Quantum Entangled Knowledge Graphs (QE-KGR)

🚀 World's First Open-Source Library for Quantum-Enhanced Knowledge Graph Reasoning

Revolutionizing knowledge representation through quantum entanglement principle

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🧠 What is QE-KGR?

QE-KGR (Quantum Entangled Knowledge Graph Reasoning) represents a paradigm shift in how we model and reason over complex knowledge. By applying quantum mechanics principles to graph theory, QE-KGR enables unprecedented capabilities in knowledge discovery and reasoning.

🌟 Key Innovations

• 🔗 Quantum Entanglement: Nodes and edges exist in quantum superposition, enabling non-classical correlations
• ⚛️ Hilbert Space Embeddings: Knowledge represented in complex vector spaces with quantum phases
• 🌊 Interference Patterns: Constructive and destructive interference for enhanced reasoning
• 🎯 Quantum Walks: Graph traversal using quantum mechanical principles
• 🔍 Grover-enhanced Search: Quantum amplitude amplification for subgraph discovery

🚀 Quick Start

Installation

pip install quantum-entangled-knowledge-graphs

Basic Example

import qekgr
from qekgr import EntangledGraph, QuantumInference, EntangledQueryEngine

# Create a quantum knowledge graph
graph = EntangledGraph(hilbert_dim=4)

# Add quantum nodes
alice = graph.add_quantum_node("Alice", state="physicist", 
                              metadata={"field": "quantum_computing"})
bob = graph.add_quantum_node("Bob", state="researcher",
                            metadata={"field": "ai"})

# Create entangled edge with superposed relations
graph.add_entangled_edge(alice, bob, 
                        relations=["collaborates", "co_authors"],
                        amplitudes=[0.8, 0.6])

# Quantum reasoning
inference = QuantumInference(graph)
walk_result = inference.quantum_walk(start_node="Alice", steps=10)

# Natural language queries
query_engine = EntangledQueryEngine(graph)
results = query_engine.query("Who might Alice collaborate with in AI research?")

print(f"Query confidence: {results[0].confidence_score:.3f}")
print(f"Answer path: {' -> '.join(results[0].reasoning_path)}")

🏗️ Architecture Overview

graph TB
    A[EntangledGraph] --> B[QuantumInference]
    A --> C[EntangledQueryEngine]
    A --> D[QuantumGraphVisualizer]
    B --> E[Quantum Walks]
    B --> F[Grover Search]
    B --> G[Interference Patterns]
    C --> H[Natural Language Processing]
    C --> I[Hilbert Space Projection]
    C --> J[Context Switching]
    D --> K[2D/3D Visualization]
    D --> L[Entanglement Heatmaps]
    D --> M[State Projections]

🔬 Scientific Foundation

QE-KGR is built on rigorous quantum mechanical and graph theoretical principles:

Quantum State Representation

Each node \(|ψ⟩\) in the graph represents a quantum state in Hilbert space \(\mathcal{H}\):

\[|ψ⟩ = \sum_{i} α_i |i⟩\]

where \(α_i\) are complex amplitudes and \(\sum_i |α_i|^2 = 1\).

Entanglement Tensors

Edges represent entanglement between quantum states through tensor products:

\[|ψ_{AB}⟩ = \sum_{ij} T_{ij} |i⟩_A ⊗ |j⟩_B\]

Quantum Walks

Graph traversal follows the quantum walk operator:

\[U = S \cdot C\]

where \(S\) is the shift operator and \(C\) is the coin operator.

📚 Core Modules

qekgr.graphs.EntangledGraph

• Quantum node and edge representation
• Tensor network storage
• Hilbert space operations

qekgr.reasoning.QuantumInference

• Quantum walk algorithms
• Grover-enhanced search
• Entanglement entropy measurements

qekgr.query.EntangledQueryEngine

• Natural language query processing
• Hilbert space projections
• Context-aware reasoning

qekgr.utils.QuantumGraphVisualizer

• Interactive 2D/3D visualizations
• Entanglement strength heatmaps
• Quantum state projections

🎯 Applications

🧬 Drug Discovery

Discover hidden molecular interaction patterns through quantum entanglement analysis.

# Model molecular interactions as quantum states
drug_graph = EntangledGraph()
drug_graph.add_quantum_node("Aspirin", state="anti_inflammatory")
drug_graph.add_quantum_node("Protein_COX1", state="enzyme")

# Quantum-enhanced interaction prediction
predictions = inference.interference_link_prediction("Aspirin")

🔬 Scientific Research

Find interdisciplinary connections between research fields.

# Query for cross-domain insights
results = query_engine.query(
    "What quantum computing techniques could enhance drug discovery?"
)

🎯 Recommendation Systems

Quantum-enhanced collaborative filtering with entanglement-based similarities.

# Discover user preference entanglements
user_similarities = inference.discover_entangled_subgraph(
    seed_nodes=["user123"], 
    min_entanglement=0.4
)

🛠️ Command Line Interface

QE-KGR includes a powerful CLI for interactive exploration:

# Display graph information
qekgr info

# Run quantum queries
qekgr query "Who collaborates with researchers in quantum AI?"

# Perform quantum walks
qekgr walk Alice --steps 10 --bias-relations "collaborates,mentors"

# Generate visualizations
qekgr visualize 3d --output quantum_graph.html

# Discover subgraphs
qekgr discover Alice,Bob --expansion-steps 3

📖 Documentation

• Theory: Mathematical foundations and quantum mechanics
• API Reference: Complete API documentation
• Tutorials: Step-by-step guides
• Examples: Real-world use cases

🤝 Community

• GitHub Discussions: Ask questions and share ideas
• Issues: Report bugs and request features
• Contributing: Help improve QE-KGR

🏆 Why QE-KGR?

Feature	Classical Graphs	QE-KGR
Relations	Single, deterministic	Superposed, probabilistic
Reasoning	Boolean logic	Quantum interference
Discovery	Pattern matching	Entanglement analysis
Uncertainty	Not handled	Native quantum uncertainty
Correlations	Local only	Non-local entanglement

🚀 Getting Started

Ready to explore quantum-enhanced knowledge graphs?

1. Install QE-KGR
2. Follow the Quick Start Guide
3. Try the Examples
4. Read the Theory

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"In the quantum realm, knowledge is not just connected—it's entangled." 🌌

Built with ❤️ by Krishna Bajpai