,\n",
      "0.0011571650373133004 * YXXXYIIIIX,\n",
      "0.0011571650373133004 * XXXXXIIIIX,\n",
      "0.00048590949100369796 * YXXXYIIZXX,\n",
      "0.00048590949100369796 * XXXXXIIZXX,\n",
      "0.00048590949100369796 * YXXXYIIIYY,\n",
      "0.00048590949100369796 * XXXXXIIIYY,\n",
      "0.0010415892080677146 * YXXXYXXXXX,\n",
      "0.0010415892080677146 * XXXXXXXXXX,\n",
      "0.0010415892080677146 * YXXXYYXXXY,\n",
      "0.0010415892080677146 * XXXXXYXXXY,\n",
      "0.1023353766713966 * IIIZZIIIIZ,\n",
      "0.002481456177619541 * IIIZZIIIZX,\n",
      "-0.002481456177619541 * IIIZZIIIIX,\n",
      "-0.0050089770260941914 * IIIZZIIZXX,\n",
      "-0.0050089770260941914 * IIIZZIIIYY,\n",
      "-0.0007256264739018705 * IIIZZXXXXX,\n",
      "-0.0007256264739018705 * IIIZZYXXXY,\n",
      "-0.0019459308214404556 * IIIXIIIIIZ,\n",
      "0.0019459308214404556 * IIZXZIIIIZ,\n",
      "0.0011333428222744205 * IIIXIIIIZX,\n",
      "-0.0011333428222744205 * IIZXZIIIZX,\n",
      "-0.0011333428222744205 * IIIXIIIIIX,\n",
      "0.0011333428222744205 * IIZXZIIIIX,\n",
      "-8.660470971587143e-05 * IIIXIIIZXX,\n",
      "8.660470971587143e-05 * IIZXZIIZXX,\n",
      "-8.660470971587143e-05 * IIIXIIIIYY,\n",
      "8.660470971587143e-05 * IIZXZIIIYY,\n",
      "4.330724731442705e-05 * IIIXIXXXXX,\n",
      "-4.330724731442705e-05 * IIZXZXXXXX,\n",
      "4.330724731442705e-05 * IIIXIYXXXY,\n",
      "-4.330724731442705e-05 * IIZXZYXXXY,\n",
      "0.0019502059099518441 * IIYYIIZXXX,\n",
      "0.0019502059099518441 * IZXXZIZXXX,\n",
      "0.0019502059099518441 * IIYYIIIYXY,\n",
      "0.0019502059099518441 * IZXXZIIYXY,\n",
      "0.0019502059099518443 * IYXYIZXXXX,\n",
      "0.0019502059099518443 * ZXXXZZXXXX,\n",
      "0.0019502059099518443 * IYXYIIYXXY,\n",
      "0.0019502059099518443 * ZXXXZIYXXY,\n",
      "0.001582266716417092 * YXXYIIIIIZ,\n",
      "0.001582266716417092 * XXXXZIIIIZ,\n",
      "0.0021145412641102915 * YXXYIIIIZX,\n",
      "0.0021145412641102915 * XXXXZIIIZX,\n",
      "-0.0021145412641102915 * YXXYIIIIIX,\n",
      "-0.0021145412641102915 * XXXXZIIIIX,\n",
      "-0.0010896006241968448 * YXXYIIIZXX,\n",
      "-0.0010896006241968448 * XXXXZIIZXX,\n",
      "-0.0010896006241968448 * YXXYIIIIYY,\n",
      "-0.0010896006241968448 * XXXXZIIIYY,\n",
      "0.0005529387467561216 * YXXYIXXXXX,\n",
      "0.0005529387467561216 * XXXXZXXXXX,\n",
      "0.0005529387467561216 * YXXYIYXXXY,\n",
      "0.0005529387467561216 * XXXXZYXXXY,\n",
      "0.09902139409072679 * IIZZIIIIIZ,\n",
      "-0.0033158977905884466 * IIZZIIIIZX,\n",
      "0.0033158977905884466 * IIZZIIIIIX,\n",
      "0.0005981239659412053 * IIZZIIIZXX,\n",
      "0.0005981239659412053 * IIZZIIIIYY,\n",
      "0.0017150557464080047 * IIZZIXXXXX,\n",
      "0.0017150557464080047 * IIZZIYXXXY,\n",
      "-0.0025578119949501866 * IIXIIIZXXX,\n",
      "0.0025578119949501866 * IZXZIIZXXX,\n",
      "-0.0025578119949501866 * IIXIIIIYXY,\n",
      "0.0025578119949501866 * IZXZIIIYXY,\n",
      "0.0025578119949501875 * IYYIIZXXXX,\n",
      "0.0025578119949501875 * ZXXZIZXXXX,\n",
      "0.0025578119949501875 * IYYIIIYXXY,\n",
      "0.0025578119949501875 * ZXXZIIYXXY,\n",
      "0.00445782345321468 * YXYIIIIIIZ,\n",
      "0.00445782345321468 * XXXZIIIIIZ,\n",
      "-0.0015153111619647054 * YXYIIIIIZX,\n",
      "-0.0015153111619647054 * XXXZIIIIZX,\n",
      "0.0015153111619647054 * YXYIIIIIIX,\n",
      "0.0015153111619647054 * XXXZIIIIIX,\n",
      "0.001183735335748459 * YXYIIIIZXX,\n",
      "0.001183735335748459 * XXXZIIIZXX,\n",
      "0.001183735335748459 * YXYIIIIIYY,\n",
      "0.001183735335748459 * XXXZIIIIYY,\n",
      "0.0008329367529079545 * YXYIIXXXXX,\n",
      "0.0008329367529079545 * XXXZIXXXXX,\n",
      "0.0008329367529079545 * YXYIIYXXXY,\n",
      "0.0008329367529079545 * XXXZIYXXXY,\n",
      "0.09906612727350243 * IZZIIIIIIZ,\n",
      "-0.0012872399946921081 * IZZIIIIIZX,\n",
      "0.0012872399946921081 * IZZIIIIIIX,\n",
