HONORS THESIS DEFENSE
Contraction-based approach to tensor isomorphism
Presented by:
Anh Kieu ‘22
Thesis Advisor: Pete Brooksbank
2nd Reader: Ben Vollmayr-Lee
Wednesday, April 20, at 4:00 PM
OLIN 372
Everyone is welcome to attend.
Abstract: Tensors are natural generalizations of linear transformations to arbitrary “frames” of vector spaces. Just as how a linear transformation can be represented by a matrix, choosing a reference frame allows a tensor to be represented by a multiway array. A fundamental question is to decide when two multiway arrays represent the same tensor relative to different reference frames. This question is commonly known as the tensor isomorphism problem. In this Honors Thesis, we developed a new approach to testing (non)-isomorphism of tensors that uses detailed local information to detect differences in global tensor structure. The method assumes isomorphism invariant “labels” for lower valence tensors can be computed, and then compares two given tensors by computing their so-called “contraction labels.” We implemented this method in a computer algebra system called Magma and applied it to 4-qubit states in QIT as a proof of concept.