diff --git a/Generator(forGPU)/README.md b/Generator(forGPU)/README.md
new file mode 100644
index 0000000..01bf31f
--- /dev/null
+++ b/Generator(forGPU)/README.md
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+# GNN Fast Quantum - QAOA Parameter Prediction
+
+Prédiction rapide des paramètres QAOA optimaux pour des problèmes d'optimisation combinatoire quantique en utilisant des Graph Neural Networks (GNN).
+
+## 📁 Structure du projet
+
+### `test_gnn_with_qiskit.py` - Validation du modèle
+Script de test pour valider les prédictions du GNN contre les optimisations QAOA réelles de Qiskit.
+
+**Usage:**
+```bash
+python test_gnn_with_qiskit.py
+```
+**prérequis:**
+- si mac os alors->   --no-gpu \
+- si on veut utilisé les GPU->  linux nécéssaire
+
+**Ce qu'il fait:**
+- Charge le modèle GNN entraîné (`FastQuantum/best_qaoa_gat_model.pt`)
+- Génère des graphes de test
+- Prédit gamma/beta avec le GNN (instantané)
+- Compare avec l'optimal trouvé par Qiskit QAOA (lent)
+- Affiche les gaps de performance
+
+**Résultats attendus:**
+- Gap moyen: ~5% (excellent)
+- Speedup: 100-1000x plus rapide que QAOA
+
+---
+
+### `Generator(forGPU)/` - Génération de dataset quantique
+
+Générateur de dataset multi-problèmes avec support GPU et parallélisation CPU.
+
+**Fichiers principaux:**
+- `gen_quantum_mp.py`: Générateur multi-problèmes optimisé
+- `check_gpu_availability.py`: Diagnostic GPU/CUDA
+
+**Problèmes supportés:**
+- MaxCut (partition de graphe)
+- Vertex Cover (couverture minimale)
+- Max Independent Set (sélection de nœuds)
+- Graph Coloring (3 couleurs avec 2 qubits par nœud) 
+
+warning :
+Graph Coloring utilise 2× plus de qubits (2 par nœud au lieu de 1):
+Graphe 10 nœuds = 20 qubits pour coloring vs 10 pour MaxCut
+-> donc Simulation BEAUCOUP plus lente (~5-10x plus lent)
+Recommandation: Limitez graph_coloring à 10% du dataset et utilisez des petits graphes (5-8 nœuds) pour ce problème.
+
+warning2 :
+Warn start utilise des données heuristique mais c'ets juste une optimisation de temps gratuites -> pas de baisse de qulité du dataset ici
+
+**Usage:**
+```bash
+# Test GPU disponible
+python Generator(forGPU)/check_gpu_availability.py
+
+# Générer dataset (CPU)
+python Generator(forGPU)/gen_quantum_mp.py \
+  --samples 200 \
+  --min_nodes 6 \
+  --max_nodes 12 \
+  --maxcut-ratio 0.70 \
+  --workers 12 \
+  --no-gpu \
+  --output Dataset/phase1_hybrid70.json
+
+# Générer dataset (GPU - Linux)
+python Generator(forGPU)/gen_quantum_mp.py \
+  --samples 200 \
+  --min_nodes 6 \
+  --max_nodes 12 \
+  --maxcut-ratio 0.70 \
+  --workers 8 \
+  --output Dataset/phase1_hybrid70.json
+```
+
+**Arguments:**
+- `--samples`: Nombre d'échantillons à générer
+- `--min_nodes`, `--max_nodes`: Taille des graphes
+- `--maxcut-ratio`: Ratio de MaxCut (ex: 0.70 = 70% MaxCut, 30% autres)
+- `--workers`: Nombre de workers parallèles
+- `--no-gpu`: Forcer CPU (Windows)
+- `--checkpoint`: Sauvegarder tous les N samples
+
+**Performance:**
+- **GPU (Linux)**: ~5-15s par sample (recommandé)
+- **CPU (16 cores)**: ~20-40s par sample
+- **CPU (4 cores)**: ~60-120s par sample
+
+---
+
+## 🚀 Quick Start
+
+### 1. Tester le modèle existant
+```bash
+python test_gnn_with_qiskit.py
+```
+
+### 2. Générer un nouveau dataset
+```bash
+# Windows (CPU seulement)
+python Generator(forGPU)/gen_quantum_mp.py --samples 50 --workers 4 --no-gpu
+
+# Linux avec GPU
+python Generator(forGPU)/gen_quantum_mp.py --samples 200 --workers 8
+```
+
+### 3. Entraîner le modèle (dans FastQuantum/)
+```bash
+python FastQuantum/GnnmodelGat.py
+```
\ No newline at end of file
diff --git a/Generator(forGPU)/check_gpu_availability.py b/Generator(forGPU)/check_gpu_availability.py
new file mode 100644
index 0000000..bf75f48
--- /dev/null
+++ b/Generator(forGPU)/check_gpu_availability.py
@@ -0,0 +1,228 @@
+"""
+GPU Availability Diagnostic for Qiskit Quantum Simulation
+Checks if your system can use GPU acceleration with Qiskit Aer
+
+Requirements for GPU:
+    - NVIDIA GPU with CUDA support
+    - CUDA Toolkit installed
+    - qiskit-aer-gpu OR qiskit-aer with GPU support
+"""
+
+import sys
+import platform
+
+def check_nvidia_gpu():
+    """Check if NVIDIA GPU is available"""
+    print("\n" + "="*70)
+    print("🔍 CHECKING NVIDIA GPU")
+    print("="*70)
+
+    try:
+        import subprocess
+        result = subprocess.run(['nvidia-smi'], capture_output=True, text=True)
+        if result.returncode == 0:
+            print("✅ NVIDIA GPU detected!")
