Opportunities for Students
Quantum computers are more powerful than classical computers. Identifying the reasons for this computational advantage is fundamental in quantum computation. In this project, you will learn about polytope-based classical simulation algorithms. Essential tools from various areas of mathematics, including group theory, operator theory, and polytope theory, are used in the construction of the algorithm. In the computational part of the project, you will get the chance to implement this algorithm using software such as Python, Julia, Polymake, and GAP.
Quantum probabilities are contextual, i.e., violate Bell inequalities. This foundational property of quantum theory can be utilized to achieve quantum advantage. In this project, you will learn about combinatorial methods originating in algebraic topology to study contextuality.
The computational part of the project involves implementing simplicial complexes (and sets) together with probability distributions defined on them. Relevant software tools are GAP, Kenzo, and Polymake.