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"| **Free** | `MaxCut` | `XMultiAngle` | 1 | N (one per qubit) |\n",
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"| **Orbit** | `MaxCutOrbit` | `X` | K (one per edge orbit) | 1 |\n",
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"\n",
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"- **Vanilla QAOA** uses the standard X mixer with a single shared γ and β per layer.\n",
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"- **Free QAOA** (multi-angle) gives each qubit its own independent β, increasing expressibility.\n",
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"- **Orbit QAOA** exploits the graph's automorphism group: edges in the same symmetry orbit share a γ parameter, enabling the optimizer to differentiate structurally distinct edge types without the full multi-angle overhead."
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"- **Vanilla QAOA** uses the standard X mixer with a single shared \u03b3 and \u03b2 per layer.\n",
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"- **Free QAOA** (multi-angle) gives each qubit its own independent \u03b2, increasing expressibility.\n",
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"- **Orbit QAOA** exploits the graph's automorphism group: edges in the same symmetry orbit share a \u03b3 parameter, enabling the optimizer to differentiate structurally distinct edge types without the full multi-angle overhead."
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]
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},
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{
@@ -101,7 +101,7 @@
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"source": [
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"### Edge Orbits of the House Graph\n",
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"\n",
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"The orbit QAOA assigns one γ parameter per edge orbit of the graph's automorphism group."
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"The orbit QAOA assigns one \u03b3 parameter per edge orbit of the graph's automorphism group."
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]
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},
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{
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"metadata": {},
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"outputs": [],
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"source": [
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"# Vanilla QAOA: X mixer, single γ and β per layer\n",
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"qaoa_vanilla = QAOA(\n",
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" problem=problems.MaxCut(G),\n",
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" mixer=mixers.X(),\n",
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" initialstate=initialstates.Plus(),\n",
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")\n",
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"\n",
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"# Free QAOA: XMultiAngle mixer, one β per qubit\n",
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"qaoa_free = QAOA(\n",
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" problem=problems.MaxCut(G),\n",
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" mixer=mixers.XMultiAngle(),\n",
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" initialstate=initialstates.Plus(),\n",
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")\n",
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"\n",
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"# Orbit QAOA: X mixer, one γ per edge orbit of the graph\n",
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