+            print("\nGPU Information:")
+            print(result.stdout)
+            return True
+        else:
+            print("❌ nvidia-smi command failed")
+            return False
+    except FileNotFoundError:
+        print("❌ nvidia-smi not found - No NVIDIA GPU or drivers not installed")
+        return False
+    except Exception as e:
+        print(f"❌ Error checking GPU: {e}")
+        return False
+
+
+def check_cuda():
+    """Check if CUDA is available"""
+    print("\n" + "="*70)
+    print("🔍 CHECKING CUDA")
+    print("="*70)
+
+    try:
+        import subprocess
+        result = subprocess.run(['nvcc', '--version'], capture_output=True, text=True)
+        if result.returncode == 0:
+            print("✅ CUDA Toolkit installed!")
+            print(result.stdout)
+            return True
+        else:
+            print("❌ CUDA not found")
+            return False
+    except FileNotFoundError:
+        print("❌ nvcc not found - CUDA Toolkit not installed")
+        print("\nInstall CUDA from: https://developer.nvidia.com/cuda-downloads")
+        return False
+    except Exception as e:
+        print(f"❌ Error checking CUDA: {e}")
+        return False
+
+
+def check_qiskit_aer_gpu():
+    """Check if Qiskit Aer with GPU support is available"""
+    print("\n" + "="*70)
+    print("🔍 CHECKING QISKIT AER GPU SUPPORT")
+    print("="*70)
+
+    try:
+        from qiskit_aer import AerSimulator
+
+        # Try to create GPU simulator
+        try:
+            simulator = AerSimulator(method='statevector', device='GPU')
+            print("✅ Qiskit Aer GPU support available!")
+            print(f"   Simulator: {simulator}")
+
+            # Get available devices
+            available_devices = AerSimulator().available_devices()
+            print(f"   Available devices: {available_devices}")
+
+            return True
+        except Exception as e:
+            print(f"❌ Qiskit Aer installed but GPU not available: {e}")
+            print("\nYou may need to install qiskit-aer-gpu:")
+            print("   pip uninstall qiskit-aer")
+            print("   pip install qiskit-aer-gpu")
+            return False
+
+    except ImportError:
+        print("❌ Qiskit Aer not installed")
+        print("\nInstall with:")
+        print("   pip install qiskit-aer")
+        print("   OR for GPU: pip install qiskit-aer-gpu")
+        return False
+
+
+def check_multiprocessing():
+    """Check CPU multiprocessing capabilities"""
+    print("\n" + "="*70)
+    print("🔍 CHECKING CPU MULTIPROCESSING")
+    print("="*70)
+
+    import multiprocessing
+    cpu_count = multiprocessing.cpu_count()
+    print(f"✅ CPU cores available: {cpu_count}")
+    print(f"   Recommended parallel workers: {max(1, cpu_count - 1)}")
+    return cpu_count
+
+
+def test_simple_gpu_simulation():
+    """Run a simple test to verify GPU actually works"""
+    print("\n" + "="*70)
+    print("🧪 TESTING GPU SIMULATION")
+    print("="*70)
+
+    try:
+        from qiskit import QuantumCircuit
+        from qiskit_aer import AerSimulator
+        import time
+
+        # Create a small quantum circuit
+        n_qubits = 10
+        qc = QuantumCircuit(n_qubits)
+        for i in range(n_qubits):
+            qc.h(i)
+        for i in range(n_qubits - 1):
+            qc.cx(i, i+1)
+
+        # Test CPU
+        print("\n⏱️  Testing CPU simulation...")
+        simulator_cpu = AerSimulator(method='statevector', device='CPU')
+        start = time.time()
+        result_cpu = simulator_cpu.run(qc, shots=1).result()
+        cpu_time = time.time() - start
+        print(f"   CPU time: {cpu_time:.4f}s")
+
+        # Test GPU
+        try:
+            print("\n⏱️  Testing GPU simulation...")
+            simulator_gpu = AerSimulator(method='statevector', device='GPU')
+            start = time.time()
+            result_gpu = simulator_gpu.run(qc, shots=1).result()
+            gpu_time = time.time() - start
+            print(f"   GPU time: {gpu_time:.4f}s")
+
+            speedup = cpu_time / gpu_time
+            print(f"\n🚀 GPU Speedup: {speedup:.2f}x")
+
+            if speedup > 1.5:
+                print("   ✅ GPU is faster - ready to use!")
+                return True
+            else:
+                print("   ⚠️  GPU not significantly faster (overhead for small circuits)")
+                print("   💡 GPU will be faster for larger circuits (15+ qubits)")
+                return True
+
+        except Exception as e:
+            print(f"   ❌ GPU test failed: {e}")
+            return False
+
+    except Exception as e:
+        print(f"❌ Simulation test failed: {e}")
+        return False
+
+
+def main():
+    """Run all diagnostics"""
+    print("="*70)
+    print("🚀 QISKIT GPU ACCELERATION DIAGNOSTIC")
+    print("="*70)
+    print(f"System: {platform.system()} {platform.release()}")
+    print(f"Python: {sys.version.split()[0]}")
+    print("="*70)
+
+    results = {
+        'gpu': check_nvidia_gpu(),
+        'cuda': check_cuda(),
+        'qiskit_gpu': check_qiskit_aer_gpu(),
+        'cpu_cores': check_multiprocessing()
+    }
+
+    # Run simulation test if Qiskit GPU is available
+    if results['qiskit_gpu']:
+        results['gpu_test'] = test_simple_gpu_simulation()
+    else:
+        results['gpu_test'] = False
+
+    # Summary
+    print("\n" + "="*70)
+    print("📊 SUMMARY")
+    print("="*70)
+
+    if results['gpu'] and results['cuda'] and results['qiskit_gpu'] and results['gpu_test']:
+        print("✅ GPU ACCELERATION FULLY READY!")
+        print("\n🚀 You can use GPU-accelerated quantum dataset generation!")
+        print("\nRecommended configuration:")
+        print("   - Use GPU for quantum simulations")
+        print(f"   - Use {max(1, results['cpu_cores'] - 1)} CPU workers for parallelization")
+        print("   - Expected speedup: 10-100x for large graphs")
+
+    elif results['gpu'] and not results['cuda']:
+        print("⚠️  GPU detected but CUDA not installed")
+        print("\nInstall CUDA Toolkit:")
+        print("   https://developer.nvidia.com/cuda-downloads")
+
+    elif results['gpu'] and results['cuda'] and not results['qiskit_gpu']:
+        print("⚠️  GPU and CUDA ready, but Qiskit Aer GPU not available")
+        print("\nInstall Qiskit Aer GPU:")
+        print("   pip uninstall qiskit-aer")
+        print("   pip install qiskit-aer-gpu")
+
+    else:
+        print("❌ GPU acceleration not available")
+        print("\n💡 Fallback to CPU multiprocessing:")
+        print(f"   - Use {max(1, results['cpu_cores'] - 1)} parallel workers")
+        print("   - Expected speedup: 4-8x")
+
+    print("\n" + "="*70)
+    print(" ! Need cuquantum ! please install it before")
+    print("="*70 + "\n")
+
+    return results
+
+
+if __name__ == "__main__":
+    main()
diff --git a/Generator(forGPU)/gen_quantum_mp.py b/Generator(forGPU)/gen_quantum_mp.py
new file mode 100644
index 0000000..1a3ce31
--- /dev/null
+++ b/Generator(forGPU)/gen_quantum_mp.py
@@ -0,0 +1,823 @@
+"""
+MULTI-PROBLEM Quantum QAOA Dataset Generator (OPTIMIZED)
+Generates datasets for MULTIPLE optimization problems with hybrid strategy
+
+Problems supported:
+- MaxCut (graph partitioning)
+- Max Independent Set (node selection)
+- Vertex Cover (covering edges with minimum nodes)
+- (Easy to extend to TSP, Graph Coloring, etc.)
+
+Hybrid Strategy:
+- Phase 1: 70% MaxCut + 30% other problems (easier start)
+- Phase 2: 50% MaxCut + 50% other problems (balanced)
+
+Features:
+- GPU acceleration (10-100x speedup)
+- CPU multiprocessing (4-8x speedup)
+- Problem-agnostic Hamiltonian features for generalization
+- Fast SPSA optimizer with warm start
+- Incremental save + resume
+
+Requirements:
+    pip install qiskit qiskit-algorithms qiskit-aer-gpu networkx numpy
+"""
+
+import numpy as np
+import networkx as nx
+from typing import Tuple, List, Dict, Optional
+import json
+from pathlib import Path
+import time
+import multiprocessing as mp
+from functools import partial
+
+# Qiskit imports
+try:
+    from qiskit_algorithms.minimum_eigensolvers import QAOA
+    from qiskit_algorithms.optimizers import SPSA, COBYLA
+    from qiskit.quantum_info import SparsePauliOp
+    from qiskit_aer import AerSimulator
+    # Qiskit 2.x uses StatevectorSampler
+    from qiskit.primitives import StatevectorSampler
+    QISKIT_AVAILABLE = True
+    print("[OK] Qiskit imported successfully")
+except ImportError as e:
+    QISKIT_AVAILABLE = False
+    print("[ERROR] Qiskit not installed!")
+    print("Install: pip install qiskit qiskit-algorithms qiskit-aer")
+    print(f"Error: {e}")
+
+
+class MultiProblemQuantumGenerator:
+    """
+    Multi-problem QAOA dataset generator with GPU acceleration
+    Supports: MaxCut, Max Independent Set, Vertex Cover
+    """
+
+    PROBLEM_TYPES = ['maxcut', 'independent_set', 'vertex_cover', 'graph_coloring']
+
+    def __init__(self, seed: int = 42, use_gpu: bool = True, n_workers: int = None):
+        """
+        Initialize multi-problem generator
+
+        Args:
+            seed: Random seed
+            use_gpu: Try to use GPU if available
+            n_workers: Number of parallel workers (None = auto-detect)
+        """
+        if not QISKIT_AVAILABLE:
+            raise ImportError("Qiskit required! Install: pip install qiskit qiskit-algorithms qiskit-aer")
+
+        np.random.seed(seed)
+        self.seed = seed
+        self.use_gpu = use_gpu
+
+        if n_workers is None:
+            n_workers = max(1, mp.cpu_count() - 1)
+        self.n_workers = n_workers
+
+        self._setup_simulator()
+
+        print(f" Multi-problem generator initialized:")
+        print(f"   - Device: {'GPU' if self.gpu_available else 'CPU'}")
+        print(f"   - Parallel workers: {self.n_workers}")
+        print(f"   - Supported problems: {', '.join(self.PROBLEM_TYPES)}")
+
+    def _setup_simulator(self):
+        """Setup Qiskit Aer simulator with GPU if available"""
+        try:
+            if self.use_gpu:
+                simulator = AerSimulator(method='statevector', device='GPU')
+                from qiskit import QuantumCircuit
+                qc = QuantumCircuit(2)
+                qc.h(0)
+                test_result = simulator.run(qc).result()
+                self.backend = simulator
+                self.gpu_available = True
+                print("[GPU] GPU acceleration enabled!")
+            else:
+                raise Exception("GPU disabled by user")
+        except Exception as e:
+            self.backend = AerSimulator(method='statevector', device='CPU')
+            self.gpu_available = False
+            print(f"[CPU] Using CPU (GPU not available: {str(e)[:50]})")
+
+        # Qiskit 2.x: Use StatevectorSampler (no backend parameter needed)
+        self.sampler = StatevectorSampler()
+
+    # ========================================================================
+    # GRAPH GENERATION
+    # ========================================================================
+
+    def generate_erdos_renyi_graph(self, n_nodes: int, edge_prob: float, seed: int) -> nx.Graph:
+        """Generate an Erds-Rnyi random graph"""
+        return nx.erdos_renyi_graph(n_nodes, edge_prob, seed=seed)
+
+    def compute_node_features(self, G: nx.Graph) -> np.ndarray:
+        """
+        Compute 7 graph-structure features (problem-agnostic)
+        These features work for ANY graph-based optimization problem
+        """
+        n_nodes = G.number_of_nodes()
+        features = np.zeros((n_nodes, 7))
+
+        degrees = dict(G.degree())
+        features[:, 0] = [degrees[i] for i in range(n_nodes)]
+
+        degree_centrality = nx.degree_centrality(G)
+        features[:, 1] = [degree_centrality[i] for i in range(n_nodes)]
+
+        clustering = nx.clustering(G)
+        features[:, 2] = [clustering[i] for i in range(n_nodes)]
+
+        betweenness = nx.betweenness_centrality(G)
+        features[:, 3] = [betweenness[i] for i in range(n_nodes)]
+
+        closeness = nx.closeness_centrality(G)
+        features[:, 4] = [closeness[i] for i in range(n_nodes)]
+
+        pagerank = nx.pagerank(G, max_iter=1000)
+        features[:, 5] = [pagerank[i] for i in range(n_nodes)]
+
+        try:
+            eigenvector = nx.eigenvector_centrality(G, max_iter=1000)
+            features[:, 6] = [eigenvector[i] for i in range(n_nodes)]
+        except:
+            features[:, 6] = 0.0
+
+        return features
+
+    def graph_to_adjacency_matrix(self, G: nx.Graph) -> np.ndarray:
+        """Convert graph to adjacency matrix"""
+        return nx.to_numpy_array(G)
+
+    # ========================================================================
+    # HAMILTONIAN CONSTRUCTION (Different for each problem!)
+    # ========================================================================
+
+    def graph_to_maxcut_hamiltonian(self, G: nx.Graph) -> SparsePauliOp:
+        """
+        MaxCut Hamiltonian: H = 0.5 * _{(i,j)E} Z_i Z_j
+        Goal: Maximize cut (partition graph into 2 sets)
+        """
+        n_nodes = G.number_of_nodes()
+        pauli_list = []
+        coeffs = []
+
+        for (i, j) in G.edges():
+            pauli_str = ['I'] * n_nodes
+            pauli_str[i] = 'Z'
+            pauli_str[j] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(0.5)
+
+        if len(pauli_list) == 0:
+            pauli_list = ['I' * n_nodes]
+            coeffs = [0.0]
+
+        return SparsePauliOp(pauli_list, coeffs=coeffs)
+
+    def graph_to_independent_set_hamiltonian(self, G: nx.Graph) -> SparsePauliOp:
+        """
+        Max Independent Set Hamiltonian:
+        H = -_i (1 - Z_i)/2 + penalty * _{(i,j)E} (1 - Z_i)(1 - Z_j)/4
+
+        Goal: Maximize number of non-adjacent nodes (Z_i = -1 means node selected)
+        Penalty: Ensure no two adjacent nodes are both selected
+        """
+        n_nodes = G.number_of_nodes()
+        pauli_list = []
+        coeffs = []
+
+        # Reward term: -_i (1 - Z_i)/2  = -n/2 + 0.5*_i Z_i
+        # We only need the Z_i terms (constant doesn't affect optimization)
+        for i in range(n_nodes):
+            pauli_str = ['I'] * n_nodes
+            pauli_str[i] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(0.5)  # Reward for selecting node
+
+        # Penalty term: prevent adjacent nodes from being selected
+        penalty = 2.0
+        for (i, j) in G.edges():
+            # (1 - Z_i)(1 - Z_j)/4 = (1 - Z_i - Z_j + Z_i Z_j)/4
+            # Constant term ignored, we add: -Z_i/4 - Z_j/4 + Z_i Z_j/4
+
+            # Z_i Z_j term (penalty for both selected)
+            pauli_str = ['I'] * n_nodes
+            pauli_str[i] = 'Z'
+            pauli_str[j] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty * 0.25)
+
+        if len(pauli_list) == 0:
+            pauli_list = ['I' * n_nodes]
+            coeffs = [0.0]
+
+        return SparsePauliOp(pauli_list, coeffs=coeffs)
+
+    def graph_to_vertex_cover_hamiltonian(self, G: nx.Graph) -> SparsePauliOp:
+        """
+        Vertex Cover Hamiltonian:
+        H = _i (1 - Z_i)/2 + penalty * _{(i,j)E} (1 + Z_i)(1 + Z_j)/4
+
+        Goal: Minimize number of nodes while covering all edges
+        Penalty: Ensure every edge has at least one endpoint selected
+        """
+        n_nodes = G.number_of_nodes()
+        pauli_list = []
+        coeffs = []
+
+        # Cost term: _i (1 - Z_i)/2 = n/2 - 0.5*_i Z_i
+        # Minimize number of selected nodes
+        for i in range(n_nodes):
+            pauli_str = ['I'] * n_nodes
+            pauli_str[i] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(-0.5)  # Negative = minimize
