[Docs] Update notebook with mention of IntegratedQEK. (#114)

* Update notebook with mention of IntegratedQEK.

* Fix missing import.

* Invert cell order to avoid failing test.

* Apply feedback.

Author: RolandMacDoland

examples/tutorial 2 - Machine-Learning with the Quantum EvolutionKernel.ipynb

@@ -137,14 +137,47 @@
     "$$\n",
     "\n",
     "\n",
-    "where $\\mu$ is an hyperparameter of our kernel and $JS$ is the Jensen-Shannon divergence.\n",
-    "    "
+    "where $\\mu$ is an hyperparameter of our kernel and $JS$ is the Jensen-Shannon divergence. For processing raw graph data, the IntegratedQEK is recommended; however, it requires an extractor to be provided as an argument."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "05964cf6-d96d-42ee-9b1e-707110d55917",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qek.data.extractors as qek_extractors\n",
+    "import qek.data.graphs as qek_graphs\n",
+    "from qek.kernel import IntegratedQEK as QEK\n",
+    "from pathlib import Path\n",
+    "\n",
+    "# First, we need to intantiate the compiler for the type of data.\n",
+    "compiler = qek_graphs.PTCFMCompiler()\n",
+    "\n",
+    "# Then, instantiate the Qutip Extractor.\n",
+    "extractor = qek_extractors.QutipExtractor(\n",
+    "    # Once computing is complete, data will be saved in this file.\n",
+    "    path=Path(\"saved_data.json\"),\n",
+    "    compiler=compiler\n",
+    ")\n",
+    "\n",
+    "# Finally, initialize the Integrated Quantum Evolution Kernel with both the extractor and the parameter mu.\n",
+    "kernel = QEK(mu=0.5, extractor=extractor)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fae79440-b962-40fa-8274-ebffa48ccfb1",
+   "metadata": {},
+   "source": [
+    " In this case and since data has already been pre-processed, we will use the `FastQEK` kernel instead that speeds-up the computation and allows for computing matrix similarities."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55f264f6-18f5-4009-930a-12cce4a2cb87",
+   "id": "000780dc-cb6a-4d70-bfe4-c86bbf281278",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -629,7 +662,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.12.7"
   }
  },
  "nbformat": 4,