diff --git a/pyproject.toml b/pyproject.toml
index 5794216..a7a3b91 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,6 +23,17 @@ tesseract = [
 mwpf = [
     "mwpf[stim]>=0.2.12",
 ]
+mle = [
+    "gurobipy>=13.0.1",
+    "scipy>=1.14.0",
+]
+mld = [
+    "polars>=1.38.1",
+    "tqdm>=4.67.0",
+]
+sinter = [
+    "sinter>=1.16.0.dev",
+]
 
 [build-system]
 requires = ["hatchling"]
@@ -38,14 +49,19 @@ packages = ["src/bloqade"]
 dev = [
     "black>=24.10.0",
     "coverage>=7.6.4",
+    "gurobipy>=13.0.1",
     "ipython>=8.29.0",
     "isort>=5.13.2",
     "mypy>=1.13.0",
+    "polars>=1.38.1",
     "pre-commit>=4.0.1",
     "pyright>=1.1.388",
     "pytest>=8.3.3",
     "ruff>=0.7.3",
     "rust-just>=1.36.0",
+    "scipy>=1.14.0",
+    "sinter>=1.16.0.dev",
+    "tqdm>=4.67.0",
 ]
 
 [tool.isort]
diff --git a/src/bloqade/decoders/__init__.py b/src/bloqade/decoders/__init__.py
index b3a5458..6a7c4e3 100644
--- a/src/bloqade/decoders/__init__.py
+++ b/src/bloqade/decoders/__init__.py
@@ -4,6 +4,8 @@
     MWPFDecoder as MWPFDecoder,
     BpLsdDecoder as BpLsdDecoder,
     BpOsdDecoder as BpOsdDecoder,
+    TableDecoder as TableDecoder,
+    GurobiDecoder as GurobiDecoder,
     TesseractDecoder as TesseractDecoder,
     BeliefFindDecoder as BeliefFindDecoder,
 )
diff --git a/src/bloqade/decoders/_decoders/__init__.py b/src/bloqade/decoders/_decoders/__init__.py
index 3245b00..3d63af2 100644
--- a/src/bloqade/decoders/_decoders/__init__.py
+++ b/src/bloqade/decoders/_decoders/__init__.py
@@ -1,3 +1,5 @@
+from .mld import TableDecoder as TableDecoder
+from .mle import GurobiDecoder as GurobiDecoder
 from .base import BaseDecoder as BaseDecoder
 from .ldpc import (
     BpLsdDecoder as BpLsdDecoder,
diff --git a/src/bloqade/decoders/_decoders/mld/__init__.py b/src/bloqade/decoders/_decoders/mld/__init__.py
new file mode 100644
index 0000000..5328c2b
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mld/__init__.py
@@ -0,0 +1 @@
+from .decoder import TableDecoder as TableDecoder
diff --git a/src/bloqade/decoders/_decoders/mld/decoder.py b/src/bloqade/decoders/_decoders/mld/decoder.py
new file mode 100644
index 0000000..3b3bae6
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mld/decoder.py
@@ -0,0 +1,259 @@
+from __future__ import annotations
+
+import logging
+
+import stim
+import numpy as np
+import numpy.typing as npt
+
+from ..base import BaseDecoder
+from .utils import shots_to_counts, pack_boolean_array, unpack_boolean_array
+
+logger = logging.getLogger(__name__)
+
+
+class TableDecoder(BaseDecoder):
+    """Maximum likelihood decoder from detector-observable lookup table.
+
+    Builds a lookup table mapping detector syndromes to the most likely
+    observable correction, using sampled detector-observable data.
+
+    Conventions:
+        - Shot convention: each row is [D0, D1, ..., L0, L1, ...].
+        - After packing, each row is an integer with bitstring
+          representation (..., L1, L0, ..., D1, D0).
+        - Counts can be reshaped as (2**L, 2**D) where row index
+          is for logical and column for detector.
+
+    Args:
+        dem: The detector error model.
+        det_obs_counts: Array of shape ``(2**(D+L),)`` counting
+            detector-observable pattern frequencies.
+    """
+
+    def __init__(
+        self,
+        dem: stim.DetectorErrorModel,
+        det_obs_counts: np.ndarray,
+    ) -> None:
+        super().__init__(dem)
+        expected_len = 2 ** (dem.num_detectors + dem.num_observables)
+        if det_obs_counts.shape != (expected_len,):
+            raise ValueError(
+                f"det_obs_counts must have shape ({expected_len},) for "
+                f"{dem.num_detectors} detectors and {dem.num_observables} "
+                f"observables, got {det_obs_counts.shape}"
+            )
+        self._dem = dem
+        self._det_obs_counts = det_obs_counts
+        self._df = None
+        self._is_cached_df = False
+        self._maximum_likelihood_correction: np.ndarray | None = None
+        self._is_cached_correction = False
+
+    @property
+    def num_detectors(self) -> int:
+        return self._dem.num_detectors
+
+    @property
+    def num_observables(self) -> int:
+        return self._dem.num_observables
+
+    @classmethod
+    def from_stim_circuit(
+        cls,
+        circuit: stim.Circuit,
+        num_shots: int = 10**8,
+        seed: int | None = None,
+        step_size: int = 65536,
+    ) -> TableDecoder:
+        """Build a TableDecoder by sampling a stim circuit.
+
+        Args:
+            circuit: The stim circuit to sample from.
+            num_shots: Number of shots to sample.
+            seed: Optional random seed.
+            step_size: Number of shots per sampling batch.
+
+        Returns:
+            A TableDecoder with counts from the sampled shots.
+        """
+        try:
+            from tqdm import tqdm
+        except ImportError as e:
+            raise ImportError(
+                "The tqdm package is required for "
+                "TableDecoder.from_stim_circuit. "
+                'Install it via: pip install "tqdm"'
+            ) from e
+
+        dem = circuit.detector_error_model(
+            decompose_errors=False, approximate_disjoint_errors=True
+        )
+        num_observables = dem.num_observables
+        num_detectors = dem.num_detectors
+        data_len = num_observables + num_detectors
+        if data_len > 64:
+            raise ValueError(
+                f"Total data length {data_len} (detectors + observables) "
+                "exceeds 64 bits and cannot be packed into int64."
+            )
+
+        sampler = circuit.compile_detector_sampler(seed=seed)
+        det_obs_counts = np.zeros(2**data_len, dtype=int)
+
+        decoder = cls(dem=dem, det_obs_counts=det_obs_counts)
+
+        progress_bar_steps = ((num_shots - 1) // step_size) + 1
+        total_sampled = 0
+
+        logger.info("Building decoder...")
