Graph Cut Search Problem with Grover Oracle English suggestions

algorithms/grover/grover_max_cut/grover_max_cut.ipynb

@@ -13,13 +13,13 @@
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    "metadata": {},
    "source": [
-    "The \"Maximum Cut Problem\" (MaxCut) [[1](#MaxCutWiki)] is an example of combinatorial optimization problem. It refers to finding a partition of a graph into two sets, such that the number of edges between the two sets is maximal.\n",
+    "The \"Maximum Cut Problem\" (MaxCut) [[1](#MaxCutWiki)] is an example of a combinatorial optimization problem. It refers to finding a partition of a graph into two sets, such that the number of edges between the two sets is the maximum.\n",
     "\n",
     "## Mathematical Formulation\n",
     "\n",
-    "Given a graph $G=(V,E)$ with $|V|=n$ nodes and $E$ edges, a cut is defined as a partition of the graph into two complementary subsets of nodes. In the MaxCut problem we look for a cut where the number of edges between the two subsets is maximal. We can represent a cut of the graph by a binary vector $x$ of size $n$, assigning 0 and 1 to nodes in the first and second subsets, respectively. The number of connecting edges for a given cut is simply given by summing over $x_i (1-x_j)+x_j (1-x_i)$ for every pair of connected nodes $(i,j)$.\n",
+    "Given a graph $G=(V,E)$ with $|V|=n$ nodes and $E$ edges, a cut is defined as a partition of the graph into two complementary subsets of nodes. In the MaxCut problem we look for a cut where the number of edges between the two subsets is the maximum. We can represent a cut of the graph by a binary vector $x$ of size $n$, assigning 0 and 1 to nodes in the first and second subsets, respectively. The number of connecting edges for a given cut is simply given by summing over $x_i (1-x_j)+x_j (1-x_i)$ for every pair of connected nodes $(i,j)$.\n",
     "\n",
-    "# Solving with the Classiq Platform\n"
+    "## Solving with the Classiq Platform\n"
    ]
   },
   {
@@ -52,15 +52,15 @@
    "id": "6e32027b-edd3-47d2-bb68-233bbea58fc9",
    "metadata": {},
    "source": [
-    "### Define the Cut Search Problem"
+    "### Defining the Cut Search Problem"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "a651a787-2c21-476d-8426-5a5f1be75e10",
    "metadata": {},
    "source": [
-    "We use SymPy to create an formula for the cut, for use later in the quantum algorithm."
+    "We use SymPy to create an formula for the cut, for use later in the quantum algorithm:"
    ]
   },
   {
@@ -90,7 +90,7 @@
    "id": "39d882bc-56e8-4680-8803-14b1dd05d115",
    "metadata": {},
    "source": [
-    "### Define a Specific Problem Input"
+    "### Defining a Specific Problem Input"
    ]
   },
   {
@@ -219,7 +219,7 @@
     }
    },
    "source": [
-    "## Synthesizing the Circuit\n",
+    "### Synthesizing the Circuit\n",
     "\n",
     "We synthesize the circuit using the Classiq synthesis engine. The synthesis takes several seconds:"
    ]
@@ -246,7 +246,7 @@
     "tags": []
    },
    "source": [
-    "## Showing the Resulting Circuit\n",
+    "### Showing the Resulting Circuit\n",
     "\n",
     "After the Classiq synthesis engine finishes the job, we display the resulting circuit in the interactive GUI:"
    ]
@@ -302,7 +302,7 @@
     }
    },
    "source": [
-    "### Execute on a Simulator to Find a Valid Solution\n",
+    "### Executing on a Simulator to Find a Valid Solution\n",
     "Lastly, we run the resulting circuit on the Classiq execute interface using the `execute` function."
    ]
   },