      "-0.0012065790014061377 * IZZIIIIZXX,\n",
      "-0.0012065790014061377 * IZZIIIIIYY,\n",
      "-0.00022966647977732104 * IZZIIXXXXX,\n",
      "-0.00022966647977732104 * IZZIIYXXXY,\n",
      "-0.0013655322766540285 * YYIIIIZXXX,\n",
      "-0.0013655322766540285 * XXZIIIZXXX,\n",
      "-0.0013655322766540285 * YYIIIIIYXY,\n",
      "-0.0013655322766540285 * XXZIIIIYXY,\n",
      "0.09906612727350246 * ZZIIIIIIIZ,\n",
      "-0.0012872399946921094 * ZZIIIIIIZX,\n",
      "0.0012872399946921094 * ZZIIIIIIIX,\n",
      "-0.0012065790014061382 * ZZIIIIIZXX,\n",
      "-0.0012065790014061382 * ZZIIIIIIYY,\n",
      "-0.00022966647977732202 * ZZIIIXXXXX,\n",
      "-0.00022966647977732202 * ZZIIIYXXXY,\n",
      "0.0013655322766540287 * XIIIIZXXXX,\n",
      "-0.0013655322766540287 * XZIIIZXXXX,\n",
      "0.0013655322766540287 * XIIIIIYXXY,\n",
      "-0.0013655322766540287 * XZIIIIYXXY,\n",
      "0.09035239410531916 * ZIIIIIIIIZ,\n",
      "0.0018939036760367448 * ZIIIIIIIZX,\n",
      "-0.0018939036760367448 * ZIIIIIIIIX,\n",
      "-0.0029483323216036037 * ZIIIIIIZXX,\n",
      "-0.0029483323216036037 * ZIIIIIIIYY,\n",
      "0.00024943962560284953 * ZIIIIXXXXX,\n",
      "0.00024943962560284953 * ZIIIIYXXXY,\n",
      "0.05573338217631587 * IIIIIIIZIZ,\n",
      "-0.004685976638314677 * IIIIIXXXIZ,\n",
      "-0.004685976638314677 * IIIIIYXYZZ,\n",
      "0.0650247438323828 * IIIIIIZZZZ,\n",
      "0.06502474383238281 * IIIIIZZIZZ,\n",
      "0.08484866446637522 * IIIIIZIIZZ,\n",
      "0.00208704147550077 * IIIIIXXYYZ,\n",
      "-0.00208704147550077 * IIIIIYXYXI,\n",
      "-0.004061607702650756 * IIIIIIZIXZ,\n",
      "0.004061607702650756 * IIIIIIZZXI,\n",
      "-0.004061607702650758 * IIIIIZZZXZ,\n",
      "0.004061607702650758 * IIIIIZZIXI,\n",
      "-0.0024637522930665325 * IIIIIZIZXZ,\n",
      "0.0024637522930665325 * IIIIIZIIXI,\n",
      "-0.005097855782014351 * IIIIIXYYXZ,\n",
      "-0.005097855782014351 * IIIIIYYYYI,\n",
      "-0.005097855782014345 * IIIIIYYXXZ,\n",
      "0.005097855782014345 * IIIIIXYXYI,\n",
      "0.1023353766713966 * IIIIZIIIZZ,\n",
      "0.0019459308214404556 * IIIIZIIZXZ,\n",
      "-0.0019459308214404556 * IIIIZIIIXI,\n",
      "0.001582266716417092 * IIIIZXXXXZ,\n",
      "0.001582266716417092 * IIIIZYXXYI,\n",
      "-0.002481456177619541 * IIIIXIIIZZ,\n",
      "0.002481456177619541 * IIIZXIIIZZ,\n",
      "0.0011333428222744207 * IIIIXIIZXZ,\n",
      "-0.0011333428222744207 * IIIZXIIZXZ,\n",
      "-0.0011333428222744207 * IIIIXIIIXI,\n",
      "0.0011333428222744207 * IIIZXIIIXI,\n",
      "-0.0021145412641102915 * IIIIXXXXXZ,\n",
      "0.0021145412641102915 * IIIZXXXXXZ,\n",
      "-0.0021145412641102915 * IIIIXYXXYI,\n",
      "0.0021145412641102915 * IIIZXYXXYI,\n",
      "-0.0050089770260941914 * IIIYYIIIZZ,\n",
      "-0.0050089770260941914 * IIZXXIIIZZ,\n",
      "8.660470971587141e-05 * IIIYYIIZXZ,\n",
      "8.660470971587141e-05 * IIZXXIIZXZ,\n",
      "-8.660470971587141e-05 * IIIYYIIIXI,\n",
      "-8.660470971587141e-05 * IIZXXIIIXI,\n",
      "-0.0010896006241968446 * IIIYYXXXXZ,\n",
      "-0.0010896006241968446 * IIZXXXXXXZ,\n",
      "-0.0010896006241968446 * IIIYYYXXYI,\n",
      "-0.0010896006241968446 * IIZXXYXXYI,\n",
      "0.0019502059099518437 * IIYXYIZXXZ,\n",
      "0.0019502059099518437 * IZXXXIZXXZ,\n",
      "0.0019502059099518437 * IIYXYIIYYI,\n",
      "0.0019502059099518437 * IZXXXIIYYI,\n",
      "0.0019502059099518441 * IYXXYZXXXZ,\n",
      "0.0019502059099518441 * ZXXXXZXXXZ,\n",
      "0.0019502059099518441 * IYXXYIYXYI,\n",
      "0.0019502059099518441 * ZXXXXIYXYI,\n",
      "-0.0007256264739018705 * YXXXYIIIZZ,\n",
      "-0.0007256264739018705 * XXXXXIIIZZ,\n",
      "-4.330724731442705e-05 * YXXXYIIZXZ,\n",
      "-4.330724731442705e-05 * XXXXXIIZXZ,\n",
      "4.330724731442705e-05 * YXXXYIIIXI,\n",
      "4.330724731442705e-05 * XXXXXIIIXI,\n",
      "0.0005529387467561216 * YXXXYXXXXZ,\n",
      "0.0005529387467561216 * XXXXXXXXXZ,\n",