+        for _ in tqdm(range(progress_bar_steps)):
+            next_shots = min(step_size, num_shots - total_sampled)
+            total_sampled += next_shots
+            det_obs_shots = sampler.sample(
+                next_shots,
+                separate_observables=False,
+                append_observables=True,
+            )
+            if not isinstance(det_obs_shots, np.ndarray):
+                raise RuntimeError(
+                    "Expected np.ndarray from sampler.sample, "
+                    f"got {type(det_obs_shots)}"
+                )
+            decoder.update_det_obs_counts(det_obs_shots)
+        return decoder
+
+    @classmethod
+    def from_det_obs_shots(
+        cls,
+        dem: stim.DetectorErrorModel,
+        det_obs_shots: np.ndarray,
+    ) -> TableDecoder:
+        """Build a TableDecoder from pre-sampled detector-observable shots.
+
+        Args:
+            dem: The detector error model.
+            det_obs_shots: Boolean array of shape (num_shots, D+L).
+
+        Returns:
+            A TableDecoder with counts from the provided shots.
+        """
+        num_detectors = dem.num_detectors
+        num_observables = dem.num_observables
+        shape: int = 2 ** (num_detectors + num_observables)
+        decoder = cls(
+            dem=dem,
+            det_obs_counts=np.zeros(shape, dtype=int),
+        )
+        decoder.update_det_obs_counts(det_obs_shots)
+        return decoder
+
+    @property
+    def det_obs_dataframe(self):  # type: ignore[no-untyped-def]
+        """Polars DataFrame of nonzero detector-observable counts."""
+        if not self._is_cached_df:
+            try:
+                import polars as pl
+            except ImportError as e:
+                raise ImportError(
+                    "The polars package is required for "
+                    "det_obs_dataframe. "
+                    'Install it via: pip install "polars"'
+                ) from e
+
+            det_obs_counts = self._det_obs_counts
+            bins_gt_zero = det_obs_counts > 0
+            nonzero_bin_ids = np.arange(len(det_obs_counts))[bins_gt_zero]
+            keys = [f"det-{i}" for i in range(self.num_detectors)] + [
+                f"obs-{i}" for i in range(self.num_observables)
+            ]
+            cols: dict[str, np.ndarray] = {
+                key: (nonzero_bin_ids & (1 << i)).astype(bool)
+                for i, key in enumerate(keys)
+            }
+            cols["samples"] = det_obs_counts[bins_gt_zero]
+            df = pl.DataFrame(cols)
+            self._df = df
+            self._is_cached_df = True
+        return self._df
+
+    def update_det_obs_counts(self, det_obs_shots: np.ndarray) -> None:
+        """Update counts from new detector-observable shots."""
+        data_len = self.num_detectors + self.num_observables
+        if data_len != det_obs_shots.shape[1]:
+            raise ValueError(
+                f"Expected {data_len} columns (detectors + observables), "
+                f"got {det_obs_shots.shape[1]}"
+            )
+        step_counts = shots_to_counts(det_obs_shots)
+        self._det_obs_counts += step_counts
+        self._is_cached_df = False
+        self._is_cached_correction = False
+
+    def cache_correction(self) -> None:
+        """Build the maximum likelihood correction lookup table."""
+        if not self._is_cached_correction:
+            det_obs_counts = self._det_obs_counts
+            obs_counts = det_obs_counts.reshape(
+                2**self.num_observables, 2**self.num_detectors
+            )
+            self._maximum_likelihood_correction = np.argmax(obs_counts, axis=0).reshape(
+                -1
+            )
+            self._is_cached_correction = True
+
+    def _decode(self, detector_bits: npt.NDArray[np.bool_]) -> npt.NDArray[np.bool_]:
+        """Decode a single shot of detector bits."""
+        self.cache_correction()
+        assert self._maximum_likelihood_correction is not None
+        packed = pack_boolean_array(detector_bits.reshape(1, -1))
+        correction_idx = self._maximum_likelihood_correction[packed[0]]
+        return unpack_boolean_array(np.array([correction_idx]), self.num_observables)[0]
+
+    def decode(self, detector_bits: npt.NDArray[np.bool_]) -> npt.NDArray[np.bool_]:
+        """Decode detector bits (batch-optimized for 2D input).
+
+        Args:
+            detector_bits: 1D (single shot) or 2D (batch) boolean array.
+
+        Returns:
+            Observable corrections as boolean array.
+        """
+        if detector_bits.ndim == 1:
+            return self._decode(detector_bits)
+        self.cache_correction()
+        assert self._maximum_likelihood_correction is not None
+        packed_det_shots = pack_boolean_array(detector_bits)
+        packed_correction = self._maximum_likelihood_correction[packed_det_shots]
+        return unpack_boolean_array(packed_correction, self.num_observables)
+
+    def decode_det_obs_counts(self, raw_det_obs_counts: np.ndarray) -> np.ndarray:
+        """Decode raw detector-observable counts.
+
+        Args:
+            raw_det_obs_counts: Array of shape ``(2**(D+L),)``.
+
+        Returns:
+            Decoded counts array of the same shape.
+        """
+        self.cache_correction()
+        assert self._maximum_likelihood_correction is not None
+        num_detectors = self.num_detectors
+        num_observables = self.num_observables
+        expected_len = 1 << (num_detectors + num_observables)
+        if expected_len != raw_det_obs_counts.shape[0]:
+            raise ValueError(
+                f"Expected array of length {expected_len}, "
+                f"got {raw_det_obs_counts.shape[0]}"
+            )
+        appended_correction = self._maximum_likelihood_correction << num_detectors
+        labels = np.arange(1 << (num_detectors + num_observables)).reshape(
+            1 << num_observables, 1 << num_detectors
+        )
+        repeated_appended_correction = appended_correction.reshape(1, -1).repeat(
+            1 << num_observables, axis=0
+        )
+        corrected_labels = labels ^ repeated_appended_correction
+        decoded_det_obs_counts = raw_det_obs_counts[corrected_labels.reshape(-1)]
+        return decoded_det_obs_counts
diff --git a/src/bloqade/decoders/_decoders/mld/sinter_interface.py b/src/bloqade/decoders/_decoders/mld/sinter_interface.py
new file mode 100644
index 0000000..711423d
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mld/sinter_interface.py
@@ -0,0 +1,61 @@
+from __future__ import annotations
+
+import stim
+import numpy as np
+from sinter import Decoder as _SinterDecoder, CompiledDecoder as _SinterCompiledDecoder
+
+from .decoder import TableDecoder
+
+
+class _CompiledTableDecoder(_SinterCompiledDecoder):
+    """Compiled decoder wrapping TableDecoder for sinter."""
