Advancing the Hidden Subgroup Problem and its Variants

The Hidden Subgroup Problem (HSP) is a foundational open question in quantum computing with far reaching applications. Special cases of the HSP play a pivotal rule in groundbreaking quantum algorithms such as the celebrated Shor’s integer factorization problem (which is based on the abelian group case of the HSP) and the Graph Isomorphism Problem (which follows from the permutation group case of the HSP). Variants of the HSP have a variety of applications in quantum algorithms. For in-stance, the Hidden Vector Problem has been used in Learning with Errors. This project will investigate how tools from the representation theory of finite groups can be applied to the HSP and its variants. Representation-theoretic methods—such as Fourier analysis on groups, decomposition of representations, and character-based measurement strategies—play a major role in the most successful approaches to HSP. One of our goals is to explore if more advanced algebraic tools (such as the construction of characters using coadjoint orbits) can be utilized to yield stronger results for the HSP or its variants.

Faculty Supervisor:

Hadi Salmasian

Student:

Partner:

Télécom Paris

Discipline:

Mathematics

Sector:

Education

University:

University of Ottawa

Program: