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README.md

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----
-license: apache-2.0
----
+---
+license: apache-2.0
+tags:
+  - quantum-computing
+  - quantum-machine-learning
+  - qiskit
+  - quantum-neural-network
+  - qnn
+  - classification
+  - hardware-efficient-ansatz
+  - nisq
+  - variational-quantum-algorithm
+datasets:
+  - two_moons
+metrics:
+  - accuracy
+library_name: qiskit
+pipeline_tag: tabular-classification
+---
+
+# Quantum Neural Network - Two Moons Classification
+
+<div align="center">
+
+<div align="center">
+    <img src="https://cdn-uploads.huggingface.co/production/uploads/67329d3f69fded92d56ab41a/X7Hq7qSzx0TIM43duGFHP.jpeg" width="50%" alt="twomoons">
+</div>
+
+**A 2-qubit Quantum Neural Network (QNN) trained for binary classification on the Two Moons dataset**
+
+[![Qiskit](https://img.shields.io/badge/Qiskit-1.0.0-purple.svg)](https://qiskit.org/)
+[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](LICENSE)
+[![Python](https://img.shields.io/badge/Python-3.8%2B-blue.svg)](https://www.python.org/)
+
+</div>
+
+## 📊 Model Overview
+
+This is a **Quantum Neural Network (QNN)** designed for binary classification tasks, demonstrating quantum machine learning on real quantum hardware. The model uses a hardware-efficient ansatz with 2 qubits and has been tested on IBM Quantum's `ibm_fez` backend.
+
+### Key Features
+
+- 🔬 **Pure Quantum Model**: Uses quantum circuits for feature encoding and classification
+- ⚡ **Hardware-Efficient**: Optimized for NISQ-era quantum devices
+- 🎯 **Binary Classification**: Trained on the Two Moons dataset
+- 🌐 **IBM Quantum**: Compatible with real quantum hardware
+- 📦 **Easy to Use**: Simple inference API with pre-trained weights
+
+## 🏗️ Model Architecture
+
+### Specifications
+
+| Feature | Value |
+|---------|-------|
+| **Qubits** | 2 |
+| **Circuit Depth** | 4 layers |
+| **Total Parameters** | 6 (2 input + 4 trainable) |
+| **Trainable Parameters** | 4 |
+| **Gates** | 6× Ry + 1× CNOT |
+| **Entanglement** | Linear topology |
+| **Ansatz Type** | Hardware-Efficient |
+| **Backend** | IBM Quantum (ibm_fez) |
+
+### Circuit Diagram
+
+```
+     ┌──────────┐┌──────────┐     ┌──────────┐
+q_0: ┤ Ry(x[0]) ├┤ Ry(w[0]) ├──■──┤ Ry(w[2]) ├
+     ├──────────┤├──────────┤┌─┴─┐├──────────┤
+q_1: ┤ Ry(x[1]) ├┤ Ry(w[1]) ├┤ X ├┤ Ry(w[3]) ├
+     └──────────┘└──────────┘└───┘└──────────┘
+```
+
+### Layer Breakdown
+
+1. **Encoding Layer** (`Ry(x[0])`, `Ry(x[1])`): Encodes 2D classical data into quantum states
+2. **Variational Layer 1** (`Ry(w[0])`, `Ry(w[1])`): First trainable rotation gates
+3. **Entanglement Layer** (`CNOT`): Creates quantum correlations between qubits
+4. **Variational Layer 2** (`Ry(w[2])`, `Ry(w[3])`): Second trainable rotation gates
+5. **Measurement**: Parity measurement on both qubits for classification
+
+## 🚀 Quick Start
+
+### Installation
+
+```bash
+pip install qiskit qiskit-machine-learning numpy huggingface-hub
+```
+
+### Basic Usage
+
+```python
+from huggingface_hub import hf_hub_download
+from qiskit import qpy
+import numpy as np
+
+# Download model files
+circuit_path = hf_hub_download(
+    repo_id="squ11z1/Two-Moons",
+    filename="circuit.qpy"
+)
+weights_path = hf_hub_download(
+    repo_id="squ11z1/Two-Moons",
+    filename="weights.npy"
+)
+
+# Load quantum circuit
+with open(circuit_path, 'rb') as f:
+    circuit = qpy.load(f)[0]
+
+# Load trained weights
+weights = np.load(weights_path)
+
+print(f"Loaded QNN with {circuit.num_qubits} qubits")
+print(f"Trained weights: {weights}")
+```
+
+### Inference Example
+
+```python
+from qiskit.circuit import ParameterVector
+from qiskit_machine_learning.neural_networks import SamplerQNN
+from qiskit_machine_learning.algorithms.classifiers import NeuralNetworkClassifier
+from qiskit.primitives import StatevectorSampler as Sampler
+
+# Load test data
+X_test = np.load(hf_hub_download(
+    repo_id="squ11z1/TwoMoons-2Q",
+    filename="X_test.npy"
+))
+
+# Setup parameters
+input_params = [p for p in circuit.parameters if p.name.startswith('x')]
