Probabilistic Quantum Reasoner

A quantum-classical hybrid reasoning engine for uncertainty-aware AI inference, fusing quantum probabilistic graphical models (QPGMs) with classical probabilistic logic.

🎯 Overview

The Probabilistic Quantum Reasoner implements a novel approach to AI reasoning by encoding knowledge using quantum amplitude distributions over Hilbert space, modeling uncertainty through entanglement and non-commutative conditional graphs, and enabling hybrid Quantum Bayesian Networks with causal, counterfactual, and abductive reasoning capabilities.

🧩 Key Features

• Quantum Bayesian Networks: Hybrid classical-quantum probabilistic graphical models
• Quantum Belief Propagation: Unitary message passing with amplitude-weighted inference
• Causal Quantum Reasoning: Do-calculus analog for quantum intervention logic
• Multiple Backends: Support for Qiskit, PennyLane, and classical simulation
• Uncertainty Modeling: Entanglement-based uncertainty representation
• Counterfactual Reasoning: Quantum counterfactuals using unitary interventions

🚀 Quick Start

Installation

pip install probabilistic-quantum-reasoner

For development with extra features:

pip install probabilistic-quantum-reasoner[dev,docs,extras]

Basic Usage

from probabilistic_quantum_reasoner import QuantumBayesianNetwork
from probabilistic_quantum_reasoner.backends import QiskitBackend

# Create a quantum Bayesian network
qbn = QuantumBayesianNetwork(backend=QiskitBackend())

# Add quantum and classical nodes
weather = qbn.add_quantum_node("weather", ["sunny", "rainy"])
mood = qbn.add_stochastic_node("mood", ["happy", "sad"])

# Create entangled relationship
qbn.add_edge(weather, mood)
qbn.entangle([weather, mood])

# Perform quantum inference
result = qbn.infer(evidence={"weather": "sunny"})
print(f"Mood probabilities: {result}")

# Quantum intervention (do-calculus)
intervention_result = qbn.intervene("weather", "rainy")
print(f"Mood under intervention: {intervention_result}")

🧬 Mathematical Foundation

The library implements quantum probabilistic reasoning using:

• Tensor Product Spaces: Joint state representation as |ψ⟩ = Σᵢⱼ αᵢⱼ|iⱼ⟩
• Amplitude Manipulation: Via Kraus operators and parameterized unitaries
• Density Matrix Operations: Mixed state inference through partial tracing
• Non-commutative Conditional Probability: P_Q(A|B) ≠ P_Q(B|A) in general

📖 Documentation

• API Reference
• Architecture Guide
• Examples & Tutorials

🧪 Examples

Quantum XOR Reasoning

# Create entangled XOR gate reasoning
qbn = QuantumBayesianNetwork()
a = qbn.add_quantum_node("A", [0, 1])
b = qbn.add_quantum_node("B", [0, 1])
xor = qbn.add_quantum_node("XOR", [0, 1])

qbn.add_quantum_xor_relationship(a, b, xor)
result = qbn.infer(evidence={"A": 1, "B": 0})

Weather-Mood Causal Graph

# Hybrid classical-quantum causal modeling
from probabilistic_quantum_reasoner.examples import WeatherMoodExample

example = WeatherMoodExample()
causal_effect = example.estimate_causal_effect("weather", "mood")
counterfactual = example.counterfactual_query("What if it was sunny?")

🛠️ Architecture

probabilistic_quantum_reasoner/
├── core/                    # Core network structures
│   ├── network.py          # QuantumBayesianNetwork
│   ├── nodes.py            # Quantum/Stochastic/Hybrid nodes
│   └── operators.py        # Quantum operators and gates
├── inference/              # Reasoning engines
│   ├── engine.py           # Main inference engine
│   ├── causal.py           # Causal reasoning
│   ├── belief_propagation.py
│   └── variational.py      # Variational quantum inference
├── backends/               # Backend implementations
│   ├── qiskit_backend.py
│   ├── pennylane_backend.py
│   └── simulator.py
└── examples/               # Example implementations

🔬 Research Applications

• AGI Inference Scaffolds: Uncertainty-aware reasoning for autonomous systems
• Quantum Explainable AI (Q-XAI): Interpretable quantum decision making
• Counterfactual Analysis: "What-if" scenarios in quantum superposition
• Epistemic Uncertainty Modeling: Non-classical uncertainty representation

🤝 Contributing

We welcome contributions! Please see our Contributing Guidelines for details.

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Commit your changes (git commit -m 'Add amazing feature')
4. Push to the branch (git push origin feature/amazing-feature)
5. Open a Pull Request

📝 License

This project is licensed under the MIT License - see the LICENSE file for details.

📚 Citation

If you use this library in your research, please cite:

@software{bajpai2025quantum,
  title={Probabilistic Quantum Reasoner: A Hybrid Quantum-Classical Reasoning Engine},
  author={Bajpai, Krishna},
  year={2025},
  url={https://github.com/krish567366/probabilistic-quantum-reasoner}
}

👨‍💻 Author

Krishna Bajpai

• Email: bajpaikrishna715@gmail.com
• GitHub: @krish567366

🙏 Acknowledgments

• Quantum computing community for foundational algorithms
• Classical probabilistic reasoning research
• Open source quantum computing frameworks (Qiskit, PennyLane)