+
+    def __init__(self, decoder: TableDecoder) -> None:
+        self._decoder = decoder
+
+    def decode_shots_bit_packed(
+        self,
+        *,
+        bit_packed_detection_event_data: np.ndarray,
+    ) -> np.ndarray:
+        num_dets = self._decoder.num_detectors
+        det_shots = np.unpackbits(
+            bit_packed_detection_event_data,
+            axis=1,
+            bitorder="little",
+        )[:, :num_dets].astype(bool)
+        obs_predictions = self._decoder.decode(det_shots)
+        return np.packbits(
+            obs_predictions.astype(np.uint8),
+            axis=1,
+            bitorder="little",
+        )
+
+
+class SinterTableDecoder(_SinterDecoder):
+    """Sinter-compatible adapter for the TableDecoder (MLD).
+
+    Samples from the DEM (not a circuit) to build the lookup table,
+    since sinter only provides a DEM in compile_decoder_for_dem. This
+    is equivalent to circuit sampling when the DEM faithfully represents
+    all error mechanisms.
+
+    Args:
+        num_shots: Number of shots to sample for building the table.
+    """
+
+    num_shots: int
+
+    def __init__(self, num_shots: int = 2**26) -> None:
+        self.num_shots = num_shots
+
+    def compile_decoder_for_dem(
+        self,
+        *,
+        dem: stim.DetectorErrorModel,
+    ) -> _SinterCompiledDecoder:
+        sampler = dem.compile_sampler()
+        det_data, obs_data, _ = sampler.sample(self.num_shots)
+        det_obs_shots = np.concatenate([det_data, obs_data], axis=1)
+        decoder = TableDecoder.from_det_obs_shots(dem, det_obs_shots)
+        return _CompiledTableDecoder(decoder)
diff --git a/src/bloqade/decoders/_decoders/mld/utils.py b/src/bloqade/decoders/_decoders/mld/utils.py
new file mode 100644
index 0000000..48ea605
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mld/utils.py
@@ -0,0 +1,28 @@
+from __future__ import annotations
+
+import numpy as np
+
+
+def pack_boolean_array(arr: np.ndarray) -> np.ndarray:
+    """Pack a boolean array into int64 (each row becomes one int)."""
+    data_len = arr.shape[1]
+    return np.sum(arr << np.arange(data_len), axis=1)  # type: ignore[arg-type]
+
+
+def unpack_boolean_array(arr: np.ndarray, data_len: int) -> np.ndarray:
+    """Unpack int64 array back to boolean array."""
+    return (arr.reshape(-1, 1) & (1 << np.arange(data_len))) > 0
+
+
+def shots_to_counts(shots: np.ndarray) -> np.ndarray:
+    """Convert boolean shots array to histogram of counts."""
+    packed_shots = pack_boolean_array(shots)
+    counts = np.bincount(packed_shots, minlength=2 ** shots.shape[1])
+    return counts
+
+
+def det_obs_shots_to_counts(det_shots: np.ndarray, obs_shots: np.ndarray) -> np.ndarray:
+    """Convert detector and observable shots into combined counts."""
+    shots = np.concatenate([det_shots, obs_shots], axis=1)
+    counts = shots_to_counts(shots)
+    return counts
diff --git a/src/bloqade/decoders/_decoders/mle/__init__.py b/src/bloqade/decoders/_decoders/mle/__init__.py
new file mode 100644
index 0000000..70fa550
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mle/__init__.py
@@ -0,0 +1 @@
+from .decoder import GurobiDecoder as GurobiDecoder
diff --git a/src/bloqade/decoders/_decoders/mle/decoder.py b/src/bloqade/decoders/_decoders/mle/decoder.py
new file mode 100644
index 0000000..87de85f
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mle/decoder.py
@@ -0,0 +1,255 @@
+from __future__ import annotations
+
+from typing import ClassVar, cast
+
+import stim
+import numpy as np
+import numpy.typing as npt
+from stim import DemInstruction
+
+from ..base import BaseDecoder
+
+
+class GurobiDecoder(BaseDecoder):
+    """MLE decoder using Gurobi mixed-integer programming solver.
+
+    Finds the most likely error pattern matching an observed syndrome
+    by solving a mixed integer program via Gurobi.
+
+    Does NOT support decomposed error models with separator targets.
+    Use ``detector_error_model(decompose_errors=False)`` instead.
+
+    Args:
+        dem: The detector error model describing the error structure.
+    """
+
+    _env: ClassVar[object | None] = None
+
+    def __init__(self, dem: stim.DetectorErrorModel) -> None:
+        try:
+            import gurobipy  # noqa: F401
+        except ImportError as e:
+            raise ImportError(
+                "The gurobipy package is required for GurobiDecoder. "
+                'You can install it via: pip install "gurobipy"'
+            ) from e
+
+        try:
+            import scipy.sparse  # noqa: F401
+        except ImportError as e:
+            raise ImportError(
+                "The scipy package is required for GurobiDecoder. "
+                'You can install it via: pip install "scipy"'
+            ) from e
+
+        super().__init__(dem)
+        self._dem = dem.flattened()
+        self._check_no_separators(dem)
+
+        import scipy.sparse
+
+        # Single pass over DEM to extract weights, hyperedges, and observables
+        weights: list[float] = []
+        max_observable_index = -1
+        hyperedge_dets: list[list[int]] = []
+        hyperedge_obs: list[list[int]] = []
+
+        # Track errors with probability 1.0 (always fire)
+        certain_det_flip = np.zeros(dem.num_detectors, dtype=int)
+        certain_obs_flip = np.zeros(dem.num_observables, dtype=int)
+
+        for instruction in self._dem:  # type: ignore[union-attr]
+            if not isinstance(instruction, DemInstruction):
+                raise Exception(
+                    "The detector-error model should be already flattened. But still got DemRepeatBlock."