+weight_params = [p for p in circuit.parameters if p.name.startswith('w')]
+
+# Parity interpretation function
+def parity(x):
+    """Convert measurement to binary classification (0 or 1)"""
+    return bin(x).count("1") % 2
+
+# Create QNN
+sampler = Sampler()
+qnn = SamplerQNN(
+    circuit=circuit,
+    input_params=input_params,
+    weight_params=weight_params,
+    interpret=parity,
+    output_shape=2,
+    sampler=sampler
+)
+
+# Create classifier with pre-trained weights
+classifier = NeuralNetworkClassifier(
+    neural_network=qnn,
+    optimizer=None  # Weights already trained
+)
+classifier._fit_result = type('obj', (object,), {'x': weights})
+
+# Make predictions
+predictions = classifier.predict(X_test)
+print(f"Predictions: {predictions}")
+```
+
+### Using the Helper Module
+
+```python
+from qnn_inference import load_qnn_model, create_qnn_classifier
+import numpy as np
+
+# Load model
+circuit, weights = load_qnn_model(repo_id="squ11z1/Two-Moons")
+
+# Create classifier
+classifier = create_qnn_classifier(circuit, weights)
+
+# Predict on new data
+X_new = np.array([[0.5, 0.2], [-0.5, 0.5]])
+predictions = classifier.predict(X_new)
+print(f"Predictions: {predictions}")
+```
+
+## 📈 Training Details
+
+### Dataset
+
+- **Name:** Two Moons (sklearn.datasets.make_moons)
+- **Type:** Synthetic binary classification dataset
+- **Features:** 2D coordinates (x, y)
+- **Classes:** 2 (crescent-shaped clusters)
+- **Train samples:** 8
+- **Test samples:** 4
+- **Total:** 12 samples
+
+### Training Configuration
+
+- **Optimizer:** COBYLA (Constrained Optimization BY Linear Approximation)
+- **Loss Function:** Cross-entropy
+- **Epochs:** Variable (convergence-based)
+- **Training Backend:** IBM Quantum (ibm_fez)
+- **Testing Backend:** IBM Quantum (ibm_fez)
+
+### Performance Metrics
+
+| Metric | Value | Notes |
+|--------|-------|-------|
+| **Test Accuracy** | 0-75% | Varies by noise and seed |
+| **Train Accuracy** | ~87.5% | On 8 training samples |
+| **Baseline (Random)** | 50% | Random guessing |
+| **Classical MLP** | ~100% | For comparison |
+
+**Note:** The low test accuracy (0% in the visualization) is typical for:
+- Small training dataset (only 8 samples)
+- Quantum noise from real hardware
+- Limited model capacity (2 qubits)
+- Early-stage NISQ device limitations
+
+This is a **proof-of-concept** model demonstrating quantum ML workflows, not production-ready accuracy.
+
+## 🔬 Technical Deep Dive
+
+### Why Hardware-Efficient Ansatz?
+
+The hardware-efficient ansatz is chosen to:
+
+1. **Minimize gate count**: Fewer gates = less noise accumulation
+2. **Use native gates**: Ry and CNOT are native to IBM Quantum hardware
+3. **Avoid compilation overhead**: Circuit runs directly on hardware
+4. **Reduce circuit depth**: Depth 4 is shallow enough for NISQ devices
+
+### Barren Plateau Mitigation
+
+This architecture avoids the barren plateau problem through:
+
+- ✅ **Small qubit count** (n=2): Gradient variance ∝ 1/2^n = 1/4 (good!)
+- ✅ **Shallow depth** (4 layers): Limits exponential gradient decay
+- ✅ **Local connectivity**: Linear entanglement structure
+- ✅ **Parameter efficiency**: Only 4 trainable parameters
+
+**Expected gradient variance:** `Var[∂L/∂θ] ≈ 0.25`
+
+### Quantum Advantage?
+
+For this small problem, **no quantum advantage** is expected or claimed. However, this model serves as:
+
+1. **Educational tool**: Demonstrates QML concepts
+2. **Research platform**: Tests quantum algorithms on real hardware
+3. **Proof of concept**: Shows end-to-end quantum workflow
+4. **Benchmark**: Compares quantum vs classical performance
+
+### Measurement Strategy
+
+The model uses **parity measurement**:
+
+```python
+def parity(x):
+    """
+    Measures both qubits and computes parity.
+    
+    Example:
+    - |00⟩ → 0 (even parity) → Class 0
+    - |01⟩ → 1 (odd parity)  → Class 1
+    - |10⟩ → 1 (odd parity)  → Class 1
+    - |11⟩ → 0 (even parity) → Class 0
+    """
+    return bin(x).count("1") % 2
+```
+
+This creates a **nonlinear decision boundary** in feature space.
+
+## 📁 Repository Contents
+
+```
+.
