Opportunities for Students
Undergraduate Students
You can be involved in the activities of the Bilkent Quantum Computing and Topology group. Below are two computational projects. If you're interested in learning more feel free to get in touch with me.
Classical simulation
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 foundations
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.
Graduate Students
I am looking for students to work in my group, Bilkent Quantum Computing and Topology.
Projects: In my group, we work on various projects on the mathematics of quantum computing that intersects with various areas, including algebra, topology, and polyhedral computation. Using such advanced tools, we investigate the computational advantage of quantum computers in two directions:
Quantum foundations investigate quantum features such as quantum contextuality, a generalization of Bell nonlocality manifested in Bell inequalities. In our research, we study the computational consequences of quantum contextuality by developing frameworks based on techniques from algebraic topology.
Classical simulation of quantum computation provides a rigorous approach to quantifying the computational advantage of quantum computers. We focus on polytope-based simulation algorithms and investigate the complexity of these simulation algorithms.
Feel free to contact me to learn more about our research.
Additional Benefits: Graduate students who enroll in Bilkent’s graduate program and are affiliated with Bilkent Quantum Computing and Topology group will have additional benefits:
You will be involved in interdisciplinary research with international collaboration and participate in projects, including various institutions worldwide.
You will be given a grant for research expenses such as travel, e.g., visiting a professor at an institution abroad or attending a workshop/conference to present a paper/poster or a summer school for learning purposes.
You will join a dynamic group of researchers (currently, three postdocs and myself) at Bilkent with who you can interact regularly and work on projects collaboratively.