diff --git a/pyproject.toml b/pyproject.toml
index b4def36c4..23bce567c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -35,7 +35,7 @@ dependencies = [
     "pytket>=2.4.0; python_version >= '3.14'",
     "pytket_qiskit>=0.61.0",
     "pytket-qiskit>=0.78.0; python_version >= '3.14'",
-    "sb3_contrib>=2.0.0",
+    "sb3_contrib>=2.3.0",
     "tqdm>=4.66.0",
     "rich>=12.6.0",
     "scikit-learn>=1.5.1",
@@ -98,6 +98,12 @@ Issues = "https://github.com/munich-quantum-toolkit/predictor/issues"
 Discussions = "https://github.com/munich-quantum-toolkit/predictor/discussions"
 Research = "https://www.cda.cit.tum.de/research/quantum/"
 
+[project.optional-dependencies]
+gnn = [
+    "torch-geometric>=2.7.0; python_version < '3.14'",
+    "torch-geometric>=2.8.0; python_version >= '3.14'",
+]
+
 [tool.hatch.build.targets.wheel]
 packages = ["src/mqt"]
 
@@ -250,6 +256,7 @@ wille = "wille"
 anc = "anc"
 aer = "aer"
 fom = "fom"
+gae = "gae"
 
 
 [tool.repo-review.ignore]
diff --git a/src/mqt/predictor/rl/gnn.py b/src/mqt/predictor/rl/gnn.py
new file mode 100644
index 000000000..82682a0e8
--- /dev/null
+++ b/src/mqt/predictor/rl/gnn.py
@@ -0,0 +1,769 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# Copyright (c) 2025 - 2026 Munich Quantum Software Company GmbH
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Graph neural network support for the reinforcement learning predictor."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from importlib import import_module
+from math import cos, pi
+from typing import TYPE_CHECKING, Any, NamedTuple, Self, cast
+
+import gymnasium as gym
+import numpy as np
+import torch
+import torch.nn.functional as functional
+from gymnasium import spaces
+from qiskit.converters import circuit_to_dag
+from qiskit.dagcircuit import DAGOpNode
+from qiskit.transpiler import PassManager
+from qiskit.transpiler.passes import RemoveBarriers
+from sb3_contrib import MaskablePPO
+from sb3_contrib.common.maskable.buffers import MaskableDictRolloutBuffer
+from sb3_contrib.common.maskable.policies import MaskableMultiInputActorCriticPolicy
+from sb3_contrib.common.maskable.utils import get_action_masks, is_masking_supported
+from stable_baselines3.common.torch_layers import BaseFeaturesExtractor
+from torch import nn
+
+try:
+    _torch_geometric_data = import_module("torch_geometric.data")
+    _torch_geometric_nn = import_module("torch_geometric.nn")
+except ModuleNotFoundError as error:
+    msg = "GNN support requires the optional dependencies. Install MQT Predictor with the 'gnn' extra."
+    raise ImportError(msg) from error
+
+AttentionalAggregation = _torch_geometric_nn.AttentionalAggregation
+_PyGBatch: Any = _torch_geometric_data.Batch
+_PyGData: Any = _torch_geometric_data.Data
+GraphNorm = _torch_geometric_nn.GraphNorm
+SAGEConv = _torch_geometric_nn.SAGEConv
+
+if TYPE_CHECKING:
+    from collections.abc import Generator, Sequence
+    from pathlib import Path
+    from typing import Protocol
+
+    from numpy.typing import NDArray
+    from qiskit import QuantumCircuit
+    from sb3_contrib.common.maskable.distributions import MaskableDistribution
+    from stable_baselines3.common.buffers import RolloutBuffer
+    from stable_baselines3.common.callbacks import BaseCallback
+    from stable_baselines3.common.type_aliases import Schedule
+    from stable_baselines3.common.vec_env import VecEnv, VecNormalize
+    from torch.optim import Optimizer
+
+    from mqt.predictor.rl.predictorenv import PredictorEnv
+
+    class GraphData(Protocol):
+        """Typed subset of the optional PyG Data API used here."""
+
+        num_nodes: int
+
+        def __getitem__(self, key: str) -> torch.Tensor:
+            """Return a graph tensor by key."""
+            ...
+
+        def to(self, device: torch.device | str) -> Self:
+            """Move the graph tensors to a device."""
+            ...
+
+    class GraphBatch(GraphData, Protocol):
+        """Typed subset of the optional PyG Batch API used here."""
+
+        batch: torch.Tensor
+        num_graphs: int
+
+
+NODE_OPERATION_NAMES = (
+    "id",
+    "x",
+    "y",
+    "z",
+    "h",
+    "s",
+    "sdg",
+    "t",
+    "tdg",
+    "sx",
+    "rx",
+    "ry",
+    "rz",
+    "u",
+    "u1",
+    "u2",
+    "u3",
+    "cx",
+    "cy",
+    "cz",
+    "ch",
+    "crx",
+    "cry",
+    "crz",
+    "cp",
+    "cu",
+    "cu1",
+    "cu2",
+    "cu3",
+    "swap",
+    "iswap",
+    "ecr",
+    "rzz",
+    "rxx",
+    "ryy",
+    "zz",
+    "ccx",
+    "reset",
+    "measure",
+    "other",
+)
+GLOBAL_FEATURE_NAMES = (
+    "num_qubits",
+    "depth",
+    "program_communication",
+    "critical_depth",
+    "entanglement_ratio",
+    "parallelism",
+    "liveness",
+    "measure",
+    "cx",
+    "id",
+    "p",
+    "x",
+    "y",
+    "z",
+    "h",
+    "s",
+    "sdg",
+    "t",
+    "tdg",
+    "rx",
+    "ry",
+    "rz",
+    "sx",
+    "sxdg",
+    "cz",
+    "cy",
+    "swap",
+    "ch",
+    "crx",
+    "cry",
+    "crz",
+    "cp",
+    "cu3",
+    "csx",
+    "rxx",
+    "rzz",
+)
+NODE_FEATURE_DIM = 52
+GLOBAL_FEATURE_DIM = 36
+NODE_SCALAR_DIM = NODE_FEATURE_DIM - len(NODE_OPERATION_NAMES)
+
+_GATE_INDICES = "gate_indices"
+_NODE_SCALARS = "node_scalars"
+_EDGE_INDEX = "edge_index"
+_GLOBAL_FEATURES = "global_features"
+_TERMINAL_GRAPH_OBSERVATION = "_mqt_gnn_terminal_observation"
+
+
+@dataclass(frozen=True, slots=True)
+class GNNConfig:
+    """Configuration for the opt-in GNN policy."""
+
+    hidden_dim: int = 128
+    num_conv_wo_resnet: int = 3
+    num_resnet_layers: int = 5
+    dropout_p: float = 0.2
+    bidirectional: bool = True
+    learning_rate: float = 3e-4
+    gnn_learning_rate: float = 1e-4
+    minimum_learning_rate_factor: float = 0.1
+    n_steps: int = 2048
+    batch_size: int = 64
+    n_epochs: int = 10
+    gamma: float = 0.98
+    gae_lambda: float = 0.95
+    clip_range: float = 0.2
+    clip_range_vf: float = 0.2
+    ent_coef: float = 0.01
+    vf_coef: float = 0.5
+    max_grad_norm: float = 0.5
+    target_kl: float = 0.01
+
+    def __post_init__(self) -> None:
+        """Validate the configuration."""
+        if self.hidden_dim < 1 or self.num_conv_wo_resnet < 1 or self.num_resnet_layers < 0:
+            msg = "hidden_dim and num_conv_wo_resnet must be positive, and num_resnet_layers must be non-negative"
