Update the tutorial on fractional gates

docs/tutorials/fractional-gates.ipynb

@@ -148,7 +148,7 @@
     "\n",
     "Before starting this tutorial, be sure you have the following installed:\n",
     "- Qiskit SDK v2.0 or later, with [visualization](/docs/api/qiskit/visualization) support\n",
-    "- Qiskit Runtime v0.37 or later (`pip install qiskit-ibm-runtime`)\n",
+    "- Qiskit Runtime v0.41 or later (`pip install qiskit-ibm-runtime`)\n",
     "- Qiskit Basis Constructor (`pip install qiskit_basis_constructor`)"
    ]
   },
@@ -188,15 +188,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "fd577102",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Backend: ibm_fez\n",
+      "Backend: ibm_boston\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "No fractional gates: ['cz', 'id', 'rz', 'sx', 'x']\n",
       "With fractional gates: ['cz', 'id', 'rx', 'rz', 'rzz', 'sx', 'x']\n"
      ]
@@ -244,7 +250,7 @@
     "where $|\\Phi(x)\\rangle$ represents the feature-mapped quantum state.\n",
     "\n",
     "We manually construct a ZZ feature map circuit using RZZ gates.\n",
-    "Although Qiskit provides a built-in `zz_feature_map`, it does not currently support RZZ gates as of Qiskit v2.0.2 ([see issue](https://github.com/Qiskit/qiskit/issues/14469)).\n",
+    "Although Qiskit provides a built-in `zz_feature_map`, it does not currently support RZZ gates as of Qiskit v2.4.1 ([see issue](https://github.com/Qiskit/qiskit/issues/14469)).\n",
     "\n",
     "Next, we compute the kernel function for identical inputs - for example, $K(x, x) = 1$.\n",
     "On noisy quantum computers, this value may be less than 1 due to noise.\n",
@@ -428,7 +434,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('rz', 35), ('rzz', 18), ('x', 13), ('rx', 9), ('measure', 4), ('barrier', 2)])\n"
+      "OrderedDict({'rz': 35, 'rzz': 18, 'x': 13, 'rx': 9, 'measure': 4, 'barrier': 2})\n"
      ]
     },
     {
@@ -505,15 +511,7 @@
    "execution_count": 12,
    "id": "a703b939",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "d4bninsi51bc738j97eg\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "job = sampler_f.run(t_qc_f, shots=shots)\n",
     "print(job.job_id())"
@@ -545,12 +543,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.9005, 0.647, 0.3345, 0.355, 0.3315, 0.174, 0.1875, 0.149, 0.1175, 0.085]\n"
+      "[0.8995, 0.7985, 0.57, 0.717, 0.5795, 0.5785, 0.456, 0.3155, 0.1785, 0.211]\n"
      ]
     }
    ],
    "source": [
-    "# job = service.job(\"d1obougt0npc73flhiag\")\n",
+    "# job = service.job(\"d8585pg0bvlc73d5aai0\")\n",
     "result = job.result()\n",
     "fidelity_f = [fidelity(result=res) for res in result]\n",
     "print(fidelity_f)\n",
@@ -589,7 +587,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('rz', 130), ('sx', 80), ('cz', 36), ('measure', 4), ('barrier', 2)])\n"
+      "OrderedDict({'rz': 130, 'sx': 80, 'cz': 36, 'measure': 4, 'barrier': 2})\n"
      ]
     },
     {
@@ -647,15 +645,7 @@
    "execution_count": 18,
    "id": "983dd26f",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "d4bnirvnmdfs73ae3a2g\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "job = sampler_c.run(pubs=zip(t_qc_c, params), shots=shots)\n",
     "print(job.job_id())"
@@ -671,13 +661,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.6675, 0.5725, 0.098, 0.102, 0.065, 0.0235, 0.006, 0.0015, 0.0015, 0.002]\n"
+      "[0.8875, 0.623, 0.4395, 0.2425, 0.1985, 0.085, 0.029, 0.003, 0.0005, 0.0]\n"
      ]
     }
    ],
    "source": [
     "# step 4: post-processing\n",
-    "# job = service.job(\"d1obp8j3rr0s73bg4810\")\n",
+    "# job = service.job(\"d8585uegbeec73aorp10\")\n",
     "result = job.result()\n",
     "fidelity_c = [fidelity(res) for res in result]\n",
     "print(fidelity_c)\n",
@@ -704,7 +694,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x12bcaac50>"
+       "<matplotlib.legend.Legend at 0x110fac830>"
       ]
      },
      "execution_count": 20,
@@ -740,7 +730,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x12bdef310>"
+       "<matplotlib.legend.Legend at 0x111b46900>"
       ]
      },
      "execution_count": 21,
@@ -776,7 +766,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x12be8ac90>"
+       "<matplotlib.legend.Legend at 0x11057d6a0>"
       ]
      },
      "execution_count": 22,
@@ -812,7 +802,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x12bea8290>"
+       "<matplotlib.legend.Legend at 0x112175a90>"
       ]
      },
      "execution_count": 23,
@@ -973,7 +963,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('rz', 23), ('sx', 16), ('cz', 4)])\n"
+      "OrderedDict({'rz': 23, 'sx': 16, 'cz': 4})\n"
      ]
     },
     {
@@ -1015,7 +1005,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('rz', 22), ('sx', 14), ('cz', 4), ('rx', 1)])\n"
+      "OrderedDict({'rz': 22, 'sx': 14, 'cz': 4, 'rx': 1})\n"
      ]
     },
     {
@@ -1122,7 +1112,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "OrderedDict([('rz', 16), ('rx', 9), ('cz', 4)])\n"
+      "OrderedDict({'rz': 16, 'rx': 9, 'cz': 4})\n"
      ]
     },
     {
@@ -1162,8 +1152,8 @@
    "source": [
     "### Issue: Invalid RZZ angles might remain after transpilation\n",
     "\n",
-    "As of Qiskit v2.0.3, there are known issues where RZZ gates with invalid angles may remain in the circuits even after transpilation.\n",
-    "The issue typically arises under the following conditions."
+    "As of Qiskit v2.4.1, there is a known issue where RZZ gates with invalid angles might remain in the circuits even after transpilation.\n",
+    "The issue typically arises under the following condition."
    ]
   },
   {
@@ -1175,17 +1165,7 @@
     "\n",
     "When the `target` option is used with `generate_preset_pass_manager` or `transpiler`, the specialized transpiler pass `FoldRzzAngle` is not invoked.\n",
     "To ensure proper handling of RZZ angles for fractional gates, we recommend always using the `backend` option instead.\n",
-    "See [this issue](https://github.com/Qiskit/qiskit/issues/14318) for more details."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ac27c7cb",
-   "metadata": {},
-   "source": [
-    "#### Failure when circuits contain certain gates\n",
-    "\n",
-    "If your circuit includes certain gates such as `XXPlusYYGate`, the Qiskit transpiler may generate RZZ gates with invalid angles.\n",
+    "See [this issue](https://github.com/Qiskit/qiskit/issues/14318) for more details.\n",
     "If you encounter this issue, see this [GitHub issue](https://github.com/Qiskit/qiskit-ibm-runtime/issues/2256#issuecomment-2889487152) for a workaround."
    ]
   },