+                )
+            if instruction.type != "error":
+                continue
+            probability = instruction.args_copy()[0]
+            if probability == 0:
+                continue
+
+            det_targets: list[int] = []
+            obs_targets: list[int] = []
+            for t in instruction.targets_copy():
+                target = cast(stim.DemTarget, t)
+                if stim.DemTarget.is_relative_detector_id(target):
+                    det_targets.append(target.val)
+                else:
+                    obs_targets.append(target.val)
+                    if target.val > max_observable_index:
+                        max_observable_index = target.val
+
+            if probability == 1:
+                # Certain errors always fire: pre-apply their contributions
+                for d in det_targets:
+                    certain_det_flip[d] ^= 1
+                for o in obs_targets:
+                    certain_obs_flip[o] ^= 1
+            else:
+                weights.append(np.log(probability / (1 - probability)))
+                hyperedge_dets.append(det_targets)
+                hyperedge_obs.append(obs_targets)
+
+        # Build hyperedges matrix and detector vertices
+        hyperedges_matrix = scipy.sparse.lil_matrix(
+            (len(weights), dem.num_detectors), dtype=bool
+        )
+        for row_idx, det_targets in enumerate(hyperedge_dets):
+            targets_arr = np.asarray(det_targets)
+            if len(targets_arr) > 0:
+                hyperedges_matrix[row_idx, targets_arr] = 1
+
+        detector_vertices: list[list[int]] = []
+        for row in hyperedges_matrix.T:  # type: ignore[union-attr]
+            detector_vertices.append(
+                [int(x) for x in np.argwhere(row)[:, 1].flatten()]  # type: ignore[arg-type]
+            )
+
+        # Build observable indices (sized from DEM, not max seen index)
+        observable_indices: list[list[int]] = [[] for _ in range(dem.num_observables)]
+        for e_idx, obs_targets in enumerate(hyperedge_obs):
+            for obs_val in obs_targets:
+                observable_indices[obs_val].append(e_idx)
+
+        self._detector_vertices = detector_vertices
+        self._weights = weights
+        self._observable_indices = observable_indices
+        self._certain_det_flip = certain_det_flip
+        self._certain_obs_flip = certain_obs_flip
+
+    @staticmethod
+    def _check_no_separators(dem: stim.DetectorErrorModel) -> None:
+        """Raise ValueError if the DEM contains separator targets."""
+        for instruction in dem:  # type: ignore[union-attr]
+            if not isinstance(instruction, DemInstruction):
+                continue
+            if instruction.type == "error":
+                for t in instruction.targets_copy():
+                    target = cast(stim.DemTarget, t)
+                    if stim.DemTarget.is_separator(target):
+                        raise ValueError(
+                            "GurobiDecoder does not support decomposed "
+                            "error models with separator targets. Use "
+                            "detector_error_model(decompose_errors=False)"
+                            " instead."
+                        )
+
+    @property
+    def num_detectors(self) -> int:
+        return self._dem.num_detectors
+
+    @property
+    def num_observables(self) -> int:
+        return self._dem.num_observables
+
+    def weight_from_error(self, error: np.ndarray) -> np.ndarray:
+        return np.sum(error * self._weights, axis=1)
+
+    def decode_error(self, det_shots: np.ndarray, verbose: bool = False) -> np.ndarray:
+        import gurobipy as gp
+        from gurobipy import GRB
+
+        num_shots = det_shots.shape[0]
+        num_errors = len(self._weights)
+        errors = np.zeros([num_shots, num_errors], dtype=bool)
+
+        if GurobiDecoder._env is None:
+            GurobiDecoder._env = gp.Env()
+        env = GurobiDecoder._env
+        env.setParam("OutputFlag", 1 if verbose else 0)  # type: ignore[union-attr]
+
+        weights = self._weights
+        detector_vertices = self._detector_vertices
+        # Pre-apply certain errors (prob=1.0) to the syndrome
+        det_shots = det_shots.astype(int) ^ self._certain_det_flip
+
+        for d, detector_shot in enumerate(det_shots):
+            m = gp.Model("mip1", env=env)
+            error_variables: list[gp.Var] = []
+            detector_variables: list[gp.Var] = []
+            objective: gp.LinExpr = gp.LinExpr(0)
+
+            for i, w in enumerate(weights):
+                error_variables.append(m.addVar(vtype=GRB.BINARY, name="e" + str(i)))
+                objective += w * error_variables[i]
+            m.setObjective(objective, GRB.MAXIMIZE)
+
+            for i, dv in enumerate(detector_vertices):
+                detector_variables.append(
+                    m.addVar(
+                        vtype=GRB.INTEGER,
+                        name="h" + str(i),
+                        ub=len(dv),
+                        lb=0,
+                    )
+                )
+                constraint: gp.LinExpr = gp.LinExpr(0)
+                for j in dv:
+                    constraint += error_variables[j]
+                constraint -= 2 * detector_variables[i]
+                m.addConstr(constraint == detector_shot[i], name="c" + str(i))
+
+            m.optimize()
+            if m.status != GRB.OPTIMAL:
+                if verbose:
+                    print("Did not find optimal solution", m.status)
+                m.close()
+                raise RuntimeError(
+                    f"Gurobi did not find an optimal solution. Status: {m.status}"
+                )
+            error = np.round(
+                np.array([e.X for e in error_variables]), decimals=0
+            ).astype(bool)
+            errors[d, :] = error
+            m.close()
+        return errors
+
+    def logical_from_error(self, errors: np.ndarray) -> np.ndarray:
+        num_shots = errors.shape[0]
+        observable_indices = self._observable_indices
+        # Start from certain error contributions (prob=1.0 errors always fire)
+        logicals = np.tile(self._certain_obs_flip, (num_shots, 1)).astype(float)
+        for i, error in enumerate(errors):
+            for o, observable_index in enumerate(observable_indices):
+                if len(observable_index) > 0:
+                    logicals[i, o] = (
+                        logicals[i, o] + np.sum(error[np.array(observable_index)])
+                    ) % 2
+        return logicals.astype(bool)
+
+    def _decode(self, detector_bits: npt.NDArray[np.bool_]) -> npt.NDArray[np.bool_]:
+        """Decode a single shot of detector bits."""
+        det_2d = detector_bits.reshape(1, -1)
+        errors = self.decode_error(det_2d)
+        obs = self.logical_from_error(errors)
+        return obs[0].astype(np.bool_)
+
+    def decode(
+        self,
+        detector_bits: npt.NDArray[np.bool_],
+        verbose: bool = False,
+        return_weights: bool = False,
+    ) -> npt.NDArray[np.bool_] | tuple[npt.NDArray[np.bool_], np.ndarray]:
+        """Decode detector bits, optionally returning weights.
+
+        Args:
+            detector_bits: 1D (single shot) or 2D (batch) boolean array.
+            verbose: If True, print Gurobi solver output.