+├── README.md                 # This file
+├── circuit.qpy               # Quantum circuit (Qiskit QPY format, 712 bytes)
+├── weights.npy               # Trained weights (4 parameters, 160 bytes)
+├── config.json               # Model configuration metadata
+├── qnn_inference.py          # Helper functions for loading and inference
+├── requirements.txt          # Python dependencies
+├── X_train.npy               # Training input data (8 samples)
+├── X_test.npy                # Test input data (4 samples)
+├── y_train.npy               # Training labels
+├── y_test.npy                # Test labels
+└── visualization_english.png # Model performance visualization
+```
+
+## 🎯 Use Cases
+
+### Educational
+- Learn quantum machine learning fundamentals
+- Understand variational quantum algorithms
+- Explore quantum circuit design
+
+### Research
+- Benchmark quantum vs classical models
+- Study quantum noise effects on ML
+- Test new quantum ML algorithms
+- Investigate NISQ-era limitations
+
+### Development
+- Template for quantum ML projects
+- Starting point for larger QNN models
+- Integration example for Hugging Face + Qiskit
+
+## ⚠️ Limitations
+
+### Model Limitations
+- **Small dataset**: Only 12 samples total (not scalable)
+- **Low capacity**: 2 qubits limit expressiveness
+- **Binary only**: Can't handle multi-class problems as-is
+- **Fixed input**: Requires exactly 2D input features
+
+### Quantum Hardware Limitations
+- **NISQ noise**: Quantum errors degrade performance
+- **Decoherence**: Qubits lose quantum state over time
+- **Gate errors**: Imperfect quantum operations
+- **Limited connectivity**: Hardware topology constraints
+
+### Practical Limitations
+- **Slow inference**: Quantum circuits are slower than classical NNs
+- **Requires quantum access**: Needs IBM Quantum account for hardware runs
+- **No gradients**: Can't fine-tune (weights are pre-trained)
+- **Stochastic**: Results vary due to quantum sampling
+
+## 🔮 Future Improvements
+
+### Immediate Next Steps
+- [ ] Increase dataset size to 100+ samples
+- [ ] Add data augmentation for better generalization
+- [ ] Test on multiple quantum backends
+- [ ] Implement error mitigation techniques
+
+### Long-term Goals
+- [ ] Scale to 4-16 qubits for more complex patterns
+- [ ] Multi-class classification support
+- [ ] Hybrid quantum-classical architecture
+- [ ] Deploy on IBM Quantum Runtime
+- [ ] Compare with classical ML benchmarks
+
+## 📚 Citation
+
+If you use this model in your research, please cite:
+
+```bibtex
+@misc{qnn-two-moons-2025,
+  author = {squ11z1},
+  title = {Quantum Neural Network for Two Moons Classification},
+  year = {2025},
+  publisher = {Hugging Face},
+  howpublished = {\url{https://huggingface.co/squ11z1/Two-Moons}},
+  note = {2-qubit QNN with hardware-efficient ansatz}
+}
+```
+
+## 📖 References
+
+### Quantum Machine Learning
+- [Qiskit Machine Learning Documentation](https://qiskit.org/ecosystem/machine-learning/)
+- [Quantum Neural Networks (arXiv:1802.06002)](https://arxiv.org/abs/1802.06002)
+- [Supervised learning with quantum enhanced feature spaces (Nature 2019)](https://www.nature.com/articles/s41586-019-0980-2)
+
+### Variational Algorithms
+- [Variational Quantum Algorithms (arXiv:2012.09265)](https://arxiv.org/abs/2012.09265)
+- [Hardware-efficient variational quantum eigensolver (arXiv:1704.05018)](https://arxiv.org/abs/1704.05018)
+
+### Barren Plateaus
+- [Barren plateaus in quantum neural network training (Nature 2018)](https://www.nature.com/articles/s41467-018-07090-4)
+- [The effect of data encoding on barren plateaus (arXiv:2008.08605)](https://arxiv.org/abs/2008.08605)
+
+### IBM Quantum
+- [IBM Quantum Platform](https://quantum.ibm.com/)
+- [Qiskit Documentation](https://docs.quantum.ibm.com/)
+
+## 🤝 Contributing
+
+This is an experimental research model. Contributions welcome!
+
+### How to Contribute
+1. Test the model on different datasets
+2. Report issues or bugs
+3. Suggest architectural improvements
+4. Share your results and findings
+
+Open an issue or discussion on the [Hugging Face model page](https://huggingface.co/squ11z1/Two-Moons).
+
+## 📄 License
+
+**Apache License 2.0**
+
+This model and all associated code are released under the Apache 2.0 license. You are free to use, modify, and distribute this model for any purpose, including commercial applications.
+
+See [LICENSE](LICENSE) for full details.
+
+---
+
+<div align="center">
+
+**Built with ❤️ using Qiskit and IBM Quantum**
+
+ *Like this model if you find it useful!* 
+ 
+
+</div>
+