examples/qubit_constrained_transpilation/qubit_constrained_transpilation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eD_4rwdBk0fl"
   },
   "source": [
    "## Qubit-Constrained Transpilation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yJT8furQE6zG"
   },
   "source": [
    "Before proceeding with computation we want to *achieve the best mapping*  between our circuit and the device's physical layout (the device's 'topology') in terms of qubit arrangement connectivity.\n",
    "\n",
    "In quantum computing we can represent **qubits as nodes** of a graph, with their **interconnections** being depicted **as edges**. The **coupling map** effectively serves as the adjacency matrix, delineating the connections between nodes (qubits). The matrix consists of elements a_ij. The adjacency matrix elements are assigned with 2 values: a_ij=0 if the nodes/qubits **i** and **j** are not connected and a_ij=1 otherwise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SJ7Ky1H2FoEo"
   },
   "source": [
    "## 1. Purpose and Relevance\n",
    "\n",
    "Depending on the circuit's and device's topology, different cases can arise where certain gate operations are difficult to directly apply to the target qubits. In such cases, additional qubits are used in the calculation, referred to as \"ancilla\" qubits. Adding the ancilla qubits can allow operations on otherwise unreachable qubits, but their addition comes at the cost of increased execution time. For large and complicated circuits, adding ancilla qubits can often increase runtime significantly.\n",
    "\n",
    "Qubit-Constrained Transpilation is a tool to help overcome these limitations by taking into account the **device’s coupling map**. It considers the device's coupling map to determine the optimal selection of the most important qubits.\n",
    "\n",
    "This challenge has prompted the emergence of a problem related to Qubit-Constrained Transpilation, taking into consideration the **device's coupling map**. To illustrate it, we can consider a simplified example of a device alongside its coupling map. From this context, we aim to propose a method for selecting qubits that are topologically significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "G91bosg5k3mx"
   },
   "source": [
    "To decrease transpilation and simulation time the Rivet transpiler function `transpile_and_compress` selects  topologically the most important qubits of a backend device and produces a limited coupling map to decrease transpilation and simulation time:\n",
    "\n",
    "![image.jpg](topological_compression.jpg) \n",
    "\n",
    "*Fig.1. Node centralities for 27-qubit IBMQ backend topology.*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Fd3PQl9ik3-u"
   },
   "source": [
    "## 2. Theory behind Qubit-Constrained Transpilation\n",
    "\n",
    "We use the flexible measure of the node importance - the node **closeness centrality** (the sum of the shortest paths between the node and all other nodes in the graph) in the backend topology graph. Here, we calculate centrality for a given backend and the transpiled circuit. We then optimally transpile them using the input data. \n",
    "\n",
    "Once importances are calculated, we traverse the topology graph using A-star search, starting from the most important node. Traversed nodes are added to a limited qubit list, which forms a connected subgraph. This discovered subgraph is used to limit the backend topology (ancilla qubits and operations used) during the transpilation, leading to decreased computation time.\n",
    "\n",
    "The flexible measure of node importance can be expanded with other metrics, for example, neighbor counts or qubit noise levels.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OoC9KoNHk-2U"
   },
   "source": [
    "## 3. Installation and imports\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X14qHgXBlAtV"
   },
   "source": [
    "To run the code below make sure you have followed and installed Rivet transpiler. Check the installation steps from   **Readme.md**.\n",
    "\n",
    "#### 3.1. Import Qiskit and Rivet transpiler functions required to run the examples below"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able execute code below - matplotlib package should be installed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "uPCRlEQrlC4P"