+            return_weights: If True, return (observable_corrections, weights).
+
+        Returns:
+            Observable corrections, or (corrections, weights) tuple.
+        """
+        if detector_bits.ndim == 1:
+            det_2d = detector_bits.reshape(1, -1)
+            errors = self.decode_error(det_2d, verbose)
+            obs = self.logical_from_error(errors)
+            if return_weights:
+                return obs[0].astype(np.bool_), self.weight_from_error(errors)
+            return obs[0].astype(np.bool_)
+        decoded_errors = self.decode_error(detector_bits, verbose)
+        decoded_obs = self.logical_from_error(decoded_errors)
+        if return_weights:
+            return decoded_obs, self.weight_from_error(decoded_errors)
+        return decoded_obs
diff --git a/src/bloqade/decoders/_decoders/mle/sinter_interface.py b/src/bloqade/decoders/_decoders/mle/sinter_interface.py
new file mode 100644
index 0000000..bbdac72
--- /dev/null
+++ b/src/bloqade/decoders/_decoders/mle/sinter_interface.py
@@ -0,0 +1,45 @@
+from __future__ import annotations
+
+import stim
+import numpy as np
+from sinter import Decoder as _SinterDecoder, CompiledDecoder as _SinterCompiledDecoder
+
+from .decoder import GurobiDecoder
+
+
+class _CompiledGurobiDecoder(_SinterCompiledDecoder):
+    """Compiled decoder wrapping GurobiDecoder for sinter."""
+
+    def __init__(self, decoder: GurobiDecoder) -> None:
+        self._decoder = decoder
+
+    def decode_shots_bit_packed(
+        self,
+        *,
+        bit_packed_detection_event_data: np.ndarray,
+    ) -> np.ndarray:
+        num_dets = self._decoder.num_detectors
+        det_shots = np.unpackbits(
+            bit_packed_detection_event_data,
+            axis=1,
+            bitorder="little",
+        )[:, :num_dets].astype(bool)
+        obs_predictions = self._decoder.decode(det_shots)
+        assert isinstance(obs_predictions, np.ndarray)
+        return np.packbits(
+            obs_predictions.astype(np.uint8),
+            axis=1,
+            bitorder="little",
+        )
+
+
+class SinterGurobiDecoder(_SinterDecoder):
+    """Sinter-compatible adapter for the GurobiDecoder (MLE)."""
+
+    def compile_decoder_for_dem(
+        self,
+        *,
+        dem: stim.DetectorErrorModel,
+    ) -> _SinterCompiledDecoder:
+        decoder = GurobiDecoder(dem)
+        return _CompiledGurobiDecoder(decoder)
diff --git a/test/decoders/conftest.py b/test/decoders/conftest.py
new file mode 100644
index 0000000..9ce9f57
--- /dev/null
+++ b/test/decoders/conftest.py
@@ -0,0 +1,33 @@
+"""Shared test helpers for sinter decoder tests."""
+
+import stim
+import numpy as np
+
+
+def simple_dem() -> stim.DetectorErrorModel:
+    return stim.DetectorErrorModel("""
+        error(0.1) D0 L0
+        error(0.1) D1 L0
+        """)
+
+
+def repetition_circuit() -> stim.Circuit:
+    return stim.Circuit("""
+        R 0 1 2
+        X_ERROR(0.1) 0 1 2
+        MZZ 0 1
+        DETECTOR rec[-1]
+        MZZ 1 2
+        DETECTOR rec[-1]
+        M 0 1 2
+        OBSERVABLE_INCLUDE(0) rec[-1] rec[-2] rec[-3]
+    """)
+
+
+def pack_dets(det_shots: np.ndarray) -> np.ndarray:
+    return np.packbits(det_shots.astype(np.uint8), axis=1, bitorder="little")
+
+
+def unpack_obs(packed_obs: np.ndarray, num_obs: int) -> np.ndarray:
+    unpacked = np.unpackbits(packed_obs, axis=1, bitorder="little")
+    return unpacked[:, :num_obs].astype(bool)
diff --git a/test/decoders/test_decoders.py b/test/decoders/test_decoders.py
index 8bd59ef..5d324dc 100644
--- a/test/decoders/test_decoders.py
+++ b/test/decoders/test_decoders.py
@@ -5,6 +5,7 @@
     MWPFDecoder,
     BpLsdDecoder,
     BpOsdDecoder,
+    GurobiDecoder,
     TesseractDecoder,
     BeliefFindDecoder,
 )
@@ -23,12 +24,15 @@
     two_logical_expected_decoded_obs,
 )
 
+# TableDecoder is excluded: it requires a det_obs_counts argument
+# and cannot be constructed from a DEM alone.
