TensorBFS
diff --git a/‎.github/workflows/docs.yml‎
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diff --git a/‎Makefile‎
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diff --git a/‎datasets/README.md‎
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@@ -0,0 +1,28 @@
+name: Deploy Documentation
+
+on:
+  push:
+    branches:
+      - main
+  workflow_dispatch:
+
+permissions:
+  contents: write
+
+jobs:
+  deploy:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.12'
+
+      - name: Install dependencies
+        run: |
+          pip install mkdocs-material mkdocstrings[python] pymdown-extensions
+
+      - name: Deploy to GitHub Pages
+        run: mkdocs gh-deploy --force
@@ -38,4 +38,4 @@ uv.lock
 *.blg
 *.fdb_latexmk
 *.synctex.gz
-note/belief_propagation_qec_plan.pdf
+note/belief_propagation_qec_plan.pdf.claude/settings.local.json
@@ -1,13 +1,17 @@
-.PHONY: help install setup test test-cov generate-dataset clean
+.PHONY: help install setup test test-cov generate-dataset generate-dem generate-syndromes docs docs-serve clean
 
 help:
 	@echo "Available targets:"
-	@echo "  install          - Install uv package manager"
-	@echo "  setup            - Set up development environment with uv"
-	@echo "  generate-dataset - Generate noisy circuit dataset"
-	@echo "  test             - Run tests"
-	@echo "  test-cov         - Run tests with coverage report"
-	@echo "  clean            - Remove generated files and caches"
+	@echo "  install            - Install uv package manager"
+	@echo "  setup              - Set up development environment with uv"
+	@echo "  generate-dataset   - Generate noisy circuit dataset"
+	@echo "  generate-dem       - Generate detector error models"
+	@echo "  generate-syndromes - Generate syndrome database (1000 shots)"
+	@echo "  test               - Run tests"
+	@echo "  test-cov           - Run tests with coverage report"
+	@echo "  docs               - Build documentation"
+	@echo "  docs-serve         - Serve documentation locally"
+	@echo "  clean              - Remove generated files and caches"
 
 install:
 	@command -v uv >/dev/null 2>&1 || { \
@@ -21,12 +25,26 @@ setup: install
 generate-dataset:
 	uv run generate-noisy-circuits --distance 3 --p 0.01 --rounds 3 5 7 --task z --output datasets/noisy_circuits
 
+generate-dem:
+	uv run generate-noisy-circuits --distance 3 --p 0.01 --rounds 3 5 7 --task z --output datasets/noisy_circuits --generate-dem
+
+generate-syndromes:
+	uv run generate-noisy-circuits --distance 3 --p 0.01 --rounds 3 5 7 --task z --output datasets/noisy_circuits --generate-syndromes 1000
+
 test:
 	uv run pytest
 
 test-cov:
 	uv run pytest --cov=bpdecoderplus --cov-report=html --cov-report=term
 
+docs:
+	pip install mkdocs-material mkdocstrings[python] pymdown-extensions
+	mkdocs build
+
+docs-serve:
+	pip install mkdocs-material mkdocstrings[python] pymdown-extensions
+	mkdocs serve
+
 clean:
 	rm -rf .pytest_cache
 	rm -rf __pycache__
 