+            raise ValueError(msg)
+        if not 0 <= self.dropout_p < 1:
+            msg = "dropout_p must be in the interval [0, 1)"
+            raise ValueError(msg)
+        if self.learning_rate <= 0 or self.gnn_learning_rate <= 0:
+            msg = "learning rates must be positive"
+            raise ValueError(msg)
+        if not 0 < self.minimum_learning_rate_factor <= 1:
+            msg = "minimum_learning_rate_factor must be in the interval (0, 1]"
+            raise ValueError(msg)
+
+    @classmethod
+    def paper(cls) -> Self:
+        """Return the tuned configuration used for the paper model."""
+        return cls(
+            hidden_dim=119,
+            num_conv_wo_resnet=1,
+            num_resnet_layers=5,
+            dropout_p=0.1,
+            bidirectional=True,
+            learning_rate=1e-3,
+            gnn_learning_rate=1e-3,
+        )
+
+
+def _safe_float(value: object) -> float:
+    try:
+        return float(cast("Any", value))
+    except (TypeError, ValueError):
+        return 0.0
+
+
+def _create_sparse_dag(
+    qc: QuantumCircuit,
+) -> tuple[NDArray[np.int32], NDArray[np.float32], NDArray[np.int32]]:
+    dag = circuit_to_dag(PassManager(RemoveBarriers()).run(qc))
+    nodes = list(dag.op_nodes())
+    node_indices = {node: index for index, node in enumerate(nodes)}
+    operation_indices = {name: index for index, name in enumerate(NODE_OPERATION_NAMES)}
+
+    gate_indices = np.zeros(len(nodes), dtype=np.int32)
+    node_scalars = np.zeros((len(nodes), NODE_SCALAR_DIM), dtype=np.float32)
+
+    for index, node in enumerate(nodes):
+        gate_indices[index] = operation_indices.get(node.op.name, operation_indices["other"])
+        raw_parameters = list(getattr(node.op, "params", ()))
+        parameters = [_safe_float(value) for value in raw_parameters[:3]]
+        parameters.extend([0.0] * (3 - len(parameters)))
+        node_scalars[index, :6] = [
+            value for parameter in parameters for value in (np.sin(parameter), np.cos(parameter))
+        ]
+        node_scalars[index, 6] = len(node.qargs)
+        node_scalars[index, 7] = getattr(node.op, "num_ctrl_qubits", 0)
+        node_scalars[index, 8] = len(raw_parameters)
+        node_scalars[index, 10] = sum(isinstance(predecessor, DAGOpNode) for predecessor in dag.predecessors(node))
+        node_scalars[index, 11] = sum(isinstance(successor, DAGOpNode) for successor in dag.successors(node))
+
+    edges = [
+        (node_indices[source], node_indices[target])
+        for source, target, _ in dag.edges()
+        if source in node_indices and target in node_indices
+    ]
+    edge_index = np.asarray(edges, dtype=np.int32).T if edges else np.empty((2, 0), dtype=np.int32)
+
+    topological_nodes = list(dag.topological_op_nodes())
+    distance_from_start: dict[DAGOpNode, int] = dict.fromkeys(topological_nodes, 0)
+    for node in topological_nodes:
+        predecessors = [predecessor for predecessor in dag.predecessors(node) if isinstance(predecessor, DAGOpNode)]
+        if predecessors:
+            distance_from_start[node] = max(distance_from_start[predecessor] + 1 for predecessor in predecessors)
+
+    distance_to_end: dict[DAGOpNode, int] = dict.fromkeys(topological_nodes, 0)
+    for node in reversed(topological_nodes):
+        successors = [successor for successor in dag.successors(node) if isinstance(successor, DAGOpNode)]
+        if successors:
+            distance_to_end[node] = max(distance_to_end[successor] + 1 for successor in successors)
+
+    if topological_nodes:
+        longest_path = max(distance_from_start[node] + distance_to_end[node] for node in topological_nodes)
+        for index, node in enumerate(nodes):
+            node_scalars[index, 9] = distance_from_start[node] + distance_to_end[node] == longest_path
+
+    return gate_indices, node_scalars, edge_index
+
+
+def _observation_scalar(observation: dict[str, Any], name: str) -> float:
+    value = np.asarray(observation[name], dtype=np.float32).reshape(-1)
+    if value.size != 1:
+        msg = f"Expected one scalar for RL feature '{name}', got shape {value.shape}."
+        raise ValueError(msg)
+    return float(value[0])
+
+
+def create_graph_observation(
+    qc: QuantumCircuit,
+    flat_observation: dict[str, Any],
+) -> GraphData:
+    """Create an exact, variable-size graph alongside the regular RL observation."""
+    gate_indices, node_scalars, edge_index = _create_sparse_dag(qc)
+    global_features = np.asarray(
+        [_observation_scalar(flat_observation, name) for name in GLOBAL_FEATURE_NAMES], dtype=np.float32
+    )
+    global_features[0] = qc.num_qubits
+    global_features[1] = qc.depth()
+
+    return cast(
+        "GraphData",
+        _PyGData(
+            gate_indices=torch.as_tensor(gate_indices, dtype=torch.long),
+            node_scalars=torch.as_tensor(node_scalars, dtype=torch.float32),
+            edge_index=torch.as_tensor(edge_index, dtype=torch.long),
+            global_features=torch.as_tensor(global_features, dtype=torch.float32).reshape(1, -1),
+            num_nodes=gate_indices.shape[0],
+        ),
+    )
+
+
+class GNNObservationWrapper(gym.Wrapper):
+    """Maintain a variable-size graph sidecar while preserving the regular RL interface."""
+
+    def _update_graph_observation(self, observation: dict[str, Any]) -> None:
+        predictor_env = cast("PredictorEnv", self.unwrapped)
+        self.graph_observation = create_graph_observation(predictor_env.state, observation)
+
+    def reset(
+        self,
+        qc: Path | str | QuantumCircuit | None = None,
+        seed: int | None = None,
+        options: dict[str, Any] | None = None,
+    ) -> tuple[dict[str, NDArray[np.generic]], dict[str, Any]]:
+        """Reset the predictor and refresh the graph sidecar."""
+        predictor_env = cast("PredictorEnv", self.unwrapped)
+        observation, info = predictor_env.reset(qc, seed=seed, options=options)
+        self._update_graph_observation(observation)
+        return observation, info
+
+    def step(self, action: int) -> tuple[dict[str, NDArray[np.generic]], float, bool, bool, dict[str, Any]]:
+        """Step the predictor and refresh the graph sidecar."""
+        observation, reward, terminated, truncated, info = self.env.step(action)