+
+        # Penalty term: ensure each edge is covered
+        penalty = 3.0
+        for (i, j) in G.edges():
+            # (1 + Z_i)(1 + Z_j)/4 = (1 + Z_i + Z_j + Z_i Z_j)/4
+            # We add: Z_i Z_j/4 (penalize if both NOT selected)
+            pauli_str = ['I'] * n_nodes
+            pauli_str[i] = 'Z'
+            pauli_str[j] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty * 0.25)
+
+        if len(pauli_list) == 0:
+            pauli_list = ['I' * n_nodes]
+            coeffs = [0.0]
+
+        return SparsePauliOp(pauli_list, coeffs=coeffs)
+
+    def graph_to_graph_coloring_hamiltonian(self, G: nx.Graph, n_colors=3) -> SparsePauliOp:
+        """
+        Graph Coloring Hamiltonian (3 colors)
+
+        Goal: Assign one of 3 colors to each node such that adjacent nodes have different colors
+
+        Encoding: Each node uses 2 qubits to represent 3 colors:
+            Color 0 (Red):   |00> (Z1=+1, Z2=+1)
+            Color 1 (Green): |01> (Z1=+1, Z2=-1)
+            Color 2 (Blue):  |10> (Z1=-1, Z2=+1)
+            Invalid:         |11> (Z1=-1, Z2=-1) <- Must penalize
+
+        Hamiltonian:
+        H = penalty1 * Sum over edges: penalty if same color
+          + penalty2 * Sum over nodes: penalty if invalid state |11>
+
+        Note: This requires 2*n_nodes qubits total
+        """
+        n_nodes = G.number_of_nodes()
+        n_qubits = 2 * n_nodes  # 2 qubits per node
+        pauli_list = []
+        coeffs = []
+
+        penalty_same_color = 5.0
+        penalty_invalid = 3.0
+
+        # Helper: Get qubit indices for node i
+        def get_qubit_indices(node):
+            return (2 * node, 2 * node + 1)  # (q1, q2) for node
+
+        # Penalty 1: Adjacent nodes must have different colors
+        # For each edge (i,j), we penalize if they have the same color
+        for (i, j) in G.edges():
+            qi1, qi2 = get_qubit_indices(i)
+            qj1, qj2 = get_qubit_indices(j)
+
+            # Same color detection: Sum of products for each color combination
+            # Color 0-0: (1+Zi1)/2 * (1+Zi2)/2 * (1+Zj1)/2 * (1+Zj2)/2
+            # Color 1-1: (1+Zi1)/2 * (1-Zi2)/2 * (1+Zj1)/2 * (1-Zj2)/2
+            # Color 2-2: (1-Zi1)/2 * (1+Zi2)/2 * (1-Zj1)/2 * (1+Zj2)/2
+
+            # Simplified: We penalize when Zi1*Zj1 and Zi2*Zj2 have same sign
+            # This happens when colors match
+
+            # Z_i1 * Z_j1 term
+            pauli_str = ['I'] * n_qubits
+            pauli_str[qi1] = 'Z'
+            pauli_str[qj1] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty_same_color * 0.25)
+
+            # Z_i2 * Z_j2 term
+            pauli_str = ['I'] * n_qubits
+            pauli_str[qi2] = 'Z'
+            pauli_str[qj2] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty_same_color * 0.25)
+
+            # Z_i1 * Z_j1 * Z_i2 * Z_j2 term (4-qubit interaction)
+            pauli_str = ['I'] * n_qubits
+            pauli_str[qi1] = 'Z'
+            pauli_str[qi2] = 'Z'
+            pauli_str[qj1] = 'Z'
+            pauli_str[qj2] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty_same_color * 0.25)
+
+        # Penalty 2: No node should be in invalid state |11>
+        # |11> means Z1=-1 and Z2=-1, so Z1*Z2 = +1
+        # We penalize (1 + Z1*Z2)/2
+        for i in range(n_nodes):
+            qi1, qi2 = get_qubit_indices(i)
+
+            # Z_i1 * Z_i2 term
+            pauli_str = ['I'] * n_qubits
+            pauli_str[qi1] = 'Z'
+            pauli_str[qi2] = 'Z'
+            pauli_list.append(''.join(pauli_str))
+            coeffs.append(penalty_invalid * 0.5)
+
+        if len(pauli_list) == 0:
+            pauli_list = ['I' * n_qubits]
+            coeffs = [0.0]
+
+        return SparsePauliOp(pauli_list, coeffs=coeffs)
+
+    def graph_to_hamiltonian(self, G: nx.Graph, problem_type: str) -> SparsePauliOp:
+        """
+        Convert graph to Hamiltonian based on problem type
+
+        Args:
+            G: NetworkX graph
+            problem_type: 'maxcut', 'independent_set', 'vertex_cover', or 'graph_coloring'
+
+        Returns:
+            SparsePauliOp Hamiltonian
+        """
+        if problem_type == 'maxcut':
+            return self.graph_to_maxcut_hamiltonian(G)
+        elif problem_type == 'independent_set':
+            return self.graph_to_independent_set_hamiltonian(G)
+        elif problem_type == 'vertex_cover':
+            return self.graph_to_vertex_cover_hamiltonian(G)
+        elif problem_type == 'graph_coloring':
+            return self.graph_to_graph_coloring_hamiltonian(G)
+        else:
+            raise ValueError(f"Unknown problem type: {problem_type}")
+
+    # ========================================================================
+    # HAMILTONIAN FEATURES (Problem-agnostic!)
+    # ========================================================================
+
+    def extract_hamiltonian_features(self, hamiltonian: SparsePauliOp) -> np.ndarray:
+        """
+        Extract problem-agnostic features from Hamiltonian
+        These features describe the STRUCTURE of the optimization problem,
+        not the specific problem type. This enables generalization!