      "0.0005529387467561216 * YXXXYYXXYI,\n",
      "0.0005529387467561216 * XXXXXYXXYI,\n",
      "0.1270634139266309 * IIIZZIIIZZ,\n",
      "-0.010965819553473841 * IIIZZIIZXZ,\n",
      "0.010965819553473841 * IIIZZIIIXI,\n",
      "0.03611266801865087 * IIIZZXXXXZ,\n",
      "0.03611266801865087 * IIIZZYXXYI,\n",
      "0.010965819553473841 * IIIXIIIIZZ,\n",
      "-0.010965819553473841 * IIZXZIIIZZ,\n",
      "-0.0026782907385781802 * IIIXIIIZXZ,\n",
      "0.0026782907385781802 * IIZXZIIZXZ,\n",
      "0.0026782907385781802 * IIIXIIIIXI,\n",
      "-0.0026782907385781802 * IIZXZIIIXI,\n",
      "0.007918643141572144 * IIIXIXXXXZ,\n",
      "-0.007918643141572144 * IIZXZXXXXZ,\n",
      "0.007918643141572144 * IIIXIYXXYI,\n",
      "-0.007918643141572144 * IIZXZYXXYI,\n",
      "0.006296882346542271 * IIYYIIZXXZ,\n",
      "0.006296882346542271 * IZXXZIZXXZ,\n",
      "0.006296882346542271 * IIYYIIIYYI,\n",
      "0.006296882346542271 * IZXXZIIYYI,\n",
      "0.006296882346542274 * IYXYIZXXXZ,\n",
      "0.006296882346542274 * ZXXXZZXXXZ,\n",
      "0.006296882346542274 * IYXYIIYXYI,\n",
      "0.006296882346542274 * ZXXXZIYXYI,\n",
      "0.03611266801865087 * YXXYIIIIZZ,\n",
      "0.03611266801865087 * XXXXZIIIZZ,\n",
      "-0.007918643141572144 * YXXYIIIZXZ,\n",
      "-0.007918643141572144 * XXXXZIIZXZ,\n",
      "0.007918643141572144 * YXXYIIIIXI,\n",
      "0.007918643141572144 * XXXXZIIIXI,\n",
      "0.03046938151236052 * YXXYIXXXXZ,\n",
      "0.03046938151236052 * XXXXZXXXXZ,\n",
      "0.03046938151236052 * YXXYIYXXYI,\n",
      "0.03046938151236052 * XXXXZYXXYI,\n",
      "0.05841167291489405 * IIZZIIIIZZ,\n",
      "0.0008621275106545669 * IIZZIIIZXZ,\n",
      "-0.0008621275106545669 * IIZZIIIIXI,\n",
      "-0.0003807652481676297 * IIZZIXXXXZ,\n",
      "-0.0003807652481676297 * IIZZIYXXYI,\n",
      "-0.0047995556699317096 * IIXIIIZXXZ,\n",
      "0.0047995556699317096 * IZXZIIZXXZ,\n",
      "-0.0047995556699317096 * IIXIIIIYYI,\n",
      "0.0047995556699317096 * IZXZIIIYYI,\n",
      "0.004799555669931711 * IYYIIZXXXZ,\n",
      "0.004799555669931711 * ZXXZIZXXXZ,\n",
      "0.004799555669931711 * IYYIIIYXYI,\n",
      "0.004799555669931711 * ZXXZIIYXYI,\n",
      "-0.012604619779886823 * YXYIIIIIZZ,\n",
      "-0.012604619779886823 * XXXZIIIIZZ,\n",
      "0.0017062762273331402 * YXYIIIIZXZ,\n",
      "0.0017062762273331402 * XXXZIIIZXZ,\n",
      "-0.0017062762273331402 * YXYIIIIIXI,\n",
      "-0.0017062762273331402 * XXXZIIIIXI,\n",
      "-0.00747567960122464 * YXYIIXXXXZ,\n",
      "-0.00747567960122464 * XXXZIXXXXZ,\n",
      "-0.00747567960122464 * YXYIIYXXYI,\n",
      "-0.00747567960122464 * XXXZIYXXYI,\n",
      "0.07132162617892507 * IZZIIIIIZZ,\n",
      "0.0007379479672809534 * IZZIIIIZXZ,\n",
      "-0.0007379479672809534 * IZZIIIIIXI,\n",
      "0.00037258604473015144 * IZZIIXXXXZ,\n",
      "0.00037258604473015144 * IZZIIYXXYI,\n",
      "-0.0047252697372842 * YYIIIIZXXZ,\n",
      "-0.0047252697372842 * XXZIIIZXXZ,\n",
      "-0.0047252697372842 * YYIIIIIYYI,\n",
      "-0.0047252697372842 * XXZIIIIYYI,\n",
      "0.07132162617892508 * ZZIIIIIIZZ,\n",
      "0.0007379479672809533 * ZZIIIIIZXZ,\n",
      "-0.0007379479672809533 * ZZIIIIIIXI,\n",
      "0.00037258604473014515 * ZZIIIXXXXZ,\n",
      "0.00037258604473014515 * ZZIIIYXXYI,\n",
      "0.0047252697372842005 * XIIIIZXXXZ,\n",
      "-0.0047252697372842005 * XZIIIZXXXZ,\n",
      "0.0047252697372842005 * XIIIIIYXYI,\n",
      "-0.0047252697372842005 * XZIIIIYXYI,\n",
      "0.11531804597873574 * ZIIIIIIIZZ,\n",
      "-0.009939431894291171 * ZIIIIIIZXZ,\n",
      "0.009939431894291171 * ZIIIIIIIXI,\n",
      "0.03765778608249772 * ZIIIIXXXXZ,\n",
      "0.03765778608249772 * ZIIIIYXXYI,\n",
      "0.06025354250147995 * IIIIIIZIZI,\n",
      "0.060253542501479976 * IIIIIZZZZI,\n",
      "0.054078128864330104 * IIIIIZIZZI,\n",
      "-0.003470877943035282 * IIIIIXYYZI,\n",
      "0.003470877943035282 * IIIIIYYXII,\n",
