QSOLKCB / QEC

Deterministic Structural Analysis & Adaptive Control System
for LDPC / QLDPC Tanner Graphs

---

QEC is a deterministic research framework for studying:

• belief propagation (BP) dynamics
• Tanner graph structure
• spectral instability
• phase behavior
• adaptive control of decoding strategies

It functions as:

• 🧠 A deterministic analysis system
• 🌌 A phase-space reconstruction engine
• ⚙️ An adaptive control loop (v98+)

---

🧠 What QEC Actually Is (Now)

QEC is not just a simulator.

It is a:

Deterministic Structural + Adaptive System for Decoding Dynamics

The system operates as a closed loop:

metrics → attractor → strategy → evaluation → adaptation → memory

Everything is:

• deterministic
• explainable
• reproducible
• externally controlled (decoder untouched)

---

🚀 Core Capabilities (v99)

---

1. Structural Diagnostics (Foundation)

• BP trajectory analysis
• attractor / basin detection
• oscillation & metastability metrics
• free-energy landscape analysis

---

2. Spectral Analysis (Graph Physics Layer)

• non-backtracking spectrum
• eigenvector localization (IPR)
• trapping-set candidate detection
• spectral instability metrics

---

3. Phase & Regime Analysis

• deterministic phase diagrams
• transition detection
• regime segmentation
• phase boundary metrics

---

4. Strategy System (Decision Layer)

• deterministic strategy scoring
• regime-aware selection
• structured transition logic

---

5. Evaluation Framework

• before/after comparison
• outcome classification
• improvement scoring

---

6. Adaptive Layer (v99)

• trajectory-based feedback
• global bias adjustment
• recency-weighted performance

---

7. Strategy Memory (v99.1)

• bounded per-strategy memory
• specialization via historical performance
• deterministic biasing (no randomness)

---

🌌 Phase-Space + Control System

QEC reconstructs both:

Phase Structure

• regimes
• boundaries
• degeneracy
• transitions

Behavioral Dynamics

• strategy effectiveness
• adaptation patterns
• system response

---

⚙️ System Architecture

Tanner Graph ↓ Diagnostics (metrics) ↓ Attractor Classification ↓ Strategy Selection ↓ Evaluation ↓ Adaptation ↓ Memory ↓ System Behavior

---

🔁 Determinism Guarantees

QEC enforces strict reproducibility:

• no hidden randomness
• deterministic ordering everywhere
• canonical JSON outputs
• stable multi-key ranking
• explicit seeded RNG only

import numpy as np
np.random.RandomState(seed)

If it cannot be reproduced byte-for-byte, it is not a result.

🔬 Invariant Framework

QEC is built on explicit, testable invariants.

Example:

QSOL-BP-INV-001
URW(min-sum, ρ = 1.0) ≡ baseline min-sum

Properties:

analytically justified
empirically validated
bitwise exact
📊 Research Applications

QEC enables:

decoding phase diagram reconstruction
spectral instability analysis
trapping-set identification
deterministic inverse design
strategy optimization without randomness
reproducible computational experiments
## What This System Is (v100)

QEC is a **deterministic adaptive control system** for belief propagation decoding dynamics on LDPC/QLDPC Tanner graphs.

- **No randomness** — all outputs are bitwise reproducible
- **No neural networks** — closed-form multiplicative scoring
- **No stochastic exploration** — measurement-driven adaptation
- **Bounded feedback** — all signals and modulation factors are bounded
- **Formally defined** — invariants, API contracts, and reproducible experiments

The full adaptive pipeline:

S₀ → metrics → attractor → strategy → transition → evaluation → adaptation → S₁

For formal definitions, see:
- [SYSTEM.md](SYSTEM.md) — Formal system definition
- [THEORY.md](THEORY.md) — Theoretical grounding
- [INVARIANTS.md](INVARIANTS.md) — System invariants
- [EXPERIMENTS.md](EXPERIMENTS.md) — Reproducible experiments
- [API_CONTRACT.md](API_CONTRACT.md) — Stable public interfaces

📖 Documentation

- [INSTALL.md](INSTALL.md) — Setup and installation
- [QUICKSTART.md](QUICKSTART.md) — One-command demo
- [USAGE_GUIDE.md](USAGE_GUIDE.md) — Workflow and entry points
- [ARCHITECTURE.md](ARCHITECTURE.md) — System architecture and design

⚡ Quick Start
Install
pip install -e .
Run the demo
python scripts/qec_demo.py
Minimal diagnostic
from qec.diagnostics.bp_dynamics import compute_bp_dynamics_metrics

out = compute_bp_dynamics_metrics(llr_trace, energy)
print(out["metrics"])
🧠 Design Philosophy

Small is beautiful.
Determinism is essential.
Structure over heuristics.
Measurement before control.

📚 Citation

Trent Slade — QSOL-IMC
QEC: Deterministic Structural Analysis & Adaptive Control Framework

ORCID: https://orcid.org/0009-0002-4515-9237

👤 Author

Trent Slade
QSOL-IMC


---