| # 🌌 QSBench: Entanglement Score Regression Guide |
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| Welcome to the **QSBench Regression Hub**. |
| This tool demonstrates how Machine Learning can predict the **degree of quantum entanglement** — measured by the **Meyer–Wallach score** — using only circuit structure and topology. |
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| ## ⚠️ Important: Demo Dataset Notice |
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| This Space uses **demo shards** of the QSBench datasets. |
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| - **Limited size:** The dataset is intentionally reduced. |
| - **Impact:** Model performance may be unstable or noisy. |
| - **Goal:** Showcase how structural features correlate with entanglement — not achieve production-level accuracy. |
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| ## 🧠 1. What is Being Predicted? |
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| The model predicts: |
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| ### `meyer_wallach` |
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| A continuous entanglement measure: |
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| - **0.0 → No entanglement** |
| - **1.0 → Maximum entanglement** |
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| This metric captures how strongly qubits are globally correlated in a circuit. |
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| ## 🧩 2. How the Model “Sees” a Circuit |
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| The model does **not simulate quantum states**. |
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| Instead, it uses **structural proxies**: |
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| ### 🔹 Topology Features |
| - `adj_density` — how densely qubits interact |
| - `adj_degree_mean` — average connectivity |
| - `adj_degree_std` — variability in connectivity |
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| → These reflect **entanglement potential** in the circuit graph. |
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| ### 🔹 Gate Structure |
| - `total_gates` |
| - `single_qubit_gates` |
| - `two_qubit_gates` |
| - `cx_count` |
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| → Two-qubit gates are the **primary drivers of entanglement**. |
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| ### 🔹 Complexity Metrics |
| - `depth` |
| - `gate_entropy` |
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| → Capture how “deep” and “structured” the circuit is. |
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| ### 🔹 QASM-derived Signals |
| - `qasm_length` |
| - `qasm_line_count` |
| - `qasm_gate_keyword_count` |
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| → Lightweight proxies for circuit complexity without parsing semantics. |
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| ## 🤖 3. Model Overview |
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| The system uses: |
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| ### Random Forest Regressor |
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| - Works well on tabular data |
| - Handles non-linear relationships |
| - Provides feature importance |
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| Pipeline includes: |
| - Missing value imputation |
| - Feature scaling |
| - Ensemble regression |
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| ## 📊 4. Understanding the Results |
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| After clicking **"Train & Evaluate"**, you get: |
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| ### A. Actual vs Predicted |
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| - Each point = one circuit |
| - Diagonal line = perfect prediction |
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| → The closer to the line → the better |
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| ### B. Residual Distribution |
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| - Shows prediction errors |
| - Centered around 0 → good model |
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| → Wide spread = uncertainty or weak features |
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| ### C. Feature Importance |
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| Top contributing features to prediction. |
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| Typical patterns: |
| - `cx_count` → strong signal |
| - `adj_density` → topology influence |
| - `depth` → complexity contribution |
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| ## 📉 5. Metrics Explained |
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| - **RMSE** — penalizes large errors |
| - **MAE** — average absolute error |
| - **R²** — goodness of fit (1 = perfect) |
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| ## 🧪 6. Experimentation Tips |
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| Try: |
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| - Removing `cx_count` → see how performance drops |
| - Using only topology → isolate structural effect |
| - Increasing trees → more stable predictions |
| - Changing test split → robustness check |
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| ## 🔬 7. Key Insight |
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| > Entanglement is not random — it is encoded in circuit structure. |
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| Even without simulation: |
| - Gate distribution |
| - Connectivity |
| - Depth |
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| …already contain enough signal to estimate entanglement. |
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| ## 🔗 8. Project Resources |
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| - 🤗 Hugging Face: https://huggingface.co/QSBench |
| - 💻 GitHub: https://github.com/QSBench |
| - 🌐 Website: https://qsbench.github.io |
