Tensor Network Guide

• 1. Basics
  • 1.1. Creating Tensors
  • 1.2. Creating Tensor Networks
  • 1.3. Graph Orientated Tensor Network Creation
  • 1.4. Contraction
  • 1.5. Decomposition
  • 1.6. Selection
  • 1.7. Modification
• 2. Contraction
  • 2.1. contraction interfaces
  • 2.2. Things you can supply to the optimize kwarg:
  • 2.3. Hyper edges
  • 2.4. Structured Contractions
  • 2.5. Approximate boundary contraction
  • 2.6. Automatic approximate / compressed contraction
• 3. Drawing
  • 3.1. Coloring
  • 3.2. Highlighting indices
  • 3.3. Highlighting tids
  • 3.4. Auto coloring edges
  • 3.5. Positioning tensors
  • 3.6. Hyper-edges
  • 3.7. Spanning trees
  • 3.8. Interaction with matplotlib
  • 3.9. 3D plotting and other backends
  • 3.10. ‘Publication style’ figures
• 4. Optimization
  • 4.1. Using tags to opt in, opt out or group tensors
  • 4.2. Optimizing Circuit objects
  • 4.3. Optimizing PTensor objects
• 5. 1D Algorithms
  • 5.1. Matrix Product States
  • 5.2. Matrix Product Operators
  • 5.3. Building Hamiltonians
  • 5.4. Quick DMRG2 Intro
  • 5.5. Quick TEBD Intro
  • 5.6. Gates: compute local quantities and simulate circuits
• 6. 2D Algorithms
  • 6.1. Structure of a 2D Tensor Network
  • 6.2. Combining 2D Tensor Networks
  • 6.3. Contracting 2D Tensor Networks
  • 6.4. Computing Quantites
  • 6.5. Specifying 2D Hamiltonians
  • 6.6. Simple Update
  • 6.7. Full Update
  • 6.8. Global Autodiff Optmization
• 7. Quantum Circuits
  • 7.1. Simulation Steps
  • 7.2. Building the Circuit
  • 7.3. Parametrized Gates
  • 7.4. Forming the Target Tensor Network
  • 7.5. Locally Simplifying the Tensor Network (the simplify_sequence kwarg)
  • 7.6. Finding a Contraction Path (the optimize kwarg)
  • 7.7. Performing the Contraction (the backend kwarg)
  • 7.8. Performance Checklist
• 8. Quantum Circuits with MPS
  • 8.1. CircuitMPS
  • 8.2. CircuitPermMPS
  • 8.3. Using a GPU or other backends
• 9. Design
  • 9.1. Tensor
  • 9.2. Creating & Contracting Tensors
  • 9.3. Copying & Modifying Tensors
  • 9.4. TensorNetwork
  • 9.5. Selecting Tensors Based on Tags - the which kwarg
  • 9.6. Copying & Modifying Tensor Networks
  • 9.7. Combining TNs
  • 9.8. Tensor ‘Owners’
  • 9.9. Structured (1D, 2D, …) Tensor Networks
  • 9.10. Standard vs. Hyper Indices & Tensor Networks