Examples: Tensor Network

• 1. Example - Tensor Renormalization Group (TRG)
  • 1.1. Define the algorithm
  • 1.2. Run the algorithm
  • 1.3. Check against exact result
  • 1.4. Extensions
• 2. Tensor Network Random Unitary Evolution
  • 2.1. Manually perform partial trace
  • 2.2. Estimate Subsystem Entropy
• 3. Periodic DMRG and Calculations
  • 3.1. Z-Correlations
  • 3.2. Compressed Density Matrix
• 4. MPS Evolution with TEBD
  • 4.1. Non-translationally invariant Hamiltonians
• 5. Basic MERA Manipulations & Optimization
  • 5.1. Computing Local Quantities
• 6. Optimizing a Tensor Network using Tensorflow
• 7. Using quimb within torch
• 8. Using quimb within jax, flax and optax
  • 8.1. Notes
• 9. Generic Tensor Fitting
• 10. Converting a hyper TN for approximate contraction
  • 10.1. Fully automatic to general TN:
  • 10.2. Manually to TensorNetwork2D
• 11. Tracing tensor network functions and reusing intermediates
  • 11.1. Lazily tracing the computation
  • 11.2. Reusing intermediates:
  • 11.3. Compiling the computation
• 12. Real time simple update (SU)

Examples: Quantum Circuits

• 1. Exploring circuit sampling with various methods
  • 1.1. check exact contraction
  • 1.2. check MPS simulation
  • 1.3. check PEPS simulation
• 2. Tensor Network Training of Quantum Circuits
  • 2.1. The Ansatz Circuit
  • 2.2. The Target Unitary
  • 2.3. The Tensor Network Optimization
  • 2.4. Extracting the New Circuit
• 3. Bayesian Optimizing QAOA Circuit Energy
  • 3.1. Setting Up the Circuit
  • 3.2. Rehearsing the Computation
  • 3.3. Bayesian Optimizing the Energy
• 4. Converting a Circuit to an MPO
  • 4.1. By direct contraction:
  • 4.2. By fitting

Examples: Matrix

• 1. 2D Antiferromagnetic Model Example
• 2. Quenching a Random Product State
  • 2.1. Evolution
• 3. MPI Interior Eigensolve with Lazy, Projected Operators

Examples: Other

• 1. schematic - manual drawing
  • 1.1. Illustrative full examples
  • 1.2. Individual elements:
  • 1.3. Lines and curves
  • 1.4. Highlighting areas and groups of objects
  • 1.5. 3D Projections