quantum-geometry-topology-research

name	quantum-geometry-topology-research
description	Research skill for quantum-geometry-topology interdisciplinary analysis. Search arxiv for quantum geometry/topology papers, import to knowledge graph (kg.db), analyze with PageRank/Louvain, extract reusable patterns. Activation: quantum geometry research, quantum topology analysis, geometry-informed quantum computing, quantum statistical analysis.

Quantum-Geometry-Topology Research Skill

Cross-disciplinary research workflow for quantum mechanics + geometry + topology + statistics.

Activation Keywords

• quantum geometry research
• quantum topology analysis
• geometry-informed quantum computing
• quantum statistical analysis
• topology quantum information
• quantum Fisher information
• Born rule statistics
• quantum probability
• 拓扑量子研究
• 量子几何分析

Tools Used

• exec: Run kg_tool, Python scripts, arxiv search
• read: Load existing skills, scripts
• write: Create new skills, save results
• web_search: Search arxiv papers

Workflow

Step 1: Search Papers

Search arxiv for quantum-geometry-topology cross-disciplinary papers:

python3 scripts/search_today_topic.py
# Keywords: quantum geometry, topology, Fisher information, Born rule, statistics

Step 2: Import to Knowledge Graph

Import papers to kg.db:

python3 scripts/import_arxiv_to_kg.py kg.db <papers_json>

Step 3: Generate Vector Embeddings

python3 scripts/generate_vectors.py

Step 4: Graph Analysis

Run PageRank and Louvain:

./scripts/kg_tool/target/release/kg_tool pagerank kg.db
./scripts/kg_tool/target/release/kg_tool louvain kg.db
./scripts/kg_tool/target/release/kg_tool search kg.db "quantum"

Step 5: Pattern Extraction

Identify reusable patterns:

• Quantum Fisher information geometry applications
• Topological quantum state encoding
• Quantum probability for statistics/ML
• Geometry-aware quantum circuit design

Step 6: Create Skill

Use skill-creator to formalize patterns:

Skill candidates:
- quantum-fisher-information-analysis
- topological-quantum-encoding
- quantum-probability-statistics

Key Concepts

Quantum Fisher Information Geometry

• Geometric viewpoint on quantum states
• Information geometry for quantum estimation
• Bloch sphere differential geometry

Topological Quantum Computing

• Toric code, loop gases, string nets
• Topological quantum memories
• Quantum Hall effects

Quantum Probability for Statistics

• Born rule applications
• Kolmogorov vs quantum probability
• Machine learning connections

Output Format

# Research Analysis Summary

## Papers Imported
- Title | arXiv ID | Key Contribution

## Graph Analysis
- PageRank top papers: [IDs]
- Communities detected: [N clusters]
- Cross-domain connections: [topics]

## Extracted Patterns
1. Pattern Name: [description]
2. Pattern Name: [description]

## Skill Recommendations
- [skill-name]: [purpose]

Resources

• kg.db: /Users/hiyenwong/wiki/kg.db
• kg_tool: scripts/kg_tool/target/release/kg_tool
• Papers: scripts/arxiv_*.json

Related Skills

• skill-creator: Create new skills from patterns
• skill-extractor: Extract patterns from conversations
• arxiv-search: Paper search