Add note on samping overhead to cutting tutorials

docs/circuit_cutting/tutorials/01_gate_cutting_to_reduce_circuit_width.ipynb

@@ -201,7 +201,11 @@
    "id": "ba3125fc",
    "metadata": {},
    "source": [
-    "### Calculate the sampling overhead for the chosen cuts"
+    "### Calculate the sampling overhead for the chosen cuts\n",
+    "\n",
+    "The sampling overhead is the required number of samples needed to get an expectation value of a target observable within some error, $\\epsilon$. Cutting CNOT and CZ gates incurs a sampling overhead of roughly $O$($9^k$/$\\epsilon^2$), where k is the number of cuts [[Mitarai, Fujii]](https://arxiv.org/abs/1909.07534); however, other gates may have higher or lower exponential bases. For example, the sampling overhead resulting from cutting SWAP gates scales with complexity $O$($49^k$/$\\epsilon^2$) [[Mitarai, Fujii]](https://arxiv.org/abs/2006.11174).\n",
+    "\n",
+    "Here we cut three CNOT gates, resulting in a sampling overhead of $9^2$."
    ]
   },
   {

docs/circuit_cutting/tutorials/02_gate_cutting_to_reduce_circuit_depth.ipynb

@@ -201,7 +201,11 @@
    "id": "c0acae3a",
    "metadata": {},
    "source": [
-    "### Calculate the sampling overhead for the chosen cuts"
+    "### Calculate the sampling overhead for the chosen cuts\n",
+    "\n",
+    "The sampling overhead is the required number of samples needed to get an expectation value of a target observable within some error, $\\epsilon$. Cutting CNOT and CZ gates incurs a sampling overhead of roughly $O$($9^k$/$\\epsilon^2$), where k is the number of cuts [[Mitarai, Fujii]](https://arxiv.org/abs/1909.07534); however, other gates may have higher or lower exponential bases. For example, the sampling overhead resulting from cutting SWAP gates scales with complexity $O$($49^k$/$\\epsilon^2$) [[Mitarai, Fujii]](https://arxiv.org/abs/2006.11174).\n",
+    "\n",
+    "Here we cut three CNOT gates, resulting in a sampling overhead of $9^3$."
    ]
   },
   {