fusion_qec_fix.patch

--- a/IMPLEMENTATION_SUMMARY.md
+++ b/IMPLEMENTATION_SUMMARY.md
@@
 ## QEC Benchmark Report
 The QEC benchmark report includes the following sections:
 ### 1. Logical Error Rate Table
 | Physical Error | Steane | Surface | Reed-Muller | Fusion-QEC (Photonic) |
 |----------------|---------|----------|--------------|------------------------|
 | 1.00e-06 | 1.00e-10 | 1.00e-12 | 1.00e-09 | - |
 | 3.00e-06 | 3.00e-10 | 3.00e-12 | 3.00e-09 | - |
 | 1.00e-05 | 1.00e-09 | 1.00e-11 | 1.00e-08 | - |
 | 3.00e-05 | 3.00e-09 | 3.00e-11 | 3.00e-08 | - |
 | 1.00e-02 | 1.00e-06 | 1.00e-08 | 1.00e-05 | 5.00e-07 |
+
+*Fusion-QEC values based on photonic fusion-based architectures (e.g., PsiQuantum, Xanadu); not reflective of IonQ’s hardware.*
@@
 ### 1.2 Pseudo-thresholds
 Steane [7,1,3]: Pseudo-threshold ≈ 1.42e-02  
 Fusion-QEC (Photonic): Pseudo-threshold ≈ 1.00e-02  
 Surface / Reed-Muller: No breakeven threshold detected.

-### 1.2 Decoder Strategies
+### 1.3 Decoder Strategies
 | Code | Decoder Type | Notes |
 |------|---------------|-------|
 | Steane | Standard stabilizer lookup | Classical decoders only |
 | Surface | Minimum-weight perfect matching (MWPM) | Hardware agnostic |
 | Reed-Muller | Recursive syndrome decoding | Requires large ancilla overhead |
 | Fusion-QEC (Photonic) | Fusion-based MBQC on cluster states; tolerant to loss and probabilistic gates |
@@
-### 1.4 Notes on IonQ and Fusion-QEC
+### 1.4 Notes on IonQ and Fusion-QEC
 Note: IonQ uses **Clifford Noise Reduction (CliNR)** for trapped-ion QEC, achieving ~2x logical error reduction with 3:1 qubit and 2:1 gate overhead.  
 IonQ integrates **photonic interconnects** for scaling/networking but does **not** use fusion-based QEC.  
 Fusion-QEC described here refers to photonic architectures (e.g. PsiQuantum, Xanadu), leveraging fusion gates on entangled resource states.