Simulating quantum systems
Tensor network provide powerful and widely used simulation techniques for isolated spin chains. In contrast, for open quantum systems comparably little work has been done. However, any system is coupled to its environment too some extent. Hence, it is very desirable to establish extensions of the known methods to open quantum systems.
Controlled truncation techniques using Lieb-Robinson bounds arXiv:1103.1122
Positivity of matrix product operators (MPOs) is hard to check
A tensor network simulation scheme based on local purifications
... more on open quantum systems later