Tensor networks, fundamental theorems, and complexity

Date:
06
Monday
March
2023
Lecture / Seminar
Time: 03:00-04:00
Location: Nella and Leon Benoziyo Physics Building
Lecturer: Prof. Michael Walter
Organizer: The Center for Quantum Science and Technology
Abstract: Tensor networks describe high-dimensional tensors succinctly, in terms of a netw ... Read more Tensor networks describe high-dimensional tensors succinctly, in terms of a network or graph of local data. Many interesting tensors arise in this way -- from many-body quantum states in physics to the matrix multiplication tensors in algebraic complexity. While widely successful, the structure of tensor networks 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 is at the heart of 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. To achieve this we draw on recent progress in theoretical computer science and geometric invariant theory.
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