   },
   "outputs": [],
   "source": [
    "import qiskit\n",
    "from qiskit.visualization import plot_gate_map\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.style.use(\"dark_background\")\n",
    "\n",
    "%cd -q ../..\n",
    "\n",
    "###Import Rivet transpiler functions\n",
    "from rivet_transpiler import transpile\n",
    "from rivet_transpiler import get_litmus_circuit\n",
    "from rivet_transpiler import transpile_and_compress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "azo_3McylES1"
   },
   "source": [
    "For Qubit-Constrained Transpilation and closeness centrality caclulations we will use `rustworkx` library functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "67bCcl0alGVN"
   },
   "outputs": [],
   "source": [
    "from rustworkx import spring_layout\n",
    "from rustworkx import closeness_centrality\n",
    "from rustworkx.visualization import mpl_draw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LprYhvUolIDa"
   },
   "source": [
    "#### 3.2. Import Backend\n",
    "\n",
    "Available backends from IBM Qiskit are listed at [4]. Some backend examples:\n",
    "- the simplest 5qubit backend (for a simple test start from this one): `FakeBackend5QV2`\n",
    "- 5qubit backend with noise:  `FakeLimaV2`\n",
    "- 32-qubit backend: `FakeMontrealV2` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "vAx0KEeUlKI1"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1154.6x492.2 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit_ibm_runtime.fake_provider import FakeMontrealV2\n",
    "backend = FakeMontrealV2() \n",
    "qiskit.visualization.plot_gate_map(backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AzWr3roSlMYv"
   },
   "source": [
    "#### 3.3. Set up `litmus_circuit`\n",
    "\n",
    "`litmus_circuit` is a quantum circuit designed for testing and diagnostic purposes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "zH3pcqWIlMmh"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">            ┌──────────────┐          ┌───┐ Litmus \n",
       "Litmus_0_0: ┤ Rz(Litmus_0) ├──■───────┤ X ├───░────\n",
       "            ├──────────────┤┌─┴─┐     └─┬─┘   ░    \n",
       "Litmus_0_1: ┤ Rz(Litmus_1) ├┤ X ├──■────┼─────░────\n",
       "            ├──────────────┤└───┘┌─┴─┐  │     ░    \n",
       "Litmus_0_2: ┤ Rz(Litmus_2) ├─────┤ X ├──■─────░────\n",
       "            └──────────────┘     └───┘        ░    </pre>"
      ],
      "text/plain": [
       "            ┌──────────────┐          ┌───┐ Litmus \n",
       "Litmus_0_0: ┤ Rz(Litmus_0) ├──■───────┤ X ├───░────\n",
       "            ├──────────────┤┌─┴─┐     └─┬─┘   ░    \n",
       "Litmus_0_1: ┤ Rz(Litmus_1) ├┤ X ├──■────┼─────░────\n",
       "            ├──────────────┤└───┘┌─┴─┐  │     ░    \n",
       "Litmus_0_2: ┤ Rz(Litmus_2) ├─────┤ X ├──■─────░────\n",
       "            └──────────────┘     └───┘        ░    "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QUBITS_COUNT = 3 #define number of qubits\n",
    "litmus_circuit = get_litmus_circuit(QUBITS_COUNT, \"Litmus\")\n",
    "litmus_circuit.draw(fold=-1) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KJ99oYuxlQsH"
   },
   "source": [
    "## 4. Experiments, results\n",
    "Here we consider the case of 3-qubit circuit defined on 32-qubit backend `FakeMontrealV2`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VT_o5qurlSf3"
   },
   "source": [
    "#### 4.1. Basic transpilation and transpilation with compression\n",
    "\n",
    "Below, it is possible to compare two circuits with basic transpilation and after `transpile_and_compress` usage. For the first case the ancilla qubits are added to run circuit for a given device topology, while in the second case taking into account the qubit centrality, we transpile the circuit to properly use the device topology without involving ancilla qubits, thereby decreasing the computation time.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "_KWKcKm3lcHP"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                 ┌──────────────┐┌───┐                            ░    \n",
       "Litmus_0_1 -> 11 ┤ Rz(Litmus_1) ├┤ X ├─────────────────■──────────░────\n",
       "                 └──────────────┘└─┬─┘                 │          ░    \n",
       "                 ┌──────────────┐  │       ┌───┐       │  ┌───┐ Litmus \n",
