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Graph Cut Search Problem with Grover Oracle English suggestions #793

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Feb 23, 2025
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Graph Cut Search Problem with Grover Oracle English suggestions #793

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18 changes: 9 additions & 9 deletions algorithms/grover/grover_max_cut/grover_max_cut.ipynb
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Expand Up @@ -13,13 +13,13 @@
"id": "5193de81-389e-4a87-89dc-1acb2f2630e0",
"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"
]
},
{
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"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:"
]
},
{
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"id": "39d882bc-56e8-4680-8803-14b1dd05d115",
"metadata": {},
"source": [
"### Define a Specific Problem Input"
"### Defining a Specific Problem Input"
]
},
{
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}
},
"source": [
"## Synthesizing the Circuit\n",
"### Synthesizing the Circuit\n",
"\n",
"We synthesize the circuit using the Classiq synthesis engine. The synthesis takes several seconds:"
]
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"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:"
]
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}
},
"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."
]
},
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