Preserve external simulator recommendations. (#3108)

This copies changes from #2811 into the Jupyter notebook.

docs/simulation.ipynb

@@ -18,7 +18,13 @@
     "that keeps the evolution in a pure state or a mixed state.\n",
     "In other words, there are some noisy evolutions\n",
     "that are supported by the pure state simulator as long as they\n",
-    "preserve the purity of the state.\n"
+    "preserve the purity of the state.\n",
+    "\n",
+    "Some external high-performance simulators also provide an interface\n",
+    "to Cirq. These can sometimes provide results faster than Cirq's\n",
+    "built-in simulators, especially when working with larger circuits.\n",
+    "For details on these tools, see the\n",
+    "[external simulators section](#external-simulators).\n"
    ]
   },
   {
@@ -600,6 +606,28 @@
     "We see that we have access to the density matrix at the\n",
     "end of the simulation via ``final_density_matrix``."
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### External simulators\n",
+    "\n",
+    "There are a few high-performance circuit simulators which\n",
+    "provide an interface for simulating Cirq ``Circuit``s.\n",
+    "These projects are listed below, along with their PyPI package\n",
+    "name and a description of simulator methods that they support.\n",
+    "\n",
+    "**Note:** In general, these simulators are optimized for\n",
+    "specific use cases. Before choosing a simulator, make sure it\n",
+    "supports the behavior that you need!\n",
+    "\n",
+    "| Project name | PyPI package | Description |\n",
+    "| --- | --- | --- |\n",
+    "| [qsim](https://github.com/quantumlib/qsim) | qsimcirq | Implements ``SimulatesAmplitudes`` and ``SimulatesFinalState``. Recommended for deep circuits with up to 30 qubits (consumes 8GB RAM). Larger circuits are possible, but RAM usage doubles with each additional qubit. |\n",
+    "| [qsimh](https://github.com/quantumlib/qsim/blob/master/qsimcirq/qsimh_simulator.py) | qsimcirq | Implements ``SimulatesAmplitudes``. Intended for heavy parallelization across several computers; Cirq users should generally prefer qsim. |\n",
+    "| [qFlex](https://github.com/ngnrsaa/qflex) | qflexcirq | Implements ``SimulatesAmplitudes``. Recommended for shallow / low-entanglement circuits with more than 30 qubits. RAM usage is highly dependent on the number of two-qubit gates in the circuit. |\n"
+   ]
   }
  ],
  "metadata": {
@@ -623,4 +651,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}