       "Litmus_0_2 -> 13 ┤ Rz(Litmus_2) ├──┼────■──┤ X ├──■────┼──┤ X ├───░────\n",
       "                 ├──────────────┤  │  ┌─┴─┐└─┬─┘┌─┴─┐┌─┴─┐└─┬─┘   ░    \n",
       "Litmus_0_0 -> 14 ┤ Rz(Litmus_0) ├──■──┤ X ├──■──┤ X ├┤ X ├──■─────░────\n",
       "                 └──────────────┘     └───┘     └───┘└───┘        ░    </pre>"
      ],
      "text/plain": [
       "                 ┌──────────────┐┌───┐                            ░    \n",
       "Litmus_0_1 -> 11 ┤ Rz(Litmus_1) ├┤ X ├─────────────────■──────────░────\n",
       "                 └──────────────┘└─┬─┘                 │          ░    \n",
       "                 ┌──────────────┐  │       ┌───┐       │  ┌───┐ Litmus \n",
       "Litmus_0_2 -> 13 ┤ Rz(Litmus_2) ├──┼────■──┤ X ├──■────┼──┤ X ├───░────\n",
       "                 ├──────────────┤  │  ┌─┴─┐└─┬─┘┌─┴─┐┌─┴─┐└─┬─┘   ░    \n",
       "Litmus_0_0 -> 14 ┤ Rz(Litmus_0) ├──■──┤ X ├──■──┤ X ├┤ X ├──■─────░────\n",
       "                 └──────────────┘     └───┘     └───┘└───┘        ░    "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compressed_litmus_circuit = transpile_and_compress(\n",
    "    litmus_circuit, \n",
    "    backend=backend,\n",
    "    optimization_level=3,\n",
    "    seed_transpiler=1234,\n",
    ")\n",
    "\n",
    "compressed_litmus_circuit.draw(idle_wires=False, fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "3DT9MDwblcZa"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1154.6x492.2 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qiskit.visualization.plot_circuit_layout(compressed_litmus_circuit, backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ilnO5FFolf4X"
   },
   "source": [
    "#### 4.2. Custom Coupling Map\n",
    "\n",
    "We are not limited by the backend device architecture. We retrieve the coupling map from the configuration of a backend and remove the edge between qubits 12 and 13 from the coupling list.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Custom Coupling Map\n",
    "\n",
    "coupling_map = backend.coupling_map\n",
    "coupling_list = [list(pair) for pair in coupling_map]\n",
    "\n",
    "# Remove edge between qubits 12 and 13:\n",
    "coupling_list.remove([12, 13])\n",
    "coupling_list.remove([13, 12])\n",
    "coupling_map = qiskit.transpiler.CouplingMap(couplinglist=coupling_list)\n",
    "\n",
    "#coupling_map.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                 ┌──────────────┐┌───┐                            ░    \n",
       "Litmus_0_1 -> 11 ┤ Rz(Litmus_1) ├┤ X ├─────────────────■──────────░────\n",
       "                 └──────────────┘└─┬─┘                 │          ░    \n",
       "                 ┌──────────────┐  │       ┌───┐       │  ┌───┐ Litmus \n",
       "Litmus_0_2 -> 13 ┤ Rz(Litmus_2) ├──┼────■──┤ X ├──■────┼──┤ X ├───░────\n",
       "                 ├──────────────┤  │  ┌─┴─┐└─┬─┘┌─┴─┐┌─┴─┐└─┬─┘   ░    \n",
       "Litmus_0_0 -> 14 ┤ Rz(Litmus_0) ├──■──┤ X ├──■──┤ X ├┤ X ├──■─────░────\n",
       "                 └──────────────┘     └───┘     └───┘└───┘        ░    </pre>"
      ],
      "text/plain": [
       "                 ┌──────────────┐┌───┐                            ░    \n",
       "Litmus_0_1 -> 11 ┤ Rz(Litmus_1) ├┤ X ├─────────────────■──────────░────\n",
       "                 └──────────────┘└─┬─┘                 │          ░    \n",
       "                 ┌──────────────┐  │       ┌───┐       │  ┌───┐ Litmus \n",
       "Litmus_0_2 -> 13 ┤ Rz(Litmus_2) ├──┼────■──┤ X ├──■────┼──┤ X ├───░────\n",
       "                 ├──────────────┤  │  ┌─┴─┐└─┬─┘┌─┴─┐┌─┴─┐└─┬─┘   ░    \n",
       "Litmus_0_0 -> 14 ┤ Rz(Litmus_0) ├──■──┤ X ├──■──┤ X ├┤ X ├──■─────░────\n",
       "                 └──────────────┘     └───┘     └───┘└───┘        ░    "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compressed_litmus_circuit = transpile_and_compress(\n",
    "    litmus_circuit, \n",
    "    backend=backend,\n",
    "    coupling_map=coupling_map,\n",
    "    optimization_level=3,\n",
    "    seed_transpiler=1234,\n",
    ")\n",
    "\n",
    "compressed_litmus_circuit.draw(idle_wires=False, fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "99X65a6fljMC"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/mnt/c/Users/mohor/Jupyter/test_rivet_release/rivet_transpiler/topological_compression.py:229: UserWarning: Provided Backend has no topology - no compression performed\n",
