Michael Walter | Tensor Networks, Fundamental Theorems, and Complexity

▶Title: Tensor Networks, Fundamental Theorems, and Complexity
▶Speaker: Michael Walter (Ruhr University Bochum)

▶Abstract: Tensor networks describe many-body quantum states and other high-dimensional data succinctly, in terms of a network or graph of local tensors. While spectacularly successful, their structure is still only partially understood. In this talk, I will give a gentle introduction to tensor networks and explain some recent advances in their theory. In particular, we will discuss the significance of the so-called "fundamental theorem", which underlies much of the success of tensor networks, and explain how to generalize it to higher dimensions. Before our work, "no go" results suggested that such a generalization might not exist! Along the way, we will see how to turn an undecidable problem into one that admits an algorithmic solution.

MCQST