      "-0.003470877943035282 * IIIIIYYXZI,\n",
      "0.003470877943035282 * IIIIIXYYII,\n",
      "0.09902139409072679 * IIIIZIIZZI,\n",
      "0.004457823453214681 * IIIIZXXXZI,\n",
      "0.004457823453214681 * IIIIZYXYII,\n",
      "0.003315897790588446 * IIIIXIIZZI,\n",
      "-0.003315897790588446 * IIIZXIIZZI,\n",
      "0.0015153111619647054 * IIIIXXXXZI,\n",
      "-0.0015153111619647054 * IIIZXXXXZI,\n",
      "0.0015153111619647054 * IIIIXYXYII,\n",
      "-0.0015153111619647054 * IIIZXYXYII,\n",
      "0.0005981239659412052 * IIIYYIIZZI,\n",
      "0.0005981239659412052 * IIZXXIIZZI,\n",
      "0.001183735335748459 * IIIYYXXXZI,\n",
      "0.001183735335748459 * IIZXXXXXZI,\n",
      "0.001183735335748459 * IIIYYYXYII,\n",
      "0.001183735335748459 * IIZXXYXYII,\n",
      "0.0025578119949501866 * IIYXYIZXZI,\n",
      "0.0025578119949501866 * IZXXXIZXZI,\n",
      "-0.0025578119949501866 * IIYXYIIXII,\n",
      "-0.0025578119949501866 * IZXXXIIXII,\n",
      "0.0025578119949501875 * IYXXYZXXZI,\n",
      "0.0025578119949501875 * ZXXXXZXXZI,\n",
      "0.0025578119949501875 * IYXXYIYYII,\n",
      "0.0025578119949501875 * ZXXXXIYYII,\n",
      "0.0017150557464080047 * YXXXYIIZZI,\n",
      "0.0017150557464080047 * XXXXXIIZZI,\n",
      "0.0008329367529079545 * YXXXYXXXZI,\n",
      "0.0008329367529079545 * XXXXXXXXZI,\n",
      "0.0008329367529079545 * YXXXYYXYII,\n",
      "0.0008329367529079545 * XXXXXYXYII,\n",
      "0.05841167291489405 * IIIZZIIZZI,\n",
      "-0.012604619779886823 * IIIZZXXXZI,\n",
      "-0.012604619779886823 * IIIZZYXYII,\n",
      "-0.0008621275106545669 * IIIXIIIZZI,\n",
      "0.0008621275106545669 * IIZXZIIZZI,\n",
      "-0.00170627622733314 * IIIXIXXXZI,\n",
      "0.00170627622733314 * IIZXZXXXZI,\n",
      "-0.00170627622733314 * IIIXIYXYII,\n",
      "0.00170627622733314 * IIZXZYXYII,\n",
      "0.00479955566993171 * IIYYIIZXZI,\n",
      "0.00479955566993171 * IZXXZIZXZI,\n",
      "-0.00479955566993171 * IIYYIIIXII,\n",
      "-0.00479955566993171 * IZXXZIIXII,\n",
      "0.004799555669931711 * IYXYIZXXZI,\n",
      "0.004799555669931711 * ZXXXZZXXZI,\n",
      "0.004799555669931711 * IYXYIIYYII,\n",
      "0.004799555669931711 * ZXXXZIYYII,\n",
      "-0.0003807652481676297 * YXXYIIIZZI,\n",
      "-0.0003807652481676297 * XXXXZIIZZI,\n",
      "-0.00747567960122464 * YXXYIXXXZI,\n",
      "-0.00747567960122464 * XXXXZXXXZI,\n",
      "-0.00747567960122464 * YXXYIYXYII,\n",
      "-0.00747567960122464 * XXXXZYXYII,\n",
      "0.08496781268823106 * IIZZIIIZZI,\n",
      "0.009063206085032586 * IIZZIXXXZI,\n",
      "0.009063206085032586 * IIZZIYXYII,\n",
      "-0.01038305439069627 * IIXIIIZXZI,\n",
      "0.01038305439069627 * IZXZIIZXZI,\n",
      "0.01038305439069627 * IIXIIIIXII,\n",
      "-0.01038305439069627 * IZXZIIIXII,\n",
      "0.010383054390696273 * IYYIIZXXZI,\n",
      "0.010383054390696273 * ZXXZIZXXZI,\n",
      "0.010383054390696273 * IYYIIIYYII,\n",
      "0.010383054390696273 * ZXXZIIYYII,\n",
      "0.009063206085032588 * YXYIIIIZZI,\n",
      "0.009063206085032588 * XXXZIIIZZI,\n",
      "0.006604932099026595 * YXYIIXXXZI,\n",
      "0.006604932099026595 * XXXZIXXXZI,\n",
      "0.006604932099026595 * YXYIIYXYII,\n",
      "0.006604932099026595 * XXXZIYXYII,\n",
      "0.07063659689217622 * IZZIIIIZZI,\n",
      "1.9426439249097232e-05 * IZZIIXXXZI,\n",
      "1.9426439249097232e-05 * IZZIIYXYII,\n",
      "-0.0034514515037861846 * YYIIIIZXZI,\n",
      "-0.0034514515037861846 * XXZIIIZXZI,\n",
      "0.0034514515037861846 * YYIIIIIXII,\n",
      "0.0034514515037861846 * XXZIIIIXII,\n",
      "0.07063659689217625 * ZZIIIIIZZI,\n",
      "1.9426439249096602e-05 * ZZIIIXXXZI,\n",
      "1.9426439249096602e-05 * ZZIIIYXYII,\n",
      "0.003451451503786185 * XIIIIZXXZI,\n",
      "-0.003451451503786185 * XZIIIZXXZI,\n",
      "0.003451451503786185 * XIIIIIYYII,\n",
      "-0.003451451503786185 * XZIIIIYYII,\n",
      "0.06068306096335671 * ZIIIIIIZZI,\n",
