diff --git a/computations/C_L_elements_and_products.ipynb b/computations/C_L_elements_and_products.ipynb
index 41dc501..903a2d3 100644
--- a/computations/C_L_elements_and_products.ipynb
+++ b/computations/C_L_elements_and_products.ipynb
@@ -306,6 +306,143 @@
     "product_table_indices = [[get_matrix_index(C_L, m) for m in row] for row in product_table]\n",
     "product_table_indices"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Also necessary to convert a graph state into a naive state are the numpy array versions of $C_L$:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[array([[ 0.70710678+0.j,  0.70710678+0.j],\n",
+       "        [ 0.70710678+0.j, -0.70710678+0.j]]), array([[1.+0.j, 0.+0.j],\n",
+       "        [0.+0.j, 0.+1.j]]), array([[1.+0.j, 0.+0.j],\n",
+       "        [0.+0.j, 1.+0.j]]), array([[0.70710678+0.j        , 0.70710678+0.j        ],\n",
+       "        [0.        +0.70710678j, 0.        -0.70710678j]]), array([[0.70710678+0.j        , 0.        +0.70710678j],\n",
+       "        [0.70710678+0.j        , 0.        -0.70710678j]]), array([[ 1.+0.j,  0.+0.j],\n",
+       "        [ 0.+0.j, -1.+0.j]]), array([[0.70710678+0.j        , 0.        +0.70710678j],\n",
+       "        [0.        +0.70710678j, 0.70710678+0.j        ]]), array([[ 0.70710678+0.j, -0.70710678+0.j],\n",
+       "        [ 0.70710678+0.j,  0.70710678+0.j]]), array([[1.+0.j, 0.+0.j],\n",
+       "        [0.+0.j, 0.-1.j]]), array([[ 0.70710678+0.j        , -0.70710678+0.j        ],\n",
+       "        [ 0.        +0.70710678j,  0.        +0.70710678j]]), array([[0.70710678+0.j        , 0.        -0.70710678j],\n",
+       "        [0.70710678+0.j        , 0.        +0.70710678j]]), array([[ 0.70710678+0.j        ,  0.        -0.70710678j],\n",
+       "        [ 0.        +0.70710678j, -0.70710678+0.j        ]]), array([[0.5+0.5j, 0.5-0.5j],\n",
+       "        [0.5-0.5j, 0.5+0.5j]]), array([[ 0.70710678+0.j,  0.70710678+0.j],\n",
+       "        [-0.70710678+0.j,  0.70710678+0.j]]), array([[0.+0.j, 1.+0.j],\n",
+       "        [1.+0.j, 0.+0.j]]), array([[0.70710678+0.j        , 0.70710678+0.j        ],\n",
+       "        [0.        -0.70710678j, 0.        +0.70710678j]]), array([[0.+0.j, 1.+0.j],\n",
+       "        [0.+1.j, 0.+0.j]]), array([[ 0.5-0.5j,  0.5+0.5j],\n",
+       "        [-0.5+0.5j,  0.5+0.5j]]), array([[0.+0.j, 0.+1.j],\n",
+       "        [1.+0.j, 0.+0.j]]), array([[ 0.70710678+0.j        ,  0.        +0.70710678j],\n",
+       "        [ 0.        -0.70710678j, -0.70710678+0.j        ]]), array([[ 0.5-0.5j, -0.5+0.5j],\n",
+       "        [-0.5+0.5j, -0.5+0.5j]]), array([[ 0.+0.j, -1.+0.j],\n",
+       "        [ 1.+0.j,  0.+0.j]]), array([[ 0.70710678+0.j        , -0.70710678+0.j        ],\n",
+       "        [ 0.        -0.70710678j,  0.        -0.70710678j]]), array([[ 0.5-0.5j, -0.5-0.5j],\n",
+       "        [-0.5+0.5j, -0.5-0.5j]])]"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[np.array(c.tolist()).astype(np.cdouble) for c in C_L]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}0 & -1\\\\1 & 0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "⎡0  -1⎤\n",
+       "⎢     ⎥\n",
+       "⎣1  0 ⎦"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X = M([[0, 1], [1, 0]])\n",
+    "Z = M([[1, 0], [0, -1]])\n",
+    "XZ = X*Z\n",
+    "XZ"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAOCAYAAAAi2ky3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVQoFZWTgW3CMBBFCWKAiBFggwIbMEJZod0AZoANYAVGIBtUZQMYoXSD8F6KUYIdQk/68vnf+Z99tntlWfawEdje8M14AG/GUjAGTiAPcfxKZB8IR2wNdOaBx8/BHljQYsYbQgbvRG3hBf4S5vURfgkaQn2IuQuyLLNi3QomObzH7jSFXHCm4m9L9mOBZNoAgUUy8tdQm31siTdodxQZx/FWPNIqCrYQSSFyvYAdu9m0rIvoSIjdeL0FIp9R9hOiIYTIh7n/FXHNXQiRd+bjugjcSJjYZZUQyTZ3hshjcxX/6RIxPrhVtLkFvv0JNsTxv73U8Ixk/407StkRoUkIUKj6TsynwId6Br6zrytJ1JPO4orZMQAAAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$\\displaystyle 21$"
+      ],
+      "text/plain": [
+       "21"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "get_matrix_index(C_L, XZ)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle 20$"
+      ],
+      "text/plain": [
+       "20"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "get_matrix_index(C_L, H * Z * X)"
+   ]
   }
  ],
  "metadata": {