Examples¶

This section provides comprehensive, executable examples demonstrating Nicole's capabilities for symmetry-aware tensor computations. Each example includes live code execution with real outputs, allowing you to see exactly what Nicole produces.

The examples are organized by complexity and topic:

Basic: Learn tensor creation, arithmetic, and block access
Symmetries: Work with U(1), Z(2), and product groups
Operations: Master contractions, decompositions, and manipulations
Advanced: Build operators and optimize performance

All code examples use markdown-exec to show both the source code and its actual output, making it easy to understand what each operation does and verify the results.

Getting Started¶

New to Nicole? Start here:

First Tensor: Create your first symmetry-aware tensor
Arithmetic Operations: Add, subtract, and scale tensors
Indexing and Blocks: Access and manipulate tensor blocks

Symmetries¶

Learn to work with different symmetry groups:

U1 Examples: Particle number conservation
Z2 Examples: Parity and binary symmetries
SU(2) Examples: Full spin-rotation symmetry
Product Groups: Multiple simultaneous symmetries

Operations¶

Master tensor operations:

Contraction: Contract, trace, and multiply tensors
Decomposition: SVD and tensor decomposition
Manipulation: Permute, transpose, conjugate
Serialization: Save and load tensors to disk

Advanced¶

For experienced users:

Build Operators: Build physical operators with symmetries
Load Space: Use load_space for quantum systems
Performance Tips: Optimize your code
Autograd: Gradient tracking with symmetry-aware tensors
GPU Acceleration: Run computations on GPU

Example Format¶

Each example page includes:

Complete runnable code
Step-by-step explanations
Expected output
Links to API reference

Running Examples¶

All examples assume Nicole is installed:

pip install nicole

Then copy-paste code directly into Python or Jupyter notebooks.

Contributing Examples¶

Have an interesting use case? Contributions welcome! See the GitHub repository to submit examples.