docs/named_topologies.ipynb

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   "source": [
    "##### Copyright 2021 The Cirq Developers"
   ]
  },
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   "source": [
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AF-CFuvzPx4x"
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   "source": [
    "# Named Topologies"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://quantumai.google/cirq/named_topologies\"><img src=\"https://quantumai.google/site-assets/images/buttons/quantumai_logo_1x.png\" />View on QuantumAI</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/quantumlib/Cirq/blob/main/docs/named_topologies.ipynb\"><img src=\"https://quantumai.google/site-assets/images/buttons/colab_logo_1x.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://github.com/quantumlib/Cirq/blob/main/docs/named_topologies.ipynb\"><img src=\"https://quantumai.google/site-assets/images/buttons/github_logo_1x.png\" />View source on GitHub</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a href=\"https://storage.googleapis.com/tensorflow_docs/Cirq/docs/named_topologies.ipynb\"><img src=\"https://quantumai.google/site-assets/images/buttons/download_icon_1x.png\" />Download notebook</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "try:\n",
    "    import cirq\n",
    "except ImportError:\n",
    "    print(\"installing cirq...\")\n",
    "    !pip install --quiet cirq\n",
    "    print(\"installed cirq.\")\n",
    "    \n",
    "import cirq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6zlksjAlum6f"
   },
   "outputs": [],
   "source": [
    "from typing import Iterable, List, Optional, Sequence\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "09358b36ef8d"
   },
   "source": [
    "## TiltedSquareLattice\n",
    "\n",
    "This is a grid lattice rotated 45-degrees.\n",
    "\n",
    "This topology is based on Google devices where plaquettes consist of four qubits in a square\n",
    "connected to a central qubit:\n",
    "\n",
    "    x   x\n",
    "      x\n",
    "    x   x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6172a6b67648"
   },
   "outputs": [],
   "source": [
    "import itertools\n",
    "from cirq import TiltedSquareLattice\n",
    "\n",
    "side_lens = np.arange(1, 4+1)\n",
    "l = len(side_lens)\n",
    "\n",
    "fig, axes = plt.subplots(l, l, figsize=(3.5*l, 3*l))\n",
    "for widthi, heighti in itertools.product(np.arange(l), repeat=2):\n",
    "    width = side_lens[widthi]\n",
    "    height = side_lens[heighti]\n",
    "    ax = axes[heighti, widthi]\n",
    "    topo = TiltedSquareLattice(width, height)\n",
    "    topo.draw(ax=ax, tilted=False)\n",
    "        \n",
    "    if widthi == 0:\n",
    "        ax.set_ylabel(f'Height {height}', fontsize=14)\n",
    "    if heighti == l-1:\n",
    "        ax.set_xlabel(f'Width {width}', fontsize=14)\n",
    "    \n",
    "    ax.set_title(f'n = {topo.n_nodes}', fontsize=14)\n",
    "        \n",
    "fig.tight_layout()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "The corner nodes are not connected to each other. `width` and `height` refer to the rectangle\n",
    "formed by rotating the lattice 45 degrees. `width` and `height` are measured in half-unit\n",
    "cells, or equivalently half the number of central nodes.\n",
    "\n",
    "Nodes are 2-tuples of integers which may be negative. Please see `get_placements` for\n",
    "mapping this topology to a GridQubit Device."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ad5780182be8"
   },
   "source": [
    "## Placement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6c977db39c1f"
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "SYC23_GRAPH = nx.from_edgelist([\n",