@@ -0,0 +1,222 @@
+# Noisy Circuit Dataset (Surface Code, d=3)
+
+Circuit-level surface-code memory experiments generated with Stim for **Belief Propagation (BP) decoding** demonstrations.
+
+## Dataset Organization
+
+The dataset is organized into subdirectories by file type:
+
+```
+datasets/
+├── circuits/     # Noisy quantum circuits (.stim)
+├── dems/         # Detector error models (.dem)
+├── uais/         # UAI format for probabilistic inference (.uai)
+└── syndromes/    # Syndrome databases (.npz)
+```
+
+## Overview
+
+| Parameter | Value |
+|-----------|-------|
+| Code | Rotated surface code |
+| Distance | d = 3 |
+| Noise model | i.i.d. depolarizing |
+| Error rate | p = 0.01 |
+| Task | Z-memory experiment |
+| Rounds | 3, 5, 7 |
+
+### Noise Application Points
+- Clifford gates (`after_clifford_depolarization`)
+- Data qubits between rounds (`before_round_data_depolarization`)
+- Resets (`after_reset_flip_probability`)
+- Measurements (`before_measure_flip_probability`)
+
+## Files
+
+| File | Description |
+|------|-------------|
+| `sc_d3_r3_p0010_z.stim` | 3 rounds, p=0.01, Z-memory |
+| `sc_d3_r5_p0010_z.stim` | 5 rounds, p=0.01, Z-memory |
+| `sc_d3_r7_p0010_z.stim` | 7 rounds, p=0.01, Z-memory |
+
+## Using This Dataset for BP Decoding
+
+### Step 1: Load Circuit and Extract Detector Error Model (DEM)
+
+The Detector Error Model is the key input for BP decoding. It describes which errors trigger which detectors.
+
+```python
+import stim
+import numpy as np
+
+# Load circuit
+circuit = stim.Circuit.from_file("datasets/circuits/sc_d3_r3_p0010_z.stim")
+
+# Extract DEM - this is what BP needs
+dem = circuit.detector_error_model(decompose_errors=True)
+print(f"Detectors: {dem.num_detectors}")      # 24
+print(f"Error mechanisms: {dem.num_errors}")  # 286
+print(f"Observables: {dem.num_observables}")  # 1
+```
+
+### Step 2: Build Parity Check Matrix H
+
+BP operates on the parity check matrix where `H[i,j] = 1` means error `j` triggers detector `i`.
+
+```python
+def build_parity_check_matrix(dem):
+    """Convert DEM to parity check matrix H and prior probabilities."""
+    errors = []
+    for inst in dem.flattened():
+        if inst.type == 'error':
+            prob = inst.args_copy()[0]
+            dets = [t.val for t in inst.targets_copy() if t.is_relative_detector_id()]
+            obs = [t.val for t in inst.targets_copy() if t.is_logical_observable_id()]
+            errors.append({'prob': prob, 'detectors': dets, 'observables': obs})
+    
+    n_detectors = dem.num_detectors
+    n_errors = len(errors)
+    
+    # Parity check matrix
+    H = np.zeros((n_detectors, n_errors), dtype=np.uint8)
+    # Prior error probabilities (for BP initialization)
+    priors = np.zeros(n_errors)
+    # Which errors flip the logical observable
+    obs_flip = np.zeros(n_errors, dtype=np.uint8)
+    
+    for j, e in enumerate(errors):
+        priors[j] = e['prob']
+        for d in e['detectors']:
+            H[d, j] = 1
+        if e['observables']:
+            obs_flip[j] = 1
+    
+    return H, priors, obs_flip
+
+H, priors, obs_flip = build_parity_check_matrix(dem)
+print(f"H shape: {H.shape}")  # (24, 286)
+```
+
+### Step 3: Sample Syndromes (Detection Events)
+
+```python
+# Compile sampler
+sampler = circuit.compile_detector_sampler()
+
+# Sample detection events + observable flip
+n_shots = 1000
+samples = sampler.sample(n_shots, append_observables=True)
+
+# Split into syndrome and observable
+syndromes = samples[:, :-1]           # shape: (n_shots, n_detectors)
+actual_obs_flips = samples[:, -1]     # shape: (n_shots,)
+
+print(f"Syndrome shape: {syndromes.shape}")
+print(f"Example syndrome: {syndromes[0]}")
+```
+
+### Step 4: BP Decoding (Pseudocode)
+
+```python
+def bp_decode(H, syndrome, priors, max_iter=50, damping=0.5):
+    """
+    Belief Propagation decoder (min-sum variant).
+    
+    Args:
+        H: Parity check matrix (n_detectors, n_errors)
+        syndrome: Detection events (n_detectors,)
+        priors: Prior error probabilities (n_errors,)
+        max_iter: Maximum BP iterations
+        damping: Message damping factor
+    
+    Returns:
+        estimated_errors: Most likely error pattern (n_errors,)
+        soft_output: Log-likelihood ratios (n_errors,)
+    """
+    n_checks, n_vars = H.shape
+    
+    # Initialize LLRs from priors: LLR = log((1-p)/p)
+    llr_prior = np.log((1 - priors) / priors)
+    
+    # Messages: check-to-variable and variable-to-check
+    # ... BP message passing iterations ...
+    
+    # Hard decision
+    estimated_errors = (soft_output < 0).astype(int)
+    
+    return estimated_errors, soft_output
+
+# Decode each syndrome
+for i in range(n_shots):
+    syndrome = syndromes[i]
+    estimated_errors, _ = bp_decode(H, syndrome, priors)
+    
+    # Predict observable flip
+    predicted_obs_flip = np.dot(estimated_errors, obs_flip) % 2
+    
+    # Check if decoding succeeded
+    success = (predicted_obs_flip == actual_obs_flips[i])
+```
+
+### Step 5: Evaluate Decoder Performance
+
+After decoding, compare predicted vs actual observable flips to measure logical error rate.
+
+```python
+def evaluate_decoder(decoder_fn, circuit, n_shots=10000):
+    """Evaluate decoder logical error rate."""
+    dem = circuit.detector_error_model(decompose_errors=True)
+    H, priors, obs_flip = build_parity_check_matrix(dem)
+    
+    sampler = circuit.compile_detector_sampler()
+    samples = sampler.sample(n_shots, append_observables=True)
+    syndromes = samples[:, :-1]
+    actual_obs = samples[:, -1]
+    
+    errors = 0
+    for i in range(n_shots):
+        est_errors, _ = decoder_fn(H, syndromes[i], priors)
+        pred_obs = np.dot(est_errors, obs_flip) % 2
+        if pred_obs != actual_obs[i]:
+            errors += 1
+    
+    return errors / n_shots
+
+# logical_error_rate = evaluate_decoder(bp_decode, circuit)
+```
+
+## Regenerating the Dataset
+
+```bash
+# Install the package with uv
+uv sync
+
+# Generate circuits using the CLI
+python -m bpdecoderplus.cli \
+  --distance 3 \
+  --p 0.01 \
+  --rounds 3 5 7 \
+  --task z \
+  --generate-dem \
+  --generate-uai \
+  --generate-syndromes 10000
+```
+
+## Extending the Dataset
+
+```bash
+# Different error rates
+python -m bpdecoderplus.cli --p 0.005 --rounds 3 5 7 --generate-dem --generate-uai
+
+# Different distances
+python -m bpdecoderplus.cli --distance 5 --rounds 5 7 9 --generate-dem --generate-uai
+
+# X-memory experiment
+python -m bpdecoderplus.cli --task x --rounds 3 5 7 --generate-dem --generate-uai
+```
+
+## References
+
+- [Stim Documentation](https://github.com/quantumlib/Stim)
+- [BP+OSD Decoder Paper](https://arxiv.org/abs/2005.07016)
+- [Surface Code Decoding Review](https://quantum-journal.org/papers/q-2024-10-10-1498/)