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 applications, and appplying category theory to physics, particularly in the study of topological phases of matter.
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. Notably, 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. The complex and exotic behaviours of these materials can be elegantly captured using categorical structures. My focus lies on bicategorical structures, which arise, for instance, in conformal field theories.
I believe that the intersection of mathematics and physics in the late 20th century is far from coincidental. Historically, new mathematical frameworks have often emerged alongside novel physical phenomena, aiding our understanding of these systems. 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 dopamine rush. However, if the question is what hooked me on it, I would say my initial entry point into quantum computing was the EPR paper (Einstein-Podolsky-Rosen). Despite its technical simplicity, the ideas it presents are profound, elegant, and intellectually stimulating. 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 primary objective is to deepen our understanding of quantum algorithms with specific applications in mind with an eye on classical practices.
How could this research potentially benefit society?
Many distinguished researchers, some from Imperial College London, have outlined a roadmap for quantum computing that will benefit society on multiple levels. As an early career researcher, I wish to use this opportunity to amplify my own understanding of “benefit” 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 often rise each day with a passion for uncovering the mysteries of nature. While they may not explicitly aim to benefit society, 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. (I can imagine the discussions with him at social receptions and conference dinners!) 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. Numerous examples from history demonstrate how researchers, motivated by curiosity rather than immediate practicality and glory, have made groundbreaking contributions.
What are the next steps in your research? Are there any challenges ahead?
I have been exploring specific 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.