+
+        Features (10 total):
+        1. Number of terms in Hamiltonian
+        2. Mean of coefficients
+        3. Std of coefficients
+        4. Min coefficient
+        5. Max coefficient
+        6. Fraction of single-qubit terms (Z_i)
+        7. Fraction of two-qubit terms (Z_i Z_j)
+        8. Fraction of multi-qubit terms (3+ qubits)
+        9. Coefficient range (max - min)
+        10. Coefficient sparsity (fraction of zero coefficients)
+
+        Returns:
+            Feature vector (10,)
+        """
+        features = np.zeros(10)
+
+        # Get Pauli terms and coefficients
+        coeffs = np.real(hamiltonian.coeffs)
+        paulis = hamiltonian.paulis
+
+        # Feature 0: Number of terms
+        features[0] = len(coeffs)
+
+        # Features 1-4: Coefficient statistics
+        features[1] = np.mean(coeffs)
+        features[2] = np.std(coeffs)
+        features[3] = np.min(coeffs)
+        features[4] = np.max(coeffs)
+
+        # Features 5-7: Term type distribution
+        single_qubit = 0
+        two_qubit = 0
+        multi_qubit = 0
+
+        for pauli in paulis:
+            # Count number of non-identity operators
+            n_ops = sum(1 for p in pauli.to_label() if p != 'I')
+            if n_ops == 1:
+                single_qubit += 1
+            elif n_ops == 2:
+                two_qubit += 1
+            else:
+                multi_qubit += 1
+
+        total_terms = len(paulis)
+        features[5] = single_qubit / total_terms if total_terms > 0 else 0
+        features[6] = two_qubit / total_terms if total_terms > 0 else 0
+        features[7] = multi_qubit / total_terms if total_terms > 0 else 0
+
+        # Feature 8: Coefficient range
+        features[8] = features[4] - features[3]  # max - min
+
+        # Feature 9: Sparsity (fraction near zero)
+        features[9] = np.sum(np.abs(coeffs) < 1e-6) / len(coeffs) if len(coeffs) > 0 else 0
+
+        return features
+
+    # ========================================================================
+    # QAOA OPTIMIZATION
+    # ========================================================================
+
+    def get_warm_start_params(self, G: nx.Graph, problem_type: str, p: int) -> np.ndarray:
+        """
+        Smart initialization based on graph structure and problem type
+        Different problems have different optimal parameter ranges
+        """
+        avg_clustering = nx.average_clustering(G)
+        avg_degree = np.mean([d for n, d in G.degree()])
+        n_nodes = G.number_of_nodes()
+
+        # Problem-specific heuristics
+        if problem_type == 'maxcut':
+            gamma_init = 0.4 + 0.3 * avg_clustering
+            beta_init = 0.3 - 0.15 * (avg_degree / n_nodes)
+        elif problem_type == 'independent_set':
+            gamma_init = 0.5 + 0.2 * (1 - avg_clustering)
+            beta_init = 0.25
+        elif problem_type == 'vertex_cover':
+            gamma_init = 0.35 + 0.25 * avg_clustering
+            beta_init = 0.35 - 0.1 * (avg_degree / n_nodes)
+        elif problem_type == 'graph_coloring':
+            # Graph coloring benefits from strong mixing
+            gamma_init = 0.45 + 0.2 * (1 - avg_clustering)
+            beta_init = 0.4  # Higher beta for more exploration
+        else:
+            gamma_init = 0.4
+            beta_init = 0.3
+
+        initial_point = []
+        for layer in range(p):
+            gamma = gamma_init * (1 - 0.1 * layer / max(p, 1))
+            beta = beta_init * (1 + 0.1 * layer / max(p, 1))
+            initial_point.extend([gamma, beta])
+
+        return np.array(initial_point)
+
+    def simulate_qaoa_optimization(self, G: nx.Graph, problem_type: str,
+                                   p: int = 1, timeout: int = 60,
+                                   fast_mode: bool = True) -> Dict:
+        """
+        Run REAL QAOA optimization with Qiskit
+
+        Args:
+            G: Graph
+            problem_type: 'maxcut', 'independent_set', or 'vertex_cover'
+            p: QAOA depth
+            timeout: Max time
+            fast_mode: Use SPSA (faster) vs COBYLA
+        """
+        start_time = time.time()
+
+        # Build Hamiltonian for specific problem
+        hamiltonian = self.graph_to_hamiltonian(G, problem_type)
+
+        # Smart initialization
+        initial_point = self.get_warm_start_params(G, problem_type, p)
+
+        # Choose optimizer
+        if fast_mode:
+            optimizer = SPSA(maxiter=50)
+        else:
+            optimizer = COBYLA(maxiter=30)
+
+        try:
+            # REAL QAOA SIMULATION
+            qaoa = QAOA(
+                sampler=self.sampler,
+                optimizer=optimizer,
+                reps=p,
+                initial_point=initial_point
+            )
+
+            result = qaoa.compute_minimum_eigenvalue(hamiltonian)
+
+            elapsed = time.time() - start_time
+            if elapsed > timeout:
+                raise TimeoutError(f"Exceeded {timeout}s")
+
+            optimal_point = result.optimal_point
+            gamma_values = optimal_point[:p]
+            beta_values = optimal_point[p:2*p]
+            energy = result.optimal_value
+            success = True
+
+        except Exception as e:
+            # Fallback heuristic (only if QAOA fails)
+            avg_clustering = nx.average_clustering(G)
+
+            if problem_type == 'maxcut':
+                gamma_values = [0.35 + 0.40 * avg_clustering]
+                beta_values = [0.20 + 0.25 * (1 - avg_clustering)]
+            elif problem_type == 'independent_set':
+                gamma_values = [0.5]
+                beta_values = [0.25]
+            elif problem_type == 'vertex_cover':
+                gamma_values = [0.4]
+                beta_values = [0.3]
+
+            energy = None
+            success = False
+
+        elapsed = time.time() - start_time
+
+        return {
+            'gamma': np.array(gamma_values),
+            'beta': np.array(beta_values),
+            'energy': float(energy) if energy is not None else None,
+            'success': success,
+            'optimization_time': elapsed
+        }
+
+    # ========================================================================
+    # SAMPLE GENERATION
+    # ========================================================================
+
+    def generate_single_sample(self, sample_id: int, n_nodes: int,
+                              edge_prob: float, problem_type: str,
+                              p: int, seed: int) -> Optional[Dict]:
+        """Generate a single sample for any problem type"""
+        try:
+            G = self.generate_erdos_renyi_graph(n_nodes, edge_prob, seed)
+
+            if not nx.is_connected(G):
+                return None
+
+            # Graph features (problem-agnostic)
+            adj_matrix = self.graph_to_adjacency_matrix(G)
+            node_features = self.compute_node_features(G)
+
+            # Hamiltonian features (problem-agnostic!)
+            hamiltonian = self.graph_to_hamiltonian(G, problem_type)
+            hamiltonian_features = self.extract_hamiltonian_features(hamiltonian)
+
+            # QAOA optimization
+            optimal_params = self.simulate_qaoa_optimization(G, problem_type, p)
+
+            sample = {
+                'id': sample_id,
+                'problem_type': problem_type,  # NEW: Problem identifier
+                'n_nodes': n_nodes,
+                'n_edges': G.number_of_edges(),
+                'adjacency_matrix': adj_matrix.tolist(),
+                'node_features': node_features.tolist(),
+                'hamiltonian_features': hamiltonian_features.tolist(),  # NEW!
+                'optimal_gamma': optimal_params['gamma'].tolist(),
+                'optimal_beta': optimal_params['beta'].tolist(),
+                'qaoa_energy': optimal_params['energy'],
+                'quantum_optimized': optimal_params['success'],
+                'optimization_time': optimal_params['optimization_time'],
+                'graph_type': 'erdos_renyi',
+                'edge_probability': edge_prob
+            }
+
+            return sample
+
+        except Exception as e:
+            print(f"Sample {sample_id} error: {str(e)[:50]}")
+            return None
+
+
+def worker_generate_sample(args):
+    """Worker function for multiprocessing"""
+    sample_id, n_nodes, edge_prob, problem_type, p, seed, use_gpu = args
+
+    gen = MultiProblemQuantumGenerator(seed=seed, use_gpu=False, n_workers=1)
+    sample = gen.generate_single_sample(sample_id, n_nodes, edge_prob, problem_type, p, seed)
+
+    if sample:
+        status = "" if sample['quantum_optimized'] else ""
+        time_str = f"{sample['optimization_time']:.1f}s"
+        problem_emoji = {'maxcut': '', 'independent_set': '', 'vertex_cover': ''}
+        emoji = problem_emoji.get(problem_type, '')
+        print(f"   {status} {emoji} Sample {sample_id} ({problem_type}, n={n_nodes}) - {time_str}")
+
+    return sample
+
+
+def generate_multiproblem_dataset(
+    total_samples: int,
+    n_nodes_range: Tuple[int, int],
+    problem_distribution: Dict[str, float] = None,
+    p: int = 1,
+    save_path: str = "Dataset/qaoa_multiproblem.json",
+    checkpoint_every: int = 10,
+    n_workers: int = None,
+    use_gpu: bool = True,
+    seed: int = 42
+) -> List[Dict]:
+    """
+    Generate multi-problem dataset with hybrid strategy
+
+    Args:
+        total_samples: Number of samples
+        n_nodes_range: (min_nodes, max_nodes)
+        problem_distribution: Dict like {'maxcut': 0.7, 'independent_set': 0.15, 'vertex_cover': 0.15}
+                             If None, defaults to hybrid strategy (70% maxcut)
+        p: QAOA depth
+        save_path: Output path
+        checkpoint_every: Checkpoint interval
+        n_workers: Parallel workers
+        use_gpu: GPU acceleration
+        seed: Random seed
+    """
+
+    # Default hybrid distribution: 70% MaxCut, 30% others
+    if problem_distribution is None:
+        problem_distribution = {
+            'maxcut': 0.70,
+            'independent_set': 0.15,
+            'vertex_cover': 0.15
+        }
+
+    if n_workers is None:
+        n_workers = max(1, mp.cpu_count() - 1)
+
+    print(f"\n{'='*70}")
+    print(f" MULTI-PROBLEM QUANTUM QAOA DATASET GENERATION")
+    print(f"{'='*70}")
+    print(f"Total samples: {total_samples}")
+    print(f"Node range: {n_nodes_range[0]}-{n_nodes_range[1]}")
+    print(f"QAOA depth: {p}")
+    print(f"Problem distribution:")
+    for prob, pct in problem_distribution.items():
+        print(f"   - {prob}: {pct*100:.0f}%")
+    print(f"Parallel workers: {n_workers}")
+    print(f"GPU: {'Enabled' if use_gpu else 'Disabled'}")
+    print(f"{'='*70}\n")
+
+    # Load existing dataset
+    dataset = []
+    save_file = Path(save_path)
+    if save_file.exists():
+        with open(save_path, 'r') as f:
+            dataset = json.load(f)
+        print(f" Loaded {len(dataset)} existing samples")
+
+    start_id = len(dataset)
+    if start_id >= total_samples:
+        print(" Dataset already complete!")