      "-0.010570962582796089 * ZIIIIXXXZI,\n",
      "-0.010570962582796089 * ZIIIIYXYII,\n",
      "0.06558452315458396 * IIIIIZIZII,\n",
      "0.06305846439752381 * IIIIIZZZII,\n",
      "0.09906612727350243 * IIIIZIZZII,\n",
      "0.0012872399946921081 * IIIIXIZZII,\n",
      "-0.0012872399946921081 * IIIZXIZZII,\n",
      "-0.0012065790014061377 * IIIYYIZZII,\n",
      "-0.0012065790014061377 * IIZXXIZZII,\n",
      "-0.001365532276654028 * IIYXYXXZII,\n",
      "-0.001365532276654028 * IZXXXXXZII,\n",
      "-0.001365532276654028 * IIYXYYYIII,\n",
      "-0.001365532276654028 * IZXXXYYIII,\n",
      "-0.0002296664797773211 * YXXXYIZZII,\n",
      "-0.0002296664797773211 * XXXXXIZZII,\n",
      "0.07132162617892507 * IIIZZIZZII,\n",
      "-0.0007379479672809536 * IIIXIIZZII,\n",
      "0.0007379479672809536 * IIZXZIZZII,\n",
      "-0.0047252697372842 * IIYYIXXZII,\n",
      "-0.0047252697372842 * IZXXZXXZII,\n",
      "-0.0047252697372842 * IIYYIYYIII,\n",
      "-0.0047252697372842 * IZXXZYYIII,\n",
      "0.00037258604473015144 * YXXYIIZZII,\n",
      "0.00037258604473015144 * XXXXZIZZII,\n",
      "0.07063659689217622 * IIZZIIZZII,\n",
      "0.003451451503786185 * IIXIIXXZII,\n",
      "-0.003451451503786185 * IZXZIXXZII,\n",
      "0.003451451503786185 * IIXIIYYIII,\n",
      "-0.003451451503786185 * IZXZIYYIII,\n",
      "1.9426439249097232e-05 * YXYIIIZZII,\n",
      "1.9426439249097232e-05 * XXXZIIZZII,\n",
      "0.07823637778985211 * IZZIIIZZII,\n",
      "-0.004217284878422706 * IXIIIZXZII,\n",
      "0.004217284878422706 * ZXZIIZXZII,\n",
      "0.004217284878422706 * IXIIIIXIII,\n",
      "-0.004217284878422706 * ZXZIIIXIII,\n",
      "0.0046076422752864155 * YYIIIXXZII,\n",
      "0.0046076422752864155 * XXZIIXXZII,\n",
      "0.0046076422752864155 * YYIIIYYIII,\n",
      "0.0046076422752864155 * XXZIIYYIII,\n",
      "0.06980180803300667 * ZZIIIIZZII,\n",
      "0.06766610667281023 * ZIIIIIZZII,\n",
      "0.0630584643975238 * IIIIIIZIII,\n",
      "0.09906612727350246 * IIIIZZZIII,\n",
      "0.0012872399946921094 * IIIIXZZIII,\n",
      "-0.0012872399946921094 * IIIZXZZIII,\n",
      "-0.001206579001406138 * IIIYYZZIII,\n",
      "-0.001206579001406138 * IIZXXZZIII,\n",
      "-0.0013655322766540285 * IYXXYXZIII,\n",
      "-0.0013655322766540285 * ZXXXXXZIII,\n",
      "0.0013655322766540285 * IYXXYXIIII,\n",
      "0.0013655322766540285 * ZXXXXXIIII,\n",
      "-0.00022966647977732196 * YXXXYZZIII,\n",
      "-0.00022966647977732196 * XXXXXZZIII,\n",
      "0.07132162617892508 * IIIZZZZIII,\n",
      "-0.0007379479672809531 * IIIXIZZIII,\n",
      "0.0007379479672809531 * IIZXZZZIII,\n",
      "-0.0047252697372842005 * IYXYIXZIII,\n",
      "-0.0047252697372842005 * ZXXXZXZIII,\n",
      "0.0047252697372842005 * IYXYIXIIII,\n",
      "0.0047252697372842005 * ZXXXZXIIII,\n",
      "0.00037258604473014515 * YXXYIZZIII,\n",
      "0.00037258604473014515 * XXXXZZZIII,\n",
      "0.07063659689217625 * IIZZIZZIII,\n",
      "-0.0034514515037861854 * IYYIIXZIII,\n",
      "-0.0034514515037861854 * ZXXZIXZIII,\n",
      "0.0034514515037861854 * IYYIIXIIII,\n",
      "0.0034514515037861854 * ZXXZIXIIII,\n",
      "1.9426439249096602e-05 * YXYIIZZIII,\n",
      "1.9426439249096602e-05 * XXXZIZZIII,\n",
      "0.06980180803300667 * IZZIIZZIII,\n",
      "0.07823637778985214 * ZZIIIZZIII,\n",
      "-0.004607642275286416 * XIIIIXZIII,\n",
      "0.004607642275286416 * XZIIIXZIII,\n",
      "0.004607642275286416 * XIIIIXIIII,\n",
      "-0.004607642275286416 * XZIIIXIIII,\n",
      "0.06766610667281021 * ZIIIIZZIII,\n",
      "0.09035239410531916 * IIIIZZIIII,\n",
      "-0.001893903676036745 * IIIIXZIIII,\n",
      "0.001893903676036745 * IIIZXZIIII,\n",
      "-0.0029483323216036037 * IIIYYZIIII,\n",
      "-0.0029483323216036037 * IIZXXZIIII,\n",
      "0.00024943962560284953 * YXXXYZIIII,\n",
      "0.00024943962560284953 * XXXXXZIIII,\n",
      "0.11531804597873574 * IIIZZZIIII,\n",
