Date of Thesis

Spring 2022


Tensor isomorphism is a hard problem in computational complexity theory. Tensor isomorphism arises not just in mathematics, but also in other applied fields like Machine Learning, Cryptography, and Quantum Information Theory (QIT). In this thesis, we develop a new approach to testing (non)-isomorphism of tensors that uses local information from "contractions" of a tensor to detect differences in global structures. Specifically, we use projective geometry and tensor contractions to create a labelling data structure for a given tensor, which can be used to compare and distinguish tensors. This contraction labelling isomorphism test is quite general, and its practical potential remains largely unexplored. As a proof of concept, however, we apply the technique to a very recent classification of 4-qubit states in QIT.


Tensor isomorphism, tensor contraction, projective geometry

Access Type

Honors Thesis

Degree Type

Bachelor of Arts



First Advisor

Peter Brooksbank

Included in

Algebra Commons