    "    ((3, 2), (4, 2)), ((4, 1), (5, 1)), ((4, 2), (4, 1)), \n",
    "    ((4, 2), (4, 3)), ((4, 2), (5, 2)), ((4, 3), (5, 3)), \n",
    "    ((5, 1), (5, 0)), ((5, 1), (5, 2)), ((5, 1), (6, 1)), \n",
    "    ((5, 2), (5, 3)), ((5, 2), (6, 2)), ((5, 3), (5, 4)), \n",
    "    ((5, 3), (6, 3)), ((5, 4), (6, 4)), ((6, 1), (6, 2)), \n",
    "    ((6, 2), (6, 3)), ((6, 2), (7, 2)), ((6, 3), (6, 4)), \n",
    "    ((6, 3), (7, 3)), ((6, 4), (6, 5)), ((6, 4), (7, 4)), \n",
    "    ((6, 5), (7, 5)), ((7, 2), (7, 3)), ((7, 3), (7, 4)), \n",
    "    ((7, 3), (8, 3)), ((7, 4), (7, 5)), ((7, 4), (8, 4)), \n",
    "    ((7, 5), (7, 6)), ((7, 5), (8, 5)), ((8, 3), (8, 4)), \n",
    "    ((8, 4), (8, 5)), ((8, 4), (9, 4)), \n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ca39fc2f6773"
   },
   "source": [
    "You can manually generate mappings between `NamedTopology` nodes and device qubits using helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "0f6a1e57db87"
   },
   "outputs": [],
   "source": [
    "topo = TiltedSquareLattice(4, 2)\n",
    "\n",
    "cirq.draw_placements(SYC23_GRAPH, topo.graph, [\n",
    "    topo.nodes_to_gridqubits(offset=(3,2)),\n",
    "    topo.nodes_to_gridqubits(offset=(5,3)),\n",
    "], tilted=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "898879ebaf69"
   },
   "source": [
    "Or you can automatically generate placements using a subgraph monomorphism algorithm in NetworkX."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "de2d879d0111"
   },
   "outputs": [],
   "source": [
    "topo = TiltedSquareLattice(4, 2)\n",
    "placements = cirq.get_placements(SYC23_GRAPH, topo.graph)\n",
    "cirq.draw_placements(SYC23_GRAPH, topo.graph, placements[::3])\n",
    "print('...\\n')\n",
    "print(f'{len(placements)} total placements')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "44efeaf1c70e"
   },
   "source": [
    "## LineTopology\n",
    "\n",
    "This is a 1D linear topology.\n",
    "\n",
    "Node indices are contiguous integers starting from 0 with edges between\n",
    "adjacent integers.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "90d5b377b10c"
   },
   "outputs": [],
   "source": [
    "from cirq import LineTopology\n",
    "\n",
    "lens = np.arange(3, 12+1, 3)\n",
    "l = len(lens)\n",
    "fig, axes = plt.subplots(1,l, figsize=(3.5*l, 3*1))\n",
    "\n",
    "for ax, n_nodes in zip(axes, lens):\n",
    "    LineTopology(n_nodes).draw(ax=ax, tilted=False)\n",
    "    ax.set_title(f'n =  {n_nodes}')\n",
    "    \n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ffbdece786d1"
   },
   "source": [
    "### Manual placement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "fb0f5289d6f5"
   },
   "outputs": [],
   "source": [
    "topo = LineTopology(9)\n",
    "\n",
    "cirq.draw_placements(SYC23_GRAPH, topo.graph, [\n",
    "    {i: q for i, q in enumerate([\n",
    "        cirq.GridQubit(4, 1), cirq.GridQubit(4, 2), cirq.GridQubit(5, 2), \n",
    "        cirq.GridQubit(5, 3), cirq.GridQubit(6, 3), cirq.GridQubit(6, 4), \n",
    "        cirq.GridQubit(7, 4), cirq.GridQubit(7, 5), cirq.GridQubit(8, 5),                              \n",
    "    ])}\n",
    "], tilted=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d3085236f6b7"
   },
   "source": [
    "### Automatic placement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "47b899ba53dc"
   },
   "outputs": [],
   "source": [
    "topo = LineTopology(9)\n",
    "placements = cirq.get_placements(SYC23_GRAPH, topo.graph)\n",
    "cirq.draw_placements(SYC23_GRAPH, topo.graph, placements[::300])\n",
    "print('...\\n')\n",
    "print(f'{len(placements)} total placements')"
   ]
  }
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