      "0.009939431894291171 * IIIXIZIIII,\n",
      "-0.009939431894291171 * IIZXZZIIII,\n",
      "0.037657786082497716 * YXXYIZIIII,\n",
      "0.037657786082497716 * XXXXZZIIII,\n",
      "0.06068306096335671 * IIZZIZIIII,\n",
      "-0.010570962582796089 * YXYIIZIIII,\n",
      "-0.010570962582796089 * XXXZIZIIII,\n",
      "0.06766610667281023 * IZZIIZIIII,\n",
      "0.06766610667281021 * ZZIIIZIIII,\n",
      "0.11380588704210495 * ZIIIIZIIII,\n",
      "0.09760890024461519 * IIIZIIIIII,\n",
      "-0.0011565826096576752 * IIZXIIIIII,\n",
      "0.0011565826096576752 * IIIXZIIIII,\n",
      "0.0027394317537303924 * XXXXIIIIII,\n",
      "0.0027394317537303924 * YXXYZIIIII,\n",
      "0.09375745007789797 * IIZZZIIIII,\n",
      "0.0039719139622109816 * XXXZZIIIII,\n",
      "0.0039719139622109816 * YXYIZIIIII,\n",
      "0.09660936871402734 * IZZIZIIIII,\n",
      "0.09660936871402735 * ZZIIZIIIII,\n",
      "0.08931080489725143 * ZIIIZIIIII,\n",
      "0.0038756342038197716 * IIZYYIIIII,\n",
      "0.0038756342038197716 * IIIXXIIIII,\n",
      "0.002840167738012162 * XXXYYIIIII,\n",
      "-0.002840167738012162 * YXXYXIIIII,\n",
      "-0.003402502500304318 * IIZIXIIIII,\n",
      "0.003402502500304318 * IIZZXIIIII,\n",
      "-0.0014720039146502784 * XXXIXIIIII,\n",
      "-0.0004257105377678607 * YXYZXIIIII,\n",
      "-0.0010462933768824179 * XXYIYIIIII,\n",
      "-0.0010462933768824179 * YXXIYIIIII,\n",
      "0.0004257105377678607 * XXXZXIIIII,\n",
      "0.0014720039146502784 * YXYIXIIIII,\n",
      "-0.0032374459046439516 * IZZZXIIIII,\n",
      "0.0032374459046439516 * IZZIXIIIII,\n",
      "-0.0032374459046439538 * ZZIZXIIIII,\n",
      "0.0032374459046439538 * ZZIIXIIIII,\n",
      "0.0013409649292806234 * ZIIZXIIIII,\n",
      "-0.0013409649292806234 * ZIIIXIIIII,\n",
      "-0.0005313204106595455 * XXYYXIIIII,\n",
      "-0.0005313204106595455 * YXYYYIIIII,\n",
      "-0.0037643909963563245 * IZIXXIIIII,\n",
      "-0.0037643909963563245 * IZZYYIIIII,\n",
      "-0.0037643909963563254 * ZZZXXIIIII,\n",
      "-0.0037643909963563254 * ZZIYYIIIII,\n",
      "-0.003781269074511558 * ZIZXXIIIII,\n",
      "-0.003781269074511558 * ZIIYYIIIII,\n",
      "-0.001135865796876707 * XYYXXIIIII,\n",
      "-0.001135865796876707 * YYYXYIIIII,\n",
      "-0.0011358657968767068 * YYXXXIIIII,\n",
      "0.0011358657968767068 * XYXXYIIIII,\n",
      "0.05573338217631587 * IIZIZIIIII,\n",
      "-0.004685976638314677 * XXXIZIIIII,\n",
      "-0.004685976638314677 * YXYZZIIIII,\n",
      "0.0650247438323828 * IZZZZIIIII,\n",
      "0.06502474383238281 * ZZIZZIIIII,\n",
      "0.08484866446637522 * ZIIZZIIIII,\n",
      "0.00208704147550077 * XXYYZIIIII,\n",
      "-0.00208704147550077 * YXYXIIIIII,\n",
      "-0.004061607702650756 * IZIXZIIIII,\n",
      "0.004061607702650756 * IZZXIIIIII,\n",
      "-0.004061607702650758 * ZZZXZIIIII,\n",
      "0.004061607702650758 * ZZIXIIIIII,\n",
      "-0.0024637522930665325 * ZIZXZIIIII,\n",
      "0.0024637522930665325 * ZIIXIIIIII,\n",
      "-0.005097855782014351 * XYYXZIIIII,\n",
      "-0.005097855782014351 * YYYYIIIIII,\n",
      "-0.005097855782014345 * YYXXZIIIII,\n",
      "0.005097855782014345 * XYXYIIIIII,\n",
      "0.06025354250147995 * IZIZIIIIII,\n",
      "0.060253542501479976 * ZZZZIIIIII,\n",
      "0.054078128864330104 * ZIZZIIIIII,\n",
      "-0.003470877943035282 * XYYZIIIIII,\n",
      "0.003470877943035282 * YYXIIIIIII,\n",
      "-0.003470877943035282 * YYXZIIIIII,\n",
      "0.003470877943035282 * XYYIIIIIII,\n",
      "0.06558452315458396 * ZIZIIIIIII,\n",
      "0.06305846439752381 * ZZZIIIIIII,\n",
      "0.0630584643975238 * IZIIIIIIII])\n"
     ]
    }
   ],
   "source": [
    "qubitOp, num_particles, num_orbitals = define_chemistry_problem(LiH, 'sto3g')\n",
    "print(qubitOp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 4)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_orbitals, num_particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Qubits: 10 Depth: 8467 #Params: 92\n"
