2018 summer study on Tensor Network Methods

This year might be the last year that I will be participating a summer self-study with my CQuIC fellows. Our focus of the summer study is Tensor Network Methods for quantum information science. The study is mainly self-organized with our main instructor Rafael Alexander as now an official summer course for credits in UNM. Students and professors will be voluneering lectures until early August when the course ends. Courteous of Raf, the self-study materials are now open to view through Dropbox. The material will closely follow these lecture notes: arxiv:1603.03039. Questions and discussions can also go to Reddit at /r/TensorNetwork.

From the syllabus:

• Core:

1. Tensor network notation
2. Examples in Quantum Information
3. Matrix Product States (MPS)
4. Tensor network algorithms
   1. Density Matrix Renormalization Group (DMRG)
   2. Time Evolved Block Decimation (TEBD)
5. Projected Entangled Pair States (PEPS)
6. Multiscale Entanglement Renormalization Ansatz (MERA)

In the final 4 weeks we will focus on some recent developments involving tensor networks, including results from high energy physics, quantum information, and condensed matter (selected based on interest). Each lecture will be a review of one or two research articles. Some examples are listed below.

• Possible Electives:

1. Classifying gapped phases in 1D
2. Simulations of open system dynamics
3. Tensor networks in quantum error correction
   1. Tensor network decoders
   2. Holographic quantum error correcting codes
4. Tensor networks in high energy physics
   1. Connection to holography
5. Tensor networks for critical frustration-free spin chains