update parallel XEB notebook

docs/noise/qcvv/parallel_xeb.ipynb

@@ -65,7 +65,7 @@
     "    import cirq\n",
     "except ImportError:\n",
     "    print(\"installing cirq...\")\n",
-    "    !pip install --quiet cirq\n",
+    "    !pip install --quiet cirq --pre\n",
     "    print(\"installed cirq.\")"
    ]
   },
@@ -88,7 +88,63 @@
    "outputs": [],
    "source": [
     "import cirq\n",
-    "import numpy as np"
+    "import numpy as np\n",
+    "\n",
+    "%matplotlib inline\n",
+    "from matplotlib import pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Parallel XEB with library functions\n",
+    "The entire XEB workflow can be run by calling `cirq.experiments.parallel_two_qubit_xeb` and the combined single-qubit randomized benchmarking (RB) and XEB workflows can be run by calling `cirq.experiments.run_rb_and_xeb`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Simulation\n",
+    "qubits = cirq.GridQubit.rect(3, 2, 4, 3)\n",
+    "result = cirq.experiments.parallel_two_qubit_xeb(\n",
+    "    sampler=cirq.DensityMatrixSimulator(noise=cirq.depolarize(5e-3)),  # Any simulator or a ProcessorSampler.\n",
+    "    qubits=qubits \n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# The returned result is an instance of the `TwoQubitXEBResult` class which provides visualization methods like \n",
+    "result.plot_heatmap();  # plot the heatmap of XEB errors\n",
+    "result.plot_fitted_exponential(*qubits[:2]);  # plot the fitted model of xeb error of a qubit pair.\n",
+    "result.plot_histogram();  # plot a histogram of all xeb errors."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# `TwoQubitXEBResult` also has methods to retrieve errors.\n",
+    "print('pauli errors:', result.pauli_error())\n",
+    "print('xeb errors:', result.xeb_error(*qubits[:2]))\n",
+    "print('xeb fidelity:', result.xeb_fidelity(*qubits[:2]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The `run_rb_and_xeb` method returns an object of type [InferredXEBResult](https://github.com/quantumlib/Cirq/blob/bc766606b94744f80da435c522d16a34529ae671/cirq-core/cirq/experiments/two_qubit_xeb.py#L188C7-L188C24) which is like [TwoQubitXEBResult](https://github.com/quantumlib/Cirq/blob/bc766606b94744f80da435c522d16a34529ae671/cirq-core/cirq/experiments/two_qubit_xeb.py#L56) except that it removes the single-qubit errors obtained from the single-qubit randomized benchmarking (RB) experiment to isolate the error from the two qubit gate."
    ]
   },
   {
@@ -97,6 +153,9 @@
     "id": "ace31cc4d258"
    },
    "source": [
+    "# Step by step XEB\n",
+    "The rest of this notebook explains how the `parallel_two_qubit_xeb` works internally. Note that the notebook uses `SQRT_ISWAP` as the entangling gate while `parallel_two_qubit_xeb` and `run_rb_and_xeb` default to `CZ`.\n",
+    "\n",
     "## Set up Random Circuits\n",
     "\n",
     "We create a library of 10 random, two-qubit `circuits` using the sqrt(ISWAP) gate. These library circuits will be mixed-and-matched among all the pairs on the device we aim to characterize."
@@ -224,9 +283,6 @@
    },
    "outputs": [],
    "source": [
-    "%matplotlib inline\n",
-    "from matplotlib import pyplot as plt\n",
-    "\n",
     "fig, axes = plt.subplots(2,2, figsize=(9,6))\n",
     "for comb_layer, ax in zip(combs_by_layer, axes.reshape(-1)):\n",
     "    active_qubits = np.array(comb_layer.pairs).reshape(-1)\n",
@@ -500,6 +556,18 @@
   "kernelspec": {
    "display_name": "Python 3",
    "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": "3.10.13"
   }
  },
  "nbformat": 4,