Fix LaTeX rendering in GateNoiseModels.ipynb

Author: karalekas

notebooks/GateNoiseModels.ipynb

@@ -4,7 +4,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Simulating Gate Noise"
+    "# Simulating Gate Noise\n",
+    "$$\n",
+    "\\newcommand{ket}[1]{\\left|{#1}\\right\\rangle}\n",
+    "\\newcommand{bra}[1]{\\left\\langle {#1}\\right|}\n",
+    "\\newcommand{tr}{\\mathrm{Tr}}\n",
+    "$$"
    ]
   },
   {
@@ -13,7 +18,6 @@
    "source": [
     "## Pure states vs. mixed states\n",
     "\n",
-    "\n",
     "Errors in quantum computing can introduce classical uncertainty in what the underlying state is.\n",
     "When this happens we sometimes need to consider not only wavefunctions but also probabilistic sums of\n",
     "wavefunctions when we are uncertain as to which one we have. For example, if we think that an X gate\n",
@@ -555,7 +559,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x1320abdd8>"
+       "<matplotlib.legend.Legend at 0x1384f5160>"
       ]
      },
      "execution_count": 12,