# Tutorials

This section will contain comprehensive, in-depth tutorials for learning tensor network methods and using Nicole effectively.

## Coming Soon

Tutorials are currently being developed and will cover:

### Fundamentals

- **Introduction to Tensor Networks**: From tensors to networks
- **Symmetries in Quantum Physics**: Why conserved quantum numbers matter
- **Block-Sparse Tensors**: Understanding the data structure
- **Charge Conservation**: How selection rules work in practice

### Nicole Basics

- **Your First Tensor Network**: Building a simple MPS
- **Understanding Indices**: Directions, charges, and sectors explained
- **Contraction Patterns**: Efficient tensor network evaluation
- **Decomposition and Truncation**: Managing bond dimensions

### Intermediate Topics

- **Matrix Product States**: Theory and practice
- **Matrix Product Operators**: Building and applying operators
- **Canonical Forms**: Why and how to canonicalize
- **Gauge Freedom**: Understanding and exploiting gauge invariance

### Advanced Topics

- **DMRG Implementation**: Building a DMRG solver from scratch
- **Time Evolution**: TEBD and other time-evolution methods
- **Finite Temperature**: Purification and other techniques
- **Optimization Techniques**: Performance and accuracy trade-offs

### Symmetry Deep Dives

- **U(1) Symmetry**: Particle number and magnetization
- **Z(2) Symmetry**: Parity and discrete symmetries
- **ProductGroup**: Multiple conservation laws
- **Custom Symmetries**: Implementing your own groups

### Algorithm Walkthroughs

- **Ground State Search**: Finding lowest energy states
- **Excited States**: Multiple eigenvalues and eigenvectors
- **Expectation Values**: Computing observables efficiently
- **Correlation Functions**: Two-point and higher correlators

### Practical Applications

- **Spin Chains**: Heisenberg, XXZ, and other models
- **Fermionic Systems**: Hubbard model and beyond
- **Bosonic Systems**: Bose-Hubbard and related models
- **Mixed Systems**: Coupled degrees of freedom

## Tutorial Format

When complete, each tutorial will include:

1. **Learning Objectives**: What you'll learn
2. **Prerequisites**: Required background knowledge
3. **Theoretical Background**: Concepts and derivations
4. **Implementation**: Step-by-step coding
5. **Exercises**: Practice problems and challenges
6. **Solutions**: Complete worked examples
7. **Further Reading**: References and extensions

## Planned Tutorial Series

### Series 1: Tensor Network Fundamentals (Coming Soon)

1. What are Tensor Networks?
2. Why Symmetries Matter
3. Building Your First MPS
4. Contracting Tensor Networks
5. The Power of Truncation

### Series 2: DMRG from Scratch (Coming Soon)

1. DMRG Theory: Variational Optimization
2. Building the Environment
3. Local Optimization
4. Sweeping Algorithm
5. Convergence and Diagnostics
6. Advanced DMRG Techniques

### Series 3: Time Evolution (Coming Soon)

1. Time-Evolution Methods Overview
2. TEBD Implementation
3. Trotter Decomposition
4. Error Analysis
5. Long-Time Evolution
6. Observables and Dynamics

### Series 4: Symmetries in Practice (Coming Soon)

1. Understanding Charge Conservation
2. U(1) Symmetry: Particle Number
3. Z(2) Symmetry: Fermion Parity
4. ProductGroup: Multiple Symmetries
5. Performance Benefits
6. Debugging Symmetry Errors

## Interactive Learning

Future tutorials may include:

- **Jupyter Notebooks**: Interactive exploration
- **Visualization Tools**: See your tensor networks
- **Code Challenges**: Test your understanding
- **Benchmarks**: Compare implementations

## Prerequisites

Most tutorials will assume:

- **Python**: Basic to intermediate Python knowledge
- **PyTorch**: Familiarity with PyTorch tensors
- **Linear Algebra**: Matrices, eigenvalues, SVD
- **Quantum Mechanics**: Basic quantum mechanics (for physics applications)