 DECODERS = [
     TesseractDecoder,
     BeliefFindDecoder,
     BpLsdDecoder,
     BpOsdDecoder,
     MWPFDecoder,
+    GurobiDecoder,
 ]
 
 TEST_CASES = [
diff --git a/test/decoders/test_mld.py b/test/decoders/test_mld.py
new file mode 100644
index 0000000..de67684
--- /dev/null
+++ b/test/decoders/test_mld.py
@@ -0,0 +1,228 @@
+import math
+
+import stim
+import numpy as np
+import pytest
+import sinter
+
+from bloqade.decoders import TableDecoder
+from bloqade.decoders._decoders.mld.utils import (
+    shots_to_counts,
+    pack_boolean_array,
+    unpack_boolean_array,
+    det_obs_shots_to_counts,
+)
+from bloqade.decoders._decoders.mld.sinter_interface import SinterTableDecoder
+
+from .conftest import pack_dets, simple_dem, unpack_obs, repetition_circuit
+
+
+def test_pack_unpack():
+    bm = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=bool)
+    packed = pack_boolean_array(bm)
+    unpacked = unpack_boolean_array(packed, bm.shape[1])
+    assert np.array_equal(bm, unpacked)
+
+
+def test_pack_boolean_array_values():
+    arr = np.array([[1, 0, 1], [0, 0, 0], [1, 1, 1]], dtype=bool)
+    packed = pack_boolean_array(arr)
+    assert np.array_equal(packed, np.array([5, 0, 7]))
+
+
+def test_unpack_boolean_array_values():
+    packed = np.array([5, 0, 7])
+    unpacked = unpack_boolean_array(packed, 3)
+    expected = np.array(
+        [[True, False, True], [False, False, False], [True, True, True]]
+    )
+    assert np.array_equal(unpacked, expected)
+
+
+def test_pack_unpack_single_bit():
+    arr = np.array([[0], [1]], dtype=bool)
+    packed = pack_boolean_array(arr)
+    unpacked = unpack_boolean_array(packed, 1)
+    assert np.array_equal(arr, unpacked)
+
+
+def test_shots_to_counts():
+    shots = np.array([[0, 0], [0, 1], [0, 1], [1, 0]], dtype=bool)
+    counts = shots_to_counts(shots)
+    assert np.array_equal(counts, np.array([1, 1, 2, 0]))
+
+
+def test_det_obs_shots_to_counts():
+    det_shots = np.array([[0, 0], [1, 0]], dtype=bool)
+    obs_shots = np.array([[0], [1]], dtype=bool)
+    counts = det_obs_shots_to_counts(det_shots, obs_shots)
+    expected = np.zeros(8, dtype=int)
+    expected[0] = 1  # (0,0,0) -> 0b000 = 0
+    expected[5] = 1  # (1,0,1) -> 0b101 = 5
+    assert np.array_equal(counts, expected)
+
+
+def test_mld_repetition():
+    circ = stim.Circuit("""
+        R 0 1 2
+        X_ERROR(0.1) 0 1 2
+        MZZ 0 1
+        DETECTOR rec[-1]
+        MZZ 1 2
+        DETECTOR rec[-1]
+        M 0 1 2
+        OBSERVABLE_INCLUDE(0) rec[-1] rec[-2] rec[-3]
+    """)
+    decoder = TableDecoder.from_stim_circuit(circ, 10000)
+    assert decoder.num_detectors == 2
+    assert decoder.num_observables == 1
+    det_shots = np.array([[1, 0], [1, 1], [0, 1], [0, 0]])
+    obs_shots = np.array([[1], [1], [1], [0]])
+    correction = decoder.decode(det_shots)
+    assert np.array_equal(correction, obs_shots)
+
+
+def test_decode_obs_det_counts():
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\nerror(0.1) D1 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([81, 0, 0, 1, 0, 9, 9, 0]))
+    assert np.array_equal(
+        decoder.decode(np.array([[0, 0], [0, 1], [1, 0], [1, 1]])),
+        np.array([[0], [1], [1], [0]]),
+    )
+    raw_det_obs_counts = np.arange(8)
+    decoded_det_obs_counts = decoder.decode_det_obs_counts(raw_det_obs_counts)
+    assert np.array_equal(decoded_det_obs_counts, np.array([0, 5, 6, 3, 4, 1, 2, 7]))
+
+
+def test_no_error_syndrome():
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\nerror(0.1) D1 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([81, 0, 0, 1, 0, 9, 9, 0]))
+    result = decoder.decode(np.array([[0, 0]]))
+    assert np.array_equal(result, np.array([[0]]))
+
+
+def test_all_detectors_fired():
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\nerror(0.1) D1 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([81, 0, 0, 1, 0, 9, 9, 0]))
+    result = decoder.decode(np.array([[1, 1]]))
+    assert result.shape == (1, 1)
+
+
+def test_single_shot_decode():
+    """Test _decode (single-shot) via the BaseDecoder interface."""
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\nerror(0.1) D1 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([81, 0, 0, 1, 0, 9, 9, 0]))
+    result = decoder.decode(np.array([0, 1], dtype=bool))
+    assert result.ndim == 1
+    assert np.array_equal(result, np.array([True]))
+
+
+# --- SinterTableDecoder tests ---
+
+
+def _repetition_dem():
+    return repetition_circuit().detector_error_model(
+        decompose_errors=False, approximate_disjoint_errors=True
+    )
+
+
+def test_sinter_table_is_sinter_decoder():
+    decoder = SinterTableDecoder()
+    assert isinstance(decoder, sinter.Decoder)
+
+
+def test_sinter_table_compile_returns_compiled_decoder():
+    dem = simple_dem()
+    decoder = SinterTableDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+    assert isinstance(compiled, sinter.CompiledDecoder)
+
+
+def test_sinter_table_decode_shape_and_dtype():
+    dem = _repetition_dem()
+    decoder = SinterTableDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.array([[1, 0], [0, 1], [0, 0]], dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+
+    num_obs_bytes = math.ceil(dem.num_observables / 8)
+    assert result.dtype == np.uint8
+    assert result.shape == (3, num_obs_bytes)
+
+
+def test_sinter_table_decode_correctness():
+    dem = _repetition_dem()
+    decoder = SinterTableDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.array([[1, 0], [1, 1], [0, 1], [0, 0]], dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+    obs_predictions = unpack_obs(result, dem.num_observables)
+
+    expected = np.array([[True], [True], [True], [False]])
+    assert np.array_equal(obs_predictions, expected)
+
+
+def test_sinter_table_no_error_syndrome():
+    dem = simple_dem()
+    decoder = SinterTableDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.zeros((1, 2), dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+    obs_predictions = unpack_obs(result, dem.num_observables)
+
+    assert np.array_equal(obs_predictions, np.array([[False]]))
+
+
+@pytest.mark.slow
+def test_sinter_collect_table():
+    circuit = repetition_circuit()
+    tasks = [
+        sinter.Task(
+            circuit=circuit,
+            decoder="table_mld",
+            json_metadata={"d": 3},
+        ),
+    ]
+    stats = sinter.collect(
+        num_workers=1,
+        tasks=tasks,
+        custom_decoders={"table_mld": SinterTableDecoder(num_shots=100000)},
+        max_shots=100,
+    )
+    assert len(stats) == 1
+    assert stats[0].shots == 100
+    assert stats[0].errors <= stats[0].shots
+    assert stats[0].errors < 50
+
+
+def test_update_det_obs_counts_wrong_columns():
+    """Wrong column count raises ValueError."""
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([10, 0, 0, 1]))
+    wrong_shots = np.array([[0, 0, 0]], dtype=bool)  # 3 cols, expected 2
+    with pytest.raises(ValueError, match="columns"):
+        decoder.update_det_obs_counts(wrong_shots)
+
+
+def test_decode_det_obs_counts_wrong_length():
+    """Wrong array length raises ValueError."""