     ]
    }
   ],
   "source": [
    "ucc = UCCSD(num_orbitals, num_particles)\n",
    "p = ParameterVector('p', ucc.num_parameters)\n",
    "ansatz = ucc.construct_circuit(p).decompose()\n",
    "\n",
    "print('#Qubits:', ansatz.num_qubits, 'Depth:', ansatz.depth(), '#Params:', ansatz.num_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Compromise?\n",
    "\n",
    "In the Jordan-Wigner mapping, a qubit state of $|1\\rangle$ can be associated with an existing particle. Since the total number of particles should be conserved, the Ansatz wavefunction should conserve the number of $|1\\rangle$ states, e.g.:\n",
    "\n",
    "$$\n",
    "\\begin{matrix}\n",
    "    & \\mid & |00\\rangle & |10\\rangle & |01\\rangle & |11\\rangle \\\\\n",
    "    \\hline\n",
    "    \\langle 00| & \\mid & 1 & 0 & 0 & 0 \\\\\n",
    "    \\langle 10|& \\mid & 0 & \\cos(\\theta/2) & -i\\sin(\\theta/2) & 0 \\\\\n",
    "    \\langle 01|& \\mid & 0 & -i\\sin(\\theta/2) & \\cos(\\theta/2) & 0 \\\\\n",
    "    \\langle 11|& \\mid & 0 & 0 & 0 & 1\n",
    "\\end{matrix}\n",
    "$$\n",
    "\n",
    "The `ExcitationPreserving` circuit does that.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 742.632x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import ExcitationPreserving\n",
    "\n",
    "ansatz = ExcitationPreserving(2)\n",
    "ansatz.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Qubits: 12 Depth: 94 #Params: 246\n"
     ]
    }
   ],
   "source": [
    "qubitOp, num_particles, num_orbitals = define_chemistry_problem(LiH, 'sto3g', reduction=False)\n",
    "ansatz = ExcitationPreserving(qubitOp.num_qubits)\n",
    "print('#Qubits:', ansatz.num_qubits, 'Depth:', ansatz.depth(), '#Params:', ansatz.num_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Contributing!\n",
    "\n",
    "* Add new circuits\n",
    "    * more arithmetic circuits\n",
    "    * more basis changes\n",
    "    * circuits that you'd like to share! \n",
    "    * ?\n",
    "* More tests\n",
    "    * Find efficient ways to test circuits\n",
    "* Optimized versions of circuits\n",
    "* More options for circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Summary\n",
    "\n",
    "1. Circuits are algorithm primitives\n",
    "2. The circuit library...\n",
    "    1. offers a building blocks for algorithms\n",
    "    2. has a selection for different algorithm inputs\n",
    "    3. is extensible!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supplementary material"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QAE\n",
    "\n",
    "Estimate $a$ in\n",
    "\n",
    "$$\n",
    "\\mathcal{A}|0\\rangle = \\sqrt{1 - a}|\\Psi_0\\rangle + \\sqrt{a}|\\Psi_1\\rangle \n",
    "$$\n",
    "\n",
    "If we set $a$ to $\\mathbb{E}[f(X)]$ we can get a quadratic speedup compared to Monte-Carlo simulations [Woerner]!\n",
    "Works by creating a circuit\n",
    "\n",
    "$$\n",
    "\\mathcal{A}|0\\rangle_{n+1} = \\sum_{i=0}^{N - 1} \\sqrt{p_{x_i} (1 - f(x_i))} |x\\rangle_n |0\\rangle + \n",
    "\\sum_{i=0}^{N - 1} \\sqrt{p_{x_i} f(x_i)} |x\\rangle_n |1\\rangle\n",
    "$$\n",
    "\n",
    "Here\n",
    "\n",
    "$$\n",
    "f_y(x) = \\sin^2(2x - y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit.library import LinearPauliRotations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 431.769x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LinearPauliRotations(3, slope=2*2, offset=-2*y).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.48021114, 0.51978886])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = LinearPauliRotations(2, slope=2*2, offset=2*1)\n",
    "equal_superpos = QuantumCircuit(3)\n",
    "equal_superpos.h([0, 1])\n",
    "\n",
    "sv = Statevector.from_label('000')\n",
    "sv = sv.evolve(equal_superpos)\n",
    "sv = sv.evolve(f)\n",
    "sv.probabilities(qargs=[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10714285714285714"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_probability_qubits = 3\n",
