Dr Rita Ahmadi is a Research Associate in the Department of Mathematics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Rita investigates quantum algorithms and their real-world applications. She also uses a branch of mathematics called category theory to study the unique behaviours of certain materials.
Can you tell us about your research area?
I am interested in two primary research themes.
The first theme focuses on quantum algorithms and their applications. We have been investigating the parallels between established quantum subroutines and classical concepts. Our goal is to establish a translation framework between them. The foundational subroutines that lead to quantum advantages are often the same across established algorithms. We are examining these subroutines considering classical practices.
The second theme involves applying category theory to physics, particularly in the study of topological phases of matter. Topological phases of matter are special states that go beyond the usual solid, liquid, and gas phases. The complex and exotic behaviours of these materials can be captured using categorical structures. My focus lies on bicategorical structures, which arise in conformal field theories.
I believe the intersection of mathematics and physics in the late 20th century is no accident. New mathematical frameworks have often emerged alongside new physical phenomena, helping our understanding of how these systems work.
Category theory was pioneered by Mac Lane in the mid-20th century and later expanded by Grothendieck. The study of topological orders and field theories gained prominence around the same time, with Atiyah applying category theory to topological field theory in 1988. Simultaneously, the development of higher categories was partly driven by efforts to comprehend a class of statistical systems known as exactly solvable models. That is why the field is intriguing to explore.
What led you to study this area?
It was a combination of coursework and a dopamine rush. I would say my entry into quantum computing was the EPR paper (Einstein-Podolsky-Rosen). My interest in topological phases of matter was sparked by Kitaev’s 1997 paper, where a complex set of physical phenomena is elegantly disguised within a simple toy model known as the Toric code, which is also one of the most efficient error-correcting codes.
What are the main aims of your current research?
My main goal is to understand how quantum algorithms work, focusing on specific applications in the real world and classical practices.
How could this research potentially benefit society?
Many researchers, some from Imperial College London, have published a roadmap to highlight how quantum computing will benefit society on multiple levels. As an early career researcher, I want to broaden my understanding and emphasise the value of curiosity-driven research.
Throughout history, many of humanity’s most fundamental discoveries and inventions have emerged not from immediate practical concerns but from a simple yet profound desire “to understand.” Researchers have a passion for uncovering the mysteries of nature and often their contributions have frequently had lasting and transformative impacts.
A clear example is Geoffrey Hinton, a recent Nobel Prize recipient (Physics, 2024) who continued to work on neural networks and deep learning at a time when the field was nearly dormant and out of favour. By purely utilitarian standards, he might have been expected to abandon the field; however, his curiosity drove him to persist—and today, AI is revolutionising our world.
What are the next steps in your research? Are there any challenges ahead?
I have been exploring examples where bicategorical structures fit well, yet certain structures are absent in the literature. The next step is to establish these missing links. Additionally, I am reassessing the computational complexity of certain quantum algorithms known for their speed-up over classical methods.
While the quantum advantage is evident, I believe the total computational cost has not been fully accounted for. By leveraging classical results, the next step is to refine these bounds and provide a clearer picture of quantum versus classical efficiency for these algorithms.