Advanced tutorials may additionally require:

- **Quantum Many-Body Physics**: Second quantization, operators
- **Statistical Mechanics**: Partition functions, thermal states
- **Numerical Methods**: Iterative algorithms, convergence

## Learning Path

### For Beginners

1. Start with [Core Concepts](../getting-started/core-concepts.md) and [Quick Examples](../getting-started/quick-examples.md)
2. Read Introduction to Tensor Networks (coming soon)
3. Work through "Your First Tensor Network" (coming soon)
4. Practice with basic [Examples](../examples/index.md)

### For Intermediate Users

1. Review fundamentals if needed
2. Work through DMRG series (coming soon)
3. Study canonical forms and gauge freedom (coming soon)
4. Implement algorithms from papers

### For Advanced Users

1. Deep dive into specific algorithms (coming soon)
2. Optimize performance for your use case
3. Implement custom symmetries
4. Contribute tutorials and examples!

## Contributing Tutorials

We welcome tutorial contributions from the community! Good tutorials:

- **Teach One Thing Well**: Focus on a specific topic
- **Build Progressively**: Start simple, add complexity
- **Include Exercises**: Help readers practice
- **Provide Code**: Fully working examples
- **Explain Why**: Not just how, but why it works

To contribute:

1. Fork the [GitHub repository](https://github.com/Ideogenesis-AI/Nicole)
2. Create your tutorial in Markdown or Jupyter notebook format
3. Include clear explanations and working code
4. Add exercises or challenges
5. Submit a pull request

## Recommended Background Reading

### Tensor Networks

- **Tensor Networks for Beginners**: [arXiv:1603.01312](https://arxiv.org/abs/1603.01312)
- **Tensor Network Techniques**: [arXiv:1603.03039](https://arxiv.org/abs/1603.03039)
- **MPS/DMRG Tutorial**: Available on [TensorNetwork.org](https://tensornetwork.org/mps/)

### Quantum Many-Body Physics

- **Quantum Many-Particle Systems** by Negele and Orland
- **Condensed Matter Field Theory** by Altland and Simons
- **Many-Body Quantum Theory in Condensed Matter Physics** by Bruus and Flensberg

### Numerical Methods

- **Numerical Recipes**: General numerical methods
- **DMRG Reviews**: Various review articles on arXiv
- **TeNPy Documentation**: Another Python tensor network library

## External Resources

While we develop Nicole-specific tutorials:

### Online Courses

- [Tensor Network Summer Schools](https://www.youtube.com/results?search_query=tensor+network+school)
- [Quantum Information and Entanglement](https://www.youtube.com/results?search_query=tensor+network+lectures)

### Software Tutorials

- [TeNPy User Guide](https://tenpy.readthedocs.io/)
- [ITensor Documentation](https://itensor.org/)
- [QSpace Manual](https://bitbucket.org/qspace4u/) (MATLAB)

### Research Papers

- Search "DMRG review" or "tensor network methods" on arXiv
- Check references in Nicole documentation
- Follow citations from key papers

## Questions and Discussion

Have questions while working through tutorials?

- **GitHub Discussions**: Ask questions and share insights
- **GitHub Issues**: Report problems or suggest improvements
- **Community**: Connect with other Nicole users

## Stay Updated

Tutorials are being actively developed:

- Star the [GitHub repository](https://github.com/Ideogenesis-AI/Nicole) for updates
- Check documentation regularly for new tutorials
- Subscribe to release notifications

## Feedback

Help us create better tutorials:

- Open an [issue](https://github.com/Ideogenesis-AI/Nicole/issues) with tutorial requests
- Suggest topics you'd like to learn
- Report errors or unclear explanations
- Share your learning experience

## See Also

- **[Core Concepts](../getting-started/core-concepts.md)**: Understanding symmetry-aware tensors
- **[Quick Examples](../getting-started/quick-examples.md)**: Hands-on introduction
- **[Examples](../examples/index.md)**: Practical code examples
- **[API Reference](../api/index.md)**: Complete documentation