+        self._update_graph_observation(observation)
+        if truncated and not terminated:
+            info[_TERMINAL_GRAPH_OBSERVATION] = self.graph_observation
+        return observation, float(reward), terminated, truncated, info
+
+    def action_masks(self) -> list[bool]:
+        """Forward the action mask required by MaskablePPO."""
+        predictor_env = cast("PredictorEnv", self.unwrapped)
+        return predictor_env.action_masks()
+
+
+class GraphSAGEEncoder(nn.Module):
+    """Encode variable-size circuit graphs with the prototype GraphSAGE topology."""
+
+    def __init__(
+        self,
+        hidden_dim: int,
+        num_conv_wo_resnet: int,
+        num_resnet_layers: int,
+        dropout_p: float,
+        *,
+        bidirectional: bool,
+    ) -> None:
+        """Initialize the GraphSAGE encoder."""
+        super().__init__()
+        layer_count = num_conv_wo_resnet + num_resnet_layers
+        self.convs = nn.ModuleList([
+            SAGEConv(NODE_FEATURE_DIM if index == 0 else hidden_dim, hidden_dim) for index in range(layer_count)
+        ])
+        self.norms = nn.ModuleList(GraphNorm(hidden_dim) for _ in range(layer_count))
+        self.activation = nn.LeakyReLU()
+        self.dropout = nn.Dropout(dropout_p)
+        self.residual_start = num_conv_wo_resnet
+        self.bidirectional = bidirectional
+        self.hidden_dim = hidden_dim
+        self.pool = AttentionalAggregation(
+            gate_nn=nn.Sequential(
+                nn.Linear(hidden_dim, hidden_dim // 2),
+                nn.Tanh(),
+                nn.Linear(hidden_dim // 2, 1),
+            )
+        )
+
+    def forward(
+        self,
+        node_features: torch.Tensor,
+        edge_index: torch.Tensor,
+        batch: torch.Tensor,
+        num_graphs: int,
+    ) -> torch.Tensor:
+        """Return one embedding per circuit graph."""
+        if node_features.shape[0] == 0:
+            return node_features.new_zeros((num_graphs, self.hidden_dim))
+
+        features = node_features
+        for index, (conv, norm) in enumerate(zip(self.convs, self.norms, strict=True)):
+            updated = conv(features, edge_index)
+            if self.bidirectional:
+                updated = 0.5 * (updated + conv(features, edge_index.flip(0)))
+            updated = self.dropout(self.activation(norm(updated, batch=batch)))
+            features = updated if index < self.residual_start else features + updated
+        return self.pool(features, index=batch, dim_size=num_graphs)
+
+
+class GNNFeaturesExtractor(BaseFeaturesExtractor):
+    """Stable-Baselines3 feature extractor implementing the prototype GNN and shared trunk."""
+
+    def __init__(
+        self,
+        observation_space: spaces.Dict,
+        hidden_dim: int = 128,
+        num_conv_wo_resnet: int = 3,
+        num_resnet_layers: int = 5,
+        dropout_p: float = 0.2,
+        *,
+        bidirectional: bool = True,
+    ) -> None:
+        """Initialize the GNN feature extractor."""
+        super().__init__(observation_space, features_dim=hidden_dim)
+        self.encoder = GraphSAGEEncoder(
+            hidden_dim,
+            num_conv_wo_resnet,
+            num_resnet_layers,
+            dropout_p,
+            bidirectional=bidirectional,
+        )
+        self.trunk = nn.Sequential(
+            nn.Linear(hidden_dim + GLOBAL_FEATURE_DIM, hidden_dim),
+            nn.LayerNorm(hidden_dim),
+            nn.GELU(),
+            nn.Dropout(dropout_p),
+            nn.Linear(hidden_dim, hidden_dim),
+            nn.LayerNorm(hidden_dim),
+            nn.GELU(),
+            nn.Dropout(dropout_p),
+        )
+
+    def forward(self, observations: GraphBatch) -> torch.Tensor:
+        """Extract a shared latent feature vector for the actor and critic."""
+        gate_indices = observations[_GATE_INDICES]
+        node_scalars = observations[_NODE_SCALARS]
+        edge_index = observations[_EDGE_INDEX]
+        batch = observations.batch
+        global_features = observations[_GLOBAL_FEATURES].reshape(-1, GLOBAL_FEATURE_DIM)
+        one_hot = functional.one_hot(gate_indices, num_classes=len(NODE_OPERATION_NAMES)).to(node_scalars.dtype)
+        node_features = torch.cat((one_hot, node_scalars), dim=1)
+        graph_embedding = self.encoder(node_features, edge_index, batch, observations.num_graphs)
+        return self.trunk(torch.cat((graph_embedding, global_features), dim=1))
+
+
+class GNNMaskableDictRolloutBufferSamples(NamedTuple):
+    """A MaskablePPO minibatch with a variable-size graph batch."""
+
+    observations: GraphBatch
+    actions: torch.Tensor
+    old_values: torch.Tensor
+    old_log_prob: torch.Tensor
+    advantages: torch.Tensor
+    returns: torch.Tensor
+    action_masks: torch.Tensor
+
+
+class GNNMaskableDictRolloutBuffer(MaskableDictRolloutBuffer):
+    """Store graph sidecars while retaining MaskablePPO's numeric rollout data and GAE."""
+
+    graph_observations: NDArray[np.object_]
+
+    def reset(self) -> None:
+        """Reset both the standard rollout data and graph sidecars."""
+        self.graph_observations = np.empty((self.buffer_size, self.n_envs), dtype=object)
+        super().reset()
+
+    def add(  # ty: ignore[invalid-method-override]
+        self,
+        obs: dict[str, NDArray[np.generic]],
+        action: NDArray[np.generic],
+        reward: NDArray[np.generic],
+        episode_start: NDArray[np.generic],
+        value: torch.Tensor,
+        log_prob: torch.Tensor,
+        *,
+        action_masks: NDArray[np.generic] | None = None,
+        graph_observations: Sequence[GraphData] | None = None,
+    ) -> None:
+        """Add one vectorized transition and its graph sidecars."""
+        if graph_observations is None:
+            msg = "GNN rollouts require graph observations."
+            raise ValueError(msg)
+        if len(graph_observations) != self.n_envs:
+            msg = f"Expected {self.n_envs} graph observations, got {len(graph_observations)}."
+            raise ValueError(msg)
+        self.graph_observations[self.pos] = graph_observations
+        super().add(obs, action, reward, episode_start, value, log_prob, action_masks=action_masks)
+
+    def get(  # ty: ignore[invalid-method-override]
+        self, batch_size: int | None = None
+    ) -> Generator[GNNMaskableDictRolloutBufferSamples, None, None]:
+        """Yield shuffled minibatches with PyG's exact ragged batching."""
+        assert self.full
+        indices = np.random.permutation(self.buffer_size * self.n_envs)  # ruff: ignore[numpy-legacy-random]
+        if not self.generator_ready:
+            self.graph_observations = self.swap_and_flatten(self.graph_observations).reshape(-1)
+            for tensor_name in ("actions", "values", "log_probs", "advantages", "returns", "action_masks"):
+                self.__dict__[tensor_name] = self.swap_and_flatten(self.__dict__[tensor_name])
+            self.generator_ready = True
+
+        if batch_size is None:
+            batch_size = self.buffer_size * self.n_envs
+
+        start_index = 0
+        while start_index < self.buffer_size * self.n_envs:
+            yield self._get_samples(indices[start_index : start_index + batch_size])
+            start_index += batch_size
+
+    def _get_samples(  # ty: ignore[invalid-method-override]
+        self,
+        batch_inds: NDArray[np.int64],
+        _env: VecNormalize | None = None,
+    ) -> GNNMaskableDictRolloutBufferSamples:
+        graphs = [cast("GraphData", self.graph_observations[index]) for index in batch_inds]
+        observations = cast("GraphBatch", _PyGBatch.from_data_list(graphs).to(self.device))
+        return GNNMaskableDictRolloutBufferSamples(
+            observations=observations,
+            actions=self.to_torch(self.actions[batch_inds]),
+            old_values=self.to_torch(self.values[batch_inds].flatten()),
+            old_log_prob=self.to_torch(self.log_probs[batch_inds].flatten()),
+            advantages=self.to_torch(self.advantages[batch_inds].flatten()),
+            returns=self.to_torch(self.returns[batch_inds].flatten()),
+            action_masks=self.to_torch(self.action_masks[batch_inds].reshape(-1, self.mask_dims)),
+        )
+
+
+class GNNMaskableMultiInputActorCriticPolicy(MaskableMultiInputActorCriticPolicy):
+    """Maskable multi-input policy with a separate learning rate for the GNN encoder."""
+
+    def __init__(
+        self,
+        observation_space: spaces.Dict,
+        action_space: spaces.Space[Any],
+        lr_schedule: Schedule,
+        *,
+        gnn_learning_rate: float,
+        **kwargs: Any,  # ruff: ignore[any-type]
+    ) -> None:
+        """Initialize the maskable GNN policy."""
+        self.gnn_learning_rate = gnn_learning_rate
+        super().__init__(observation_space, action_space, lr_schedule, **kwargs)
+
+    def obs_to_tensor(  # ty: ignore[invalid-method-override]
+        self,
+        observation: GraphData | GraphBatch | Sequence[GraphData],
+    ) -> tuple[GraphBatch, bool]:
+        """Move one graph or an exact ragged graph batch to the policy device."""
+        if isinstance(observation, _PyGBatch):
+            batch = observation
+            vectorized = True
+        elif isinstance(observation, _PyGData):
+            batch = _PyGBatch.from_data_list([observation])
+            vectorized = False
+        else:
+            batch = _PyGBatch.from_data_list(list(observation))
+            vectorized = True
+        return cast("GraphBatch", batch.to(self.device)), vectorized
+
+    def extract_features(  # ty: ignore[invalid-method-override]
+        self,
+        obs: GraphBatch,
+        features_extractor: BaseFeaturesExtractor | None = None,
+    ) -> torch.Tensor | tuple[torch.Tensor, torch.Tensor]:
+        """Apply the GNN extractor directly, without SB3's fixed-shape preprocessing."""
+        if features_extractor is not None:
+            return features_extractor(obs)
+        if self.share_features_extractor:
+            return self.features_extractor(obs)
+        return self.pi_features_extractor(obs), self.vf_features_extractor(obs)
+
+    def get_distribution(  # ty: ignore[invalid-method-override]
+        self,
+        obs: GraphBatch,
+        action_masks: NDArray[np.bool_] | None = None,
+    ) -> MaskableDistribution:
+        """Return the masked action distribution for a graph batch."""
+        features = cast("torch.Tensor", self.extract_features(obs, self.pi_features_extractor))
+        latent_pi = self.mlp_extractor.forward_actor(features)
+        distribution = self._get_action_dist_from_latent(latent_pi)
+        if action_masks is not None:
+            distribution.apply_masking(action_masks)
+        return distribution
+
+    def predict_values(self, obs: GraphBatch) -> torch.Tensor:  # ty: ignore[invalid-method-override]
+        """Estimate values for a graph batch."""
+        features = cast("torch.Tensor", self.extract_features(obs, self.vf_features_extractor))
+        latent_vf = self.mlp_extractor.forward_critic(features)
+        return self.value_net(latent_vf)
+
+    def _build(self, lr_schedule: Schedule) -> None:
+        super()._build(lr_schedule)
+        extractor = cast("GNNFeaturesExtractor", self.features_extractor)
+        encoder_parameters = list(extractor.encoder.parameters())
+        encoder_parameter_ids = {id(parameter) for parameter in encoder_parameters}
+        policy_parameters = [parameter for parameter in self.parameters() if id(parameter) not in encoder_parameter_ids]
+        policy_learning_rate = float(lr_schedule(1.0))
+        self.optimizer = self.optimizer_class(
+            [
+                {
+                    "params": encoder_parameters,
+                    "lr": self.gnn_learning_rate,
+                    "learning_rate_scale": self.gnn_learning_rate / policy_learning_rate,
+                },
+                {"params": policy_parameters, "lr": policy_learning_rate, "learning_rate_scale": 1.0},
+            ],
+            **self.optimizer_kwargs,
+        )
+
+    def _get_constructor_parameters(self) -> dict[str, Any]:
+        data = super()._get_constructor_parameters()
+        data["gnn_learning_rate"] = self.gnn_learning_rate
+        return data
+
+
+class GNNMaskablePPO(MaskablePPO):
+    """MaskablePPO variant that retains the encoder-to-policy learning-rate ratio."""
+
+    def collect_rollouts(
+        self,
+        env: VecEnv,
+        callback: BaseCallback,
+        rollout_buffer: RolloutBuffer,
+        n_rollout_steps: int,
+        use_masking: bool = True,
+    ) -> bool:
+        """Collect rollouts with graph sidecars while retaining MaskablePPO's rollout logic."""