      "  warnings.warn(\"Provided Backend has no topology - no compression performed\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">            ┌──────────────┐          ┌───┐ Litmus \n",
       "Litmus_0_0: ┤ Rz(Litmus_0) ├──■───────┤ X ├───░────\n",
       "            ├──────────────┤┌─┴─┐     └─┬─┘   ░    \n",
       "Litmus_0_1: ┤ Rz(Litmus_1) ├┤ X ├──■────┼─────░────\n",
       "            ├──────────────┤└───┘┌─┴─┐  │     ░    \n",
       "Litmus_0_2: ┤ Rz(Litmus_2) ├─────┤ X ├──■─────░────\n",
       "            └──────────────┘     └───┘        ░    </pre>"
      ],
      "text/plain": [
       "            ┌──────────────┐          ┌───┐ Litmus \n",
       "Litmus_0_0: ┤ Rz(Litmus_0) ├──■───────┤ X ├───░────\n",
       "            ├──────────────┤┌─┴─┐     └─┬─┘   ░    \n",
       "Litmus_0_1: ┤ Rz(Litmus_1) ├┤ X ├──■────┼─────░────\n",
       "            ├──────────────┤└───┘┌─┴─┐  │     ░    \n",
       "Litmus_0_2: ┤ Rz(Litmus_2) ├─────┤ X ├──■─────░────\n",
       "            └──────────────┘     └───┘        ░    "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Backend None\n",
    "\n",
    "compressed_litmus_circuit = transpile_and_compress(\n",
    "    litmus_circuit, \n",
    "    backend=None,\n",
    "    seed_transpiler=1234,\n",
    ")\n",
    "\n",
    "compressed_litmus_circuit.draw(idle_wires=False, fold=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">            ┌──────────────┐          ┌───┐ Litmus \n",
    "Litmus_0_0: ┤ Rz(Litmus_0) ├──■───────┤ X ├───░────\n",
    "            ├──────────────┤┌─┴─┐     └─┬─┘   ░    \n",
    "Litmus_0_1: ┤ Rz(Litmus_1) ├┤ X ├──■────┼─────░────\n",
    "            ├──────────────┤└───┘┌─┴─┐  │     ░    \n",
    "Litmus_0_2: ┤ Rz(Litmus_2) ├─────┤ X ├──■─────░────\n",
    "            └──────────────┘     └───┘        ░    </pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Em_i8zn2lpr7"
   },
   "source": [
    "#### 4.3. Plot Backend Importances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "ihkgVpdxlqQY"
   },
   "outputs": [],
   "source": [
    "def get_backend_importances_figure(backend, layout_seed=3):\n",
    "    \n",
    "    coupling_list = backend.coupling_map\n",
    "\n",
    "    coupling_map = qiskit.transpiler.CouplingMap(couplinglist=coupling_list)\n",
    "    \n",
    "    graph = coupling_map.graph.to_undirected()\n",
    "    \n",
    "    positions = spring_layout(graph, seed=layout_seed)\n",
    "\n",
    "    centralities = closeness_centrality(graph)\n",
    "\n",
    "    importances = list(centralities.values())\n",
    "\n",
    "    mpl_draw(graph,\n",
    "             cmap=\"plasma\",\n",
    "             pos=positions,\n",
    "             with_labels=True,\n",
    "             node_color=importances)\n",
    "\n",
    "    normalizer = plt.Normalize(vmin=min(importances), \n",
    "                               vmax=max(importances))\n",
    "\n",
    "    scalar_mappable = plt.cm.ScalarMappable(cmap=\"plasma\", norm=normalizer)\n",
    "    \n",
    "    colorbar = plt.colorbar(mappable=scalar_mappable, \n",
    "                            ax=plt.gca(), \n",
    "                            aspect=40)\n",
    "\n",
    "    colorbar.ax.get_yaxis().labelpad = 15\n",
    "    colorbar.ax.set_ylabel('Centrality', rotation=270)\n",
    "    \n",
    "    figure = plt.gcf()\n",
    "    \n",
    "    figure.patch.set_facecolor('white')\n",
    "    figure.patch.set_alpha(0.05)\n",
    "    \n",
    "    plt.close()\n",
    "\n",
    "    return figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "r5Pyx7oylsDG"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_backend_importances_figure(backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0J_rVtTjlvto"
   },
   "source": [
    "## References\n",
    "\n",
    "[1] https://qiskit.org/ecosystem/rustworkx/dev/apiref/rustworkx.closeness_centrality.html\n",
    "\n",
    "[2] https://github.com/Qiskit/qiskit/blob/stable/0.14/qiskit/transpiler/coupling.py  \n",
    "\n",
    "[3] https://docs.quantum.ibm.com/api/qiskit/0.19/qiskit.transpiler.CouplingMap\n",
    "\n",
    "[4] Qiskit fake backends https://docs.quantum.ibm.com/api/qiskit/0.37/providers_fake_provider"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}