    "y = 0.5\n",
    "M = 2 ** num_probability_qubits\n",
    "1 / M * sum((i / (M - 1) - y) ** 2 for i in range(M))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_probability_qubits = 3\n",
    "uniform_distribution = QuantumCircuit(num_probability_qubits)\n",
    "uniform_distribution.h(list(range(num_probability_qubits)))\n",
    "\n",
    "slope = 2 / (2 ** num_probability_qubits - 1)\n",
    "offset = -2 * y\n",
    "linear_function = LinearPauliRotations(num_probability_qubits, slope, offset)\n",
    "\n",
    "unitary = QuantumCircuit(num_probability_qubits + 1)\n",
    "unitary.compose(uniform_distribution, qubits=list(range(num_probability_qubits)), inplace=True)\n",
    "unitary.compose(linear_function, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 381.577x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitary.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Building Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1352ed0d0>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S_psi_0 = QuantumCircuit(4)\n",
    "S_psi_0.x(3)\n",
    "S_psi_0.z(3)\n",
    "S_psi_0.x(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x13534d1d0>"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import ZGate\n",
    "\n",
    "S_0 = QuantumCircuit(4)\n",
    "S_0.x([0, 1, 2, 3])\n",
    "S_0.append(ZGate().control(3), [0, 1, 2, 3])\n",
    "S_0.x([0, 1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = QuantumCircuit(4)\n",
    "Q.compose(S_psi_0, inplace=True)\n",
    "Q.barrier()\n",
    "Q.compose(unitary.inverse(), inplace=True)\n",
    "Q.barrier()\n",
    "Q.compose(S_0, inplace=True)\n",
    "Q.barrier()\n",
    "Q.compose(unitary, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224.38x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = QuantumCircuit(4)\n",
    "Q.compose(S_psi_0, inplace=True)\n",
    "Q.compose(unitary.inverse(), inplace=True)\n",
    "Q.compose(S_0, inplace=True)\n",
    "Q.compose(unitary, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x134dd4810>"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_eval_qubits = 3\n",
    "qae = QuantumCircuit(num_eval_qubits + num_probability_qubits + 1, num_eval_qubits)\n",
    "qae.compose(unitary, qubits=[3, 4, 5, 6], inplace=True)\n",
    "qae.compose(PhaseEstimation(3, Q), inplace=True)\n",
    "qae.measure([0, 1, 2], [0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1164.18x505.68 with 1 Axes>"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qae.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'000': 44, '001': 6, '010': 14, '011': 12, '100': 456, '101': 8, '110': 5, '111': 479}\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "counts = execute(qae, backend).result().get_counts()\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accumulate states with same outcome and get most likely"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "accumulated = {}\n",
    "for state, count in counts.items():\n",
    "    y = int(state[::-1], 2)\n",
    "    if y > M / 2:\n",
    "        y = M - y\n",
    "    accumulated[y] = accumulated.get(y, 0) + count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "most_likely = ''\n",
    "max_count = 0\n",
    "for state, count in accumulated.items():\n",
    "    if count > max_count:\n",
    "        most_likely = state\n",
    "        max_count = count\n",
    "        \n",
    "print(most_likely)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(accumulated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1464466094067263"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(np.pi * most_likely / 2 ** num_eval_qubits) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 0.14644660940672624, 0.4999999999999999, 0.8535533905932737, 1.0]\n"
     ]
    }
   ],
   "source": [
    "print([np.sin(np.pi * i / 2 ** num_eval_qubits) ** 2 for i in range(2 ** (num_eval_qubits - 1) + 1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}