+        assert isinstance(rollout_buffer, GNNMaskableDictRolloutBuffer)
+        assert self._last_obs is not None
+        policy = cast("GNNMaskableMultiInputActorCriticPolicy", self.policy)
+        policy.set_training_mode(False)
+        n_steps = 0
+        action_masks = None
+        rollout_buffer.reset()
+
+        if use_masking and not is_masking_supported(env):
+            msg = "Environment does not support action masking. Consider using ActionMasker wrapper."
+            raise ValueError(msg)
+
+        graph_observations = cast("list[GraphData]", env.get_attr("graph_observation"))
+        callback.on_rollout_start()
+
+        while n_steps < n_rollout_steps:
+            with torch.no_grad():
+                obs_tensor, _ = policy.obs_to_tensor(graph_observations)
+                if use_masking:
+                    action_masks = get_action_masks(env)
+                actions, values, log_probs = policy(obs_tensor, action_masks=action_masks)
+
+            actions = actions.cpu().numpy()
+            new_obs, rewards, dones, infos = env.step(actions)
+            terminal_graph_observations = [info.pop(_TERMINAL_GRAPH_OBSERVATION, None) for info in infos]
+            new_graph_observations = cast("list[GraphData]", env.get_attr("graph_observation"))
+
+            self.num_timesteps += env.num_envs
+            callback.update_locals(locals())
+            if not callback.on_step():
+                return False
+
+            self._update_info_buffer(infos, dones)
+            n_steps += 1
+
+            if isinstance(self.action_space, spaces.Discrete):
+                actions = actions.reshape(-1, 1)
+
+            for index, done in enumerate(dones):
+                if (
+                    done
+                    and infos[index].get("terminal_observation") is not None
+                    and infos[index].get("TimeLimit.truncated", False)
+                ):
+                    terminal_graph_observation = terminal_graph_observations[index]
+                    if terminal_graph_observation is None:
+                        msg = "The GNN environment did not provide the graph for a truncated episode."
+                        raise RuntimeError(msg)
+                    terminal_obs, _ = policy.obs_to_tensor(cast("GraphData", terminal_graph_observation))
+                    with torch.no_grad():
+                        terminal_value = policy.predict_values(terminal_obs)[0]
+                    rewards[index] += self.gamma * float(terminal_value.item())
+
+            rollout_buffer.add(
+                cast("dict[str, NDArray[np.generic]]", self._last_obs),
+                actions,
+                rewards,
+                cast("NDArray[np.generic]", self._last_episode_starts),
+                values,
+                log_probs,
+                action_masks=action_masks,
+                graph_observations=graph_observations,
+            )
+            self._last_obs = new_obs
+            self._last_episode_starts = dones
+            graph_observations = new_graph_observations
+
+        with torch.no_grad():
+            final_obs, _ = policy.obs_to_tensor(graph_observations)
+            values = policy.predict_values(final_obs)
+
+        rollout_buffer.compute_returns_and_advantage(last_values=values, dones=dones)
+        callback.on_rollout_end()
+        return True
+
+    def _update_learning_rate(self, optimizers: list[Optimizer] | Optimizer) -> None:
+        current_learning_rate = self.lr_schedule(self._current_progress_remaining)
+        self.logger.record("train/learning_rate", current_learning_rate)
+        optimizer_sequence = optimizers if isinstance(optimizers, list) else (optimizers,)
+        for optimizer in optimizer_sequence:
+            for parameter_group in optimizer.param_groups:
+                parameter_group["lr"] = current_learning_rate * parameter_group.get("learning_rate_scale", 1.0)
+
+
+def _cosine_schedule(initial_value: float, minimum_factor: float) -> Schedule:
+    def schedule(progress_remaining: float) -> float:
+        completed_fraction = 1.0 - progress_remaining
+        factor = minimum_factor + (1.0 - minimum_factor) * 0.5 * (1.0 + cos(pi * completed_fraction))
+        return initial_value * factor
+
+    return schedule
+
+
+def create_gnn_model(
+    env: GNNObservationWrapper,
+    config: GNNConfig,
+    *,
+    verbose: int,
+    tensorboard_log: str,
+    seed: int | None,
+) -> GNNMaskablePPO:
+    """Create the GNN policy on top of the existing MaskablePPO implementation."""
+    return GNNMaskablePPO(
+        GNNMaskableMultiInputActorCriticPolicy,
+        env,
+        learning_rate=_cosine_schedule(config.learning_rate, config.minimum_learning_rate_factor),
+        n_steps=config.n_steps,
+        batch_size=config.batch_size,
+        n_epochs=config.n_epochs,
+        gamma=config.gamma,
+        gae_lambda=config.gae_lambda,
+        clip_range=config.clip_range,
+        clip_range_vf=config.clip_range_vf,
+        ent_coef=config.ent_coef,
+        vf_coef=config.vf_coef,
+        max_grad_norm=config.max_grad_norm,
+        target_kl=config.target_kl,
+        verbose=verbose,
+        tensorboard_log=tensorboard_log,
+        seed=seed,
+        rollout_buffer_class=GNNMaskableDictRolloutBuffer,
+        policy_kwargs={
+            "features_extractor_class": GNNFeaturesExtractor,
+            "features_extractor_kwargs": {
+                "hidden_dim": config.hidden_dim,
+                "num_conv_wo_resnet": config.num_conv_wo_resnet,
+                "num_resnet_layers": config.num_resnet_layers,
+                "dropout_p": config.dropout_p,
+                "bidirectional": config.bidirectional,
+            },
+            "net_arch": {"pi": [config.hidden_dim], "vf": [config.hidden_dim]},
+            "activation_fn": nn.GELU,
+            "optimizer_class": torch.optim.AdamW,
+            "optimizer_kwargs": {"eps": 1e-5},
+            "gnn_learning_rate": config.gnn_learning_rate,
+        },
+    )
diff --git a/src/mqt/predictor/rl/predictor.py b/src/mqt/predictor/rl/predictor.py
index 8f787d7e9..b6136dac0 100644
--- a/src/mqt/predictor/rl/predictor.py
+++ b/src/mqt/predictor/rl/predictor.py
@@ -11,6 +11,7 @@
 from __future__ import annotations
 
 import logging
+from dataclasses import replace
 from pathlib import Path
 from typing import TYPE_CHECKING
 
@@ -27,6 +28,7 @@
     from qiskit.transpiler import Target
 
     from mqt.predictor.reward import figure_of_merit
+    from mqt.predictor.rl.gnn import GNNConfig, GNNObservationWrapper
 
 
 class Predictor:
@@ -41,6 +43,8 @@ def __init__(
         max_steps: int | None = None,
         tracer_output_path: str | Path | None = None,
         mdp: MDPPolicy = "v3",
+        graph: bool = False,
+        gnn_config: GNNConfig | None = None,
     ) -> None:
         """Initializes the Predictor object.
 
@@ -53,6 +57,8 @@ def __init__(
             tracer_output_path: Path to export the compilation trace JSON. Defaults to None.
             mdp: The MDP transition policy. ``v2`` is the original strategy and
                 ``v3`` is the default.
+            graph: Whether to use the opt-in GNN policy. Defaults to False.
+            gnn_config: Configuration for the GNN policy. Defaults to the prototype training configuration.
         """
         logger.setLevel(logger_level)
 
@@ -66,7 +72,15 @@ def __init__(
         )
         self.device_name = device.description
         self.figure_of_merit = figure_of_merit
-        self.model_name = f"model_{self.figure_of_merit}_{self.device_name}_{mdp}"
+        self.graph = graph
+        if graph:
+            from mqt.predictor.rl.gnn import GNNConfig  # ruff: ignore[import-outside-top-level]
+
+            self.gnn_config = gnn_config or GNNConfig()
+        else:
+            self.gnn_config = gnn_config
+        model_prefix = "gnn" if graph else "model"
+        self.model_name = f"{model_prefix}_{self.figure_of_merit}_{self.device_name}_{mdp}"
 
     def compile_as_predicted(
         self,
@@ -99,20 +113,32 @@ def compile_as_predicted(
                 self.env.tracer_output_path = tracer_output_path
             self.env.pass_timeout = pass_timeout
 