+    dem = stim.DetectorErrorModel("error(0.1) D0 L0\n")
+    decoder = TableDecoder(dem, det_obs_counts=np.array([10, 0, 0, 1]))
+    wrong_counts = np.array([1, 2, 3])  # length 3, expected 4
+    with pytest.raises(ValueError, match="length"):
+        decoder.decode_det_obs_counts(wrong_counts)
diff --git a/test/decoders/test_mle.py b/test/decoders/test_mle.py
new file mode 100644
index 0000000..a312a7a
--- /dev/null
+++ b/test/decoders/test_mle.py
@@ -0,0 +1,301 @@
+import math
+
+import stim
+import numpy as np
+import pytest
+import sinter
+
+from bloqade.decoders import GurobiDecoder
+from bloqade.decoders._decoders.mle.sinter_interface import SinterGurobiDecoder
+
+from .conftest import pack_dets, simple_dem, unpack_obs, repetition_circuit
+
+
+def regular_dem():
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D9 D0 L0
+        error(0.1) D0 D1
+        error(0.1) D1 D2
+        error(0.1) D2 D3
+        error(0.1) D3 D4
+        error(0.1) D4 D5
+        error(0.1) D5 D6
+        error(0.1) D6 D7
+        error(0.1) D7 D8
+        error(0.1) D8 D9
+        """)
+    return dem
+
+
+def regular_samples():
+    det_shots = np.array(
+        [[1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]],
+        bool,
+    )
+    obs_shots = np.array([[1], [0]], bool)
+    return det_shots, obs_shots
+
+
+def test_regular():
+    dem = regular_dem()
+    det_shots, obs_shots = regular_samples()
+    decoder = GurobiDecoder(dem)
+    result = decoder.decode(det_shots)
+    assert (obs_shots == result).all()
+
+
+def test_hyper():
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D9 D0 D1 L0
+        error(0.1) D0 D1
+        error(0.1) D1 D2
+        error(0.1) D2 D3
+        error(0.1) D3 D4
+        error(0.1) D4 D5
+        error(0.1) D5 D6
+        error(0.1) D6 D7
+        error(0.1) D7 D8
+        error(0.1) D8 D9
+        """)
+    det_shots = np.array(
+        [[1, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0]],
+        bool,
+    )
+    obs_shots = np.array([[1], [0]], bool)
+    decoder = GurobiDecoder(dem)
+    result = decoder.decode(det_shots)
+    assert (obs_shots == result).all()
+
+
+def test_decode_returns_weights():
+    dem = regular_dem()
+    det_shots, _ = regular_samples()
+    decoder = GurobiDecoder(dem)
+    obs, weights = decoder.decode(det_shots, return_weights=True)
+    assert obs.shape == (2, 1)
+    assert weights.shape == (2,)
+    assert np.all(weights < 0)
+
+
+def test_decode_error_shape():
+    dem = regular_dem()
+    det_shots, _ = regular_samples()
+    decoder = GurobiDecoder(dem)
+    errors = decoder.decode_error(det_shots)
+    assert errors.shape == (2, 10)
+    assert errors.dtype == bool
+
+
+def test_logical_from_error():
+    dem = regular_dem()
+    det_shots, obs_shots = regular_samples()
+    decoder = GurobiDecoder(dem)
+    errors = decoder.decode_error(det_shots)
+    logicals = decoder.logical_from_error(errors)
+    assert np.array_equal(logicals, obs_shots)
+
+
+def test_no_error_syndrome():
+    dem = regular_dem()
+    decoder = GurobiDecoder(dem)
+    det_shots = np.zeros((1, 10), dtype=bool)
+    result = decoder.decode(det_shots)
+    assert np.array_equal(result, np.array([[False]]))
+
+
+def test_single_shot_decode():
+    """Test _decode (single-shot) via the BaseDecoder interface."""
+    dem = regular_dem()
+    det_shots = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 1], dtype=bool)
+    decoder = GurobiDecoder(dem)
+    result = decoder.decode(det_shots)
+    assert result.ndim == 1
+    assert np.array_equal(result, np.array([True]))
+
+
+# --- SinterGurobiDecoder tests ---
+
+
+def test_sinter_gurobi_is_sinter_decoder():
+    decoder = SinterGurobiDecoder()
+    assert isinstance(decoder, sinter.Decoder)
+
+
+def test_sinter_gurobi_compile_returns_compiled_decoder():
+    dem = simple_dem()
+    decoder = SinterGurobiDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+    assert isinstance(compiled, sinter.CompiledDecoder)
+
+
+def test_sinter_gurobi_decode_shape_and_dtype():
+    dem = simple_dem()
+    decoder = SinterGurobiDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.array([[1, 0], [0, 1], [0, 0]], dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+
+    num_obs_bytes = math.ceil(dem.num_observables / 8)
+    assert result.dtype == np.uint8
+    assert result.shape == (3, num_obs_bytes)
+
+
+def test_sinter_gurobi_decode_correctness():
+    dem = simple_dem()
+    decoder = SinterGurobiDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.array([[1, 0], [0, 1], [0, 0]], dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+    obs_predictions = unpack_obs(result, dem.num_observables)
+
+    expected = np.array([[True], [True], [False]])
+    assert np.array_equal(obs_predictions, expected)
+
+
+def test_sinter_gurobi_no_error_syndrome():
+    dem = simple_dem()
+    decoder = SinterGurobiDecoder()
+    compiled = decoder.compile_decoder_for_dem(dem=dem)
+
+    det_shots = np.zeros((1, 2), dtype=bool)
+    packed_dets = pack_dets(det_shots)
+
+    result = compiled.decode_shots_bit_packed(
+        bit_packed_detection_event_data=packed_dets
+    )
+    obs_predictions = unpack_obs(result, dem.num_observables)
+
+    assert np.array_equal(obs_predictions, np.array([[False]]))
+
+
+@pytest.mark.slow
+def test_sinter_collect_gurobi():
+    circuit = repetition_circuit()
+    tasks = [
+        sinter.Task(
+            circuit=circuit,
+            decoder="gurobi_mle",
+            json_metadata={"d": 3},
+        ),
+    ]
+    stats = sinter.collect(
+        num_workers=1,
+        tasks=tasks,
+        custom_decoders={"gurobi_mle": SinterGurobiDecoder()},
+        max_shots=100,
+    )
+    assert len(stats) == 1
+    assert stats[0].shots == 100
+    assert stats[0].errors <= stats[0].shots
+    assert stats[0].errors < 50
+
+
+def test_single_shot_decode_with_weights():
+    """Single-shot decode with return_weights=True."""
+    dem = regular_dem()
+    det_shots = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 1], dtype=bool)
+    decoder = GurobiDecoder(dem)
+    obs, weights = decoder.decode(det_shots, return_weights=True)
+    assert obs.ndim == 1
+    assert np.array_equal(obs, np.array([True]))
+    assert isinstance(weights, np.ndarray)
+
+
+def test_separator_targets_rejected():
+    """DEM with separator targets raises ValueError."""