+        return dataset
+
+    save_file.parent.mkdir(parents=True, exist_ok=True)
+
+    # Prepare worker arguments with problem distribution
+    np.random.seed(seed + start_id)
+    worker_args = []
+
+    problems = list(problem_distribution.keys())
+    probs = list(problem_distribution.values())
+
+    for i in range(start_id, total_samples + 1000):
+        n_nodes = np.random.randint(n_nodes_range[0], n_nodes_range[1] + 1)
+        edge_prob = np.random.uniform(0.3, 0.9)
+        problem_type = np.random.choice(problems, p=probs)
+        sample_seed = seed + i
+        worker_args.append((i, n_nodes, edge_prob, problem_type, p, sample_seed, use_gpu))
+
+    # Run parallel generation
+    start_time = time.time()
+
+    print(f" Starting parallel generation with {n_workers} workers...\n")
+
+    with mp.Pool(n_workers) as pool:
+        chunk_size = checkpoint_every
+
+        for chunk_start in range(0, len(worker_args), chunk_size):
+            if len(dataset) >= total_samples:
+                break
+
+            chunk_end = min(chunk_start + chunk_size, len(worker_args))
+            chunk_args = worker_args[chunk_start:chunk_end]
+
+            results = pool.map(worker_generate_sample, chunk_args)
+
+            for result in results:
+                if result is not None and len(dataset) < total_samples:
+                    dataset.append(result)
+
+            # Checkpoint
+            if len(dataset) >= start_id + checkpoint_every or len(dataset) >= total_samples:
+                with open(save_path, 'w') as f:
+                    json.dump(dataset, f, indent=2)
+
+                elapsed = time.time() - start_time
+                progress = len(dataset) - start_id
+                rate = progress / elapsed if elapsed > 0 else 0
+                remaining = total_samples - len(dataset)
+                eta = remaining / rate if rate > 0 else 0
+
+                # Count by problem type
+                problem_counts = {}
+                for s in dataset:
+                    pt = s['problem_type']
+                    problem_counts[pt] = problem_counts.get(pt, 0) + 1
+
+                print(f"\n Checkpoint: {len(dataset)}/{total_samples}")
+                print(f"   Problem breakdown:")
+                for prob, count in problem_counts.items():
+                    print(f"      {prob}: {count} ({100*count/len(dataset):.1f}%)")
+                print(f"     Elapsed: {elapsed/60:.1f} min")
+                print(f"    Rate: {rate*60:.1f} samples/min")
+                print(f"    ETA: {eta/60:.1f} min\n")
+
+    # Final save
+    dataset = dataset[:total_samples]
+    with open(save_path, 'w') as f:
+        json.dump(dataset, f, indent=2)
+
+    total_time = time.time() - start_time
+    quantum_success = sum(1 for s in dataset if s.get('quantum_optimized', False))
+
+    print(f"\n{'='*70}")
+    print(f" MULTI-PROBLEM DATASET COMPLETE!")
+    print(f"{'='*70}")
+    print(f"Total samples: {len(dataset)}")
+    print(f"Quantum optimized: {quantum_success} ({100*quantum_success/len(dataset):.1f}%)")
+
+    # Final problem distribution
+    problem_counts = {}
+    for s in dataset:
+        pt = s['problem_type']
+        problem_counts[pt] = problem_counts.get(pt, 0) + 1
+
+    print(f"\nFinal problem distribution:")
+    for prob, count in problem_counts.items():
+        print(f"   {prob}: {count} ({100*count/len(dataset):.1f}%)")
+
+    print(f"\nTotal time: {total_time/60:.1f} min ({total_time/3600:.2f}h)")
+    print(f"Average: {total_time/len(dataset):.1f}s per sample")
+    print(f"Saved to: {save_path}")
+    print(f"{'='*70}\n")
+
+    return dataset
+
+
+if __name__ == "__main__":
+    import argparse
+
+    parser = argparse.ArgumentParser(description='Multi-problem quantum dataset generation')
+    parser.add_argument('--samples', type=int, default=100, help='Number of samples')
+    parser.add_argument('--min_nodes', type=int, default=6, help='Min nodes')
+    parser.add_argument('--max_nodes', type=int, default=12, help='Max nodes')
+    parser.add_argument('--p', type=int, default=1, help='QAOA depth')
+    parser.add_argument('--output', type=str, default='Dataset/qaoa_multiproblem_hybrid.json')
+    parser.add_argument('--checkpoint', type=int, default=10)
+    parser.add_argument('--workers', type=int, default=None)
+    parser.add_argument('--no-gpu', action='store_true')
+    parser.add_argument('--seed', type=int, default=42)
+    parser.add_argument('--maxcut-ratio', type=float, default=0.70, help='Ratio of MaxCut samples (0.70 = 70 percent)')
+
+    args = parser.parse_args()
+
+    if not QISKIT_AVAILABLE:
+        print(" Qiskit not installed!")
+        print("Install: pip install qiskit qiskit-algorithms qiskit-aer")
+        exit(1)
+
+    # Hybrid distribution
+    other_ratio = 1.0 - args.maxcut_ratio
+    problem_dist = {
+        'maxcut': args.maxcut_ratio,
+        'independent_set': other_ratio / 2,
+        'vertex_cover': other_ratio / 2
+    }
+
+    print(f"\n Hybrid Strategy:")
+    print(f"   MaxCut: {problem_dist['maxcut']*100:.0f}%")
+    print(f"   Independent Set: {problem_dist['independent_set']*100:.0f}%")
+    print(f"   Vertex Cover: {problem_dist['vertex_cover']*100:.0f}%")
+
+    dataset = generate_multiproblem_dataset(
+        total_samples=args.samples,
+        n_nodes_range=(args.min_nodes, args.max_nodes),
+        problem_distribution=problem_dist,
+        p=args.p,
+        save_path=args.output,
+        checkpoint_every=args.checkpoint,
+        n_workers=args.workers,
+        use_gpu=not args.no_gpu,
+        seed=args.seed
+    )
+
+    print(" Multi-problem dataset ready!")
+    print("\n Features included:")
+    print("   - 7 graph structure features (problem-agnostic)")
+    print("   - 10 Hamiltonian features (problem-agnostic)")
+    print("   - Optimal QAOA parameters (gamma, beta)")
+    print("\n Your GNN can now generalize across multiple problems!")