-            trained_rl_model = load_model(self.model_name)
+            trained_rl_model = load_model(self.model_name, graph=True) if self.graph else load_model(self.model_name)
+
+            graph_env: GNNObservationWrapper | None = None
+            policy_env = self.env
+            if self.graph:
+                from mqt.predictor.rl.gnn import GNNObservationWrapper  # ruff: ignore[import-outside-top-level]
+
+                graph_env = GNNObservationWrapper(self.env)
+                policy_env = graph_env
 
-            obs, _ = self.env.reset(qc)
+            obs, _ = policy_env.reset(qc)
 
             used_compilation_passes = []
             terminated = False
             truncated = False
             while not (terminated or truncated):
-                action_masks = get_action_masks(self.env)
-                action, _ = trained_rl_model.predict(obs, action_masks=action_masks)
+                action_masks = get_action_masks(policy_env)
+                policy_observation = graph_env.graph_observation if graph_env is not None else obs
+                action, _ = trained_rl_model.predict(
+                    policy_observation,  # ty: ignore[invalid-argument-type]
+                    action_masks=action_masks,
+                )
                 action = int(action)
                 action_item = self.env.action_set[action]
                 used_compilation_passes.append(action_item.name)
-                obs, _reward_val, terminated, truncated, _info = self.env.step(action)
+                obs, _reward_val, terminated, truncated, _info = policy_env.step(action)
 
             if not self.env.error_occurred:
                 return self.env.state, used_compilation_passes
@@ -132,17 +158,20 @@ def train_model(
         test: bool = False,
         seed: int | None = None,
         pass_timeout: float | None = None,
+        iterations: int | None = None,
     ) -> None:
         """Trains all models for the given reward functions and device.
 
         Arguments:
-            timesteps: The number of timesteps to train the model. Defaults to 1000.
+            timesteps: The number of timesteps for flat-policy training. Ignored by the GNN policy. Defaults to 1000.
             verbose: The verbosity level. Defaults to 2.
             test: Whether to train the model for testing purposes. Defaults to False.
             seed: The random seed to use for reproducible training. Set to None to use true randomness.
                 Defaults to None.
             pass_timeout: Maximum duration in seconds for one compilation pass.
                 Defaults to None, which disables pass timeouts.
+            iterations: The number of GNN rollout iterations. Defaults to 1000, or 10 in test mode.
+                Ignored by the flat policy.
 
         Raises:
             ValueError: If ``pass_timeout`` is not positive.
@@ -152,7 +181,7 @@ def train_model(
             set_random_seed(seed)
         if test:
             # minimum training overhead
-            n_steps = max(timesteps, 2)
+            n_steps = 20 if self.graph else max(timesteps, 2)
             n_epochs = 1
             batch_size = n_steps
             progress_bar = False
@@ -167,30 +196,58 @@ def train_model(
         self.env.pass_timeout = pass_timeout
         try:
             logger.debug("Start training for: " + self.figure_of_merit + " on " + self.device_name)
-            model = MaskablePPO(
-                MaskableMultiInputActorCriticPolicy,
-                self.env,
-                verbose=verbose,
-                tensorboard_log=f"./{self.model_name}",
-                gamma=0.98,
-                n_steps=n_steps,
-                batch_size=batch_size,
-                n_epochs=n_epochs,
-                seed=seed,
-            )
+            if self.graph:
+                from mqt.predictor.rl.gnn import (  # ruff: ignore[import-outside-top-level]
+                    GNNObservationWrapper,
+                    create_gnn_model,
+                )
+
+                assert self.gnn_config is not None
+                effective_gnn_config = (
+                    replace(self.gnn_config, n_steps=n_steps, n_epochs=n_epochs, batch_size=batch_size)
+                    if test
+                    else self.gnn_config
+                )
+                n_steps = effective_gnn_config.n_steps
+                graph_env = GNNObservationWrapper(self.env)
+                model = create_gnn_model(
+                    graph_env,
+                    effective_gnn_config,
+                    verbose=verbose,
+                    tensorboard_log=f"./{self.model_name}",
+                    seed=seed,
+                )
+            else:
+                model = MaskablePPO(
+                    MaskableMultiInputActorCriticPolicy,
+                    self.env,
+                    verbose=verbose,
+                    tensorboard_log=f"./{self.model_name}",
+                    gamma=0.98,
+                    n_steps=n_steps,
+                    batch_size=batch_size,
+                    n_epochs=n_epochs,
+                    seed=seed,
+                )
             # Training Loop: In each iteration, the agent collects n_steps steps (rollout),
             # updates the policy for n_epochs, and then repeats the process until total_timesteps steps have been taken.
-            model.learn(total_timesteps=timesteps, progress_bar=progress_bar)
+            total_timesteps = (
+                n_steps * (iterations if iterations is not None else (10 if test else 1000))
+                if self.graph
+                else timesteps
+            )
+            model.learn(total_timesteps=total_timesteps, progress_bar=progress_bar)
             model.save(get_path_trained_model() / self.model_name)
         finally:
             self.env.pass_timeout = original_pass_timeout
 
 
-def load_model(model_name: str) -> MaskablePPO:
+def load_model(model_name: str, *, graph: bool = False) -> MaskablePPO:
     """Loads a trained model from the trained model folder.
 
     Arguments:
         model_name: The name of the model to be loaded.
+        graph: Whether the model uses the GNN policy. Defaults to False.
 