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D0 ^ D1 L0
+        """)
+    with pytest.raises(ValueError, match="separator"):
+        GurobiDecoder(dem)
+
+
+def test_multi_observable_dem():
+    """DEM with multiple observables."""
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D0 L0
+        error(0.1) D1 L1
+        """)
+    decoder = GurobiDecoder(dem)
+    assert decoder.num_observables == 2
+    det_shots = np.array([[1, 0], [0, 1]], dtype=bool)
+    result = decoder.decode(det_shots)
+    assert result.shape == (2, 2)
+
+
+def test_repeat_block_decode_correctness():
+    """DEM with repeat block produces correct decode results after flattening."""
+    dem = stim.DetectorErrorModel("""
+        repeat 2 {
+            error(0.1) D0 D1 L0
+        }
+        error(0.1) D1 D2
+        """)
+    decoder = GurobiDecoder(dem)
+    assert decoder.num_detectors == 3
+    # Syndrome that triggers first error
+    det_shots = np.array([[1, 1, 0]], dtype=bool)
+    result = decoder.decode(det_shots)
+    assert result.shape == (1, 1)
+    assert result[0, 0]  # L0 should be flipped
+
+
+def test_observable_indices_align_with_weights():
+    """observable_indices must reference weight-list indices, not raw DEM positions.
+
+    A DEM with detector coordinate annotations has non-error DemInstructions mixed
+    in. A naive enumerate()-based counter would increment for those instructions,
+    causing observable_indices to reference wrong (out-of-bounds) weight indices.
+    """
+    dem = stim.DetectorErrorModel("""
+        detector(0, 0) D0
+        detector(1, 0) D1
+        error(0.1) D0 L0
+        error(0.1) D0 D1
+        """)
+    decoder = GurobiDecoder(dem)
+    # Verify decoding works correctly (no index errors)
+    det_shots = np.array([[1, 0]], dtype=bool)
+    result = decoder.decode(det_shots)
+    assert result.shape == (1, 1)
+    assert result[0, 0]  # L0 should be flipped
+
+
+def test_prob_zero_error_skipped():
+    """error(0.0) is silently dropped and does not affect decoding."""
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D0 D1 L0
+        error(0.0) D1 D2 L0
+        error(0.05) D0 D2
+        """)
+    decoder = GurobiDecoder(dem)
+    # Syndrome [0, 1, 1] matches D1 D2 which is only the prob=0 error.
+    # Since that error is dropped, the solver sees it as noise.
+    result = decoder.decode(np.array([[0, 1, 1]], dtype=bool))
+    assert result.shape == (1, 1)
+
+
+def test_prob_one_error_pre_applied():
+    """error(1.0) always fires and is pre-applied to the syndrome."""
+    dem = stim.DetectorErrorModel("""
+        error(0.1) D0 D1 L0
+        error(1.0) D1 D2 L0
+        error(0.05) D0 D2
+        """)
+    decoder = GurobiDecoder(dem)
+    # The certain error flips D1 and D2, so syndrome [0,1,1] after
+    # pre-application becomes [0,0,0] (no errors to solve for).
+    result = decoder.decode(np.array([[0, 1, 1]], dtype=bool))
+    assert result.shape == (1, 1)
+    # The certain error flips L0, so the observable should be True
+    assert result[0, 0]
diff --git a/test/test_imports.py b/test/test_imports.py
index 83935d7..aeb68b1 100644
--- a/test/test_imports.py
+++ b/test/test_imports.py
@@ -7,6 +7,8 @@ def test_decoder_exports():
     assert hasattr(decoders, "BpLsdDecoder")
     assert hasattr(decoders, "BpOsdDecoder")
     assert hasattr(decoders, "MWPFDecoder")
+    assert hasattr(decoders, "GurobiDecoder")
+    assert hasattr(decoders, "TableDecoder")
     assert hasattr(decoders, "dialects")
 
     assert hasattr(decoders, "Detector")
diff --git a/uv.lock b/uv.lock
index 89a5bc1..20cb4e2 100644
--- a/uv.lock
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+    { url = "https://files.pythonhosted.org/packages/71/cc/18245721fa7747065ab478316c7fea7c74777d07f37ae60db2e84f8172e8/beartype-0.22.9-py3-none-any.whl", hash = "sha256:d16c9bbc61ea14637596c5f6fbff2ee99cbe3573e46a716401734ef50c3060c2", size = 1333658 },
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-version = "0.5.0.dev0"
+version = "0.6.0.dev0"
 source = { editable = "." }
 dependencies = [
     { name = "beliefmatching" },
@@ -97,9 +96,21 @@ dependencies = [
 ]
 
 [package.optional-dependencies]
+mld = [
+    { name = "polars" },
+    { name = "tqdm" },
+]
+mle = [
+    { name = "gurobipy" },
+    { name = "scipy", version = "1.15.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
+    { name = "scipy", version = "1.17.0", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+]
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 ]
+sinter = [
+    { name = "sinter" },
+]
 tesseract = [
     { name = "tesseract-decoder" },
 ]
@@ -108,50 +119,65 @@ tesseract = [
 dev = [
     { name = "black" },
     { name = "coverage" },
+    { name = "gurobipy" },
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     { name = "isort" },
     { name = "mypy" },
+    { name = "polars" },
     { name = "pre-commit" },
     { name = "pyright" },
     { name = "pytest" },
     { name = "ruff" },
     { name = "rust-just" },
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+    { name = "sinter" },
+    { name = "tqdm" },
 ]
 
 [package.metadata]
 requires-dist = [
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+    { name = "gurobipy", marker = "extra == 'mle'", specifier = ">=13.0.1" },
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     { name = "mwpf", extras = ["stim"], marker = "extra == 'mwpf'", specifier = ">=0.2.12" },
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+    { name = "scipy", marker = "extra == 'mle'", specifier = ">=1.14.0" },
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     { name = "tesseract-decoder", marker = "extra == 'tesseract'", specifier = ">=0.1.1.dev20260109233451" },
+    { name = "tqdm", marker = "extra == 'mld'", specifier = ">=4.67.0" },
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     { name = "isort", specifier = ">=5.13.2" },
     { name = "mypy", specifier = ">=1.13.0" },
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     { name = "ruff", specifier = ">=0.7.3" },
     { name = "rust-just", specifier = ">=1.36.0" },
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+    { name = "sinter", specifier = ">=1.16.0.dev0" },
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