     Returns:
         The loaded model.
@@ -200,6 +257,10 @@ def load_model(model_name: str) -> MaskablePPO:
     """
     path = get_path_trained_model()
     if Path(path / (model_name + ".zip")).is_file():
+        if graph:
+            from mqt.predictor.rl.gnn import GNNMaskablePPO  # ruff: ignore[import-outside-top-level]
+
+            return GNNMaskablePPO.load(path / (model_name + ".zip"))
         return MaskablePPO.load(path / (model_name + ".zip"))
 
     error_msg = f"The RL model '{model_name}' is not trained yet. Please train the model before using it."
@@ -215,6 +276,7 @@ def rl_compile(
     tracer_output_path: str | Path | None = None,
     mdp: MDPPolicy = "v3",
     pass_timeout: float | None = None,
+    graph: bool = False,
 ) -> tuple[QuantumCircuit, list[str]]:
     """Compiles a given quantum circuit to a device optimizing for the given figure of merit.
 
@@ -229,6 +291,8 @@ def rl_compile(
             ``predictor_singleton`` is provided, its configured policy is used instead.
         pass_timeout: Maximum duration in seconds for one compilation pass.
             Defaults to None, which disables pass timeouts.
+        graph: Whether to use the opt-in GNN policy. Ignored when ``predictor_singleton`` is provided.
+            Defaults to False.
 
     Returns:
         A tuple containing the compiled quantum circuit and the compilation information. If compilation fails, False is returned.
@@ -249,6 +313,7 @@ def rl_compile(
             device=device,
             tracer_output_path=tracer_output_path,
             mdp=mdp,
+            graph=graph,
         )
         return predictor.compile_as_predicted(qc, pass_timeout=pass_timeout)
 
diff --git a/uv.lock b/uv.lock
index 0f98ecc1e..8efb4a47a 100644
--- a/uv.lock
+++ b/uv.lock
@@ -30,6 +30,146 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/8d/3f/95338030883d8c8b91223b4e21744b04d11b161a3ef117295d8241f50ab4/accessible_pygments-0.0.5-py3-none-any.whl", hash = "sha256:88ae3211e68a1d0b011504b2ffc1691feafce124b845bd072ab6f9f66f34d4b7", size = 1395903, upload-time = "2024-05-10T11:23:08.421Z" },
 ]
 
+[[package]]
+name = "aiohappyeyeballs"
+version = "2.7.1"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/ce/f4/eec0465c2f67b2664688d0240b3212d5196fd89e741df67ddb81f8d35658/aiohappyeyeballs-2.7.1.tar.gz", hash = "sha256:065665c041c42a5938ed220bdcd7230f22527fbec085e1853d2402c8a3615d9d", size = 24757, upload-time = "2026-07-01T17:11:55.501Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/71/43/1947f06babed6b3f1d7f38b0c767f52df66bfb2bc10b468c4a7de9eceff2/aiohappyeyeballs-2.7.1-py3-none-any.whl", hash = "sha256:9243213661e29250eb41368e5daa826fc017156c3b8a11440826b2e3ed376472", size = 15038, upload-time = "2026-07-01T17:11:54.055Z" },
+]
+
+[[package]]
+name = "aiohttp"
+version = "3.14.3"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "aiohappyeyeballs" },
+    { name = "aiosignal" },
+    { name = "attrs" },
+    { name = "frozenlist" },
+    { name = "multidict" },
+    { name = "propcache" },
+    { name = "typing-extensions", marker = "python_full_version < '3.13'" },
+    { name = "yarl" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/58/d9/22ce5786ac0c1653ae8b6c23bded02c1686d11f0dbb45b31ce128e0df985/aiohttp-3.14.3.tar.gz", hash = "sha256:9491196535a88924a60afd5b5f434b5b203b6cc616250878dbdb223a8f7844bc", size = 7971213, upload-time = "2026-07-23T01:57:27.037Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/f8/5c/b3e4ff8ad43a8afef9602c5e90285936da1beaea8b029016b793891f03c3/aiohttp-3.14.3-cp311-cp311-macosx_10_9_universal2.whl", hash = "sha256:e568e14940c09955aa51f4e645b6daa18a581c5dcfcd73744dcc86a856e3ced3", size = 764250, upload-time = "2026-07-23T01:52:48.525Z" },
+    { url = "https://files.pythonhosted.org/packages/0e/da/f1b384465e51449d844056b75070461da03a9a23e6c1747003695bf4172a/aiohttp-3.14.3-cp311-cp311-macosx_10_9_x86_64.whl", hash = "sha256:54cfcdee2770dac994417cbb0ee1f3eb0e7cb6b30c79bf44f2c02ff79ec5124a", size = 516281, upload-time = "2026-07-23T01:52:51.047Z" },
+    { url = "https://files.pythonhosted.org/packages/b9/3f/01264f820ee2e3712a827892b1cd6ff80f3300c1fcbffbb45714a915d47a/aiohttp-3.14.3-cp311-cp311-macosx_11_0_arm64.whl", hash = "sha256:21c016079415ed3fd676963e9793700a566d85dbbd6bfc564b9b2d209147dcc8", size = 514742, upload-time = "2026-07-23T01:52:53.779Z" },
+    { url = "https://files.pythonhosted.org/packages/9e/8d/a71c6f2db52ac1ed142b133f7feddaa6b70539c3f4de24d7e226c95b794c/aiohttp-3.14.3-cp311-cp311-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl", hash = "sha256:d6088ec9894113802bddb3c09e974929aed2c7b3a8c456219b8aab4481f1a239", size = 1780613, upload-time = "2026-07-23T01:52:56.948Z" },
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 source = { registry = "https://pypi.org/simple" }
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 version = "2026.7.0"
@@ -1425,6 +1670,11 @@ dependencies = [
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 ]
 
+[package.optional-dependencies]
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 ]
+provides-extras = ["gnn"]
 
 [package.metadata.requires-dev]
 dev = [
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