Quantum and emerging computational models

Quantum computing is a rapidly developing area that leverages the principles of quantum mechanics to redefine the foundations of computation.

In recent years, we have witnessed tremendous advances in computer engineering, and technology, especially in the areas of machine learning, data science, artificial intelligence, and quantum computing. The ideas central to these advances have now found applications in almost every area of science that involves computation. This theme focuses on obtaining a rigorous understanding of these ideas to pave the way to not only uncover the fundamental capabilities and limitations of these modern ideas, but also to extend them and discover new ones.

Research

Our core research topics include

• Quantum complexity: we design efficient quantum algorithms as well as show when speed-ups are impossible. We develop algorithms and protocols (e.g., for search problems, optimisation problems, etc.) and prove limits via lower bounds, separations, and no-go theorems.
• Neuromorphic complexity aims to classify the power of computing architectures based around spiking neural networks, a model designed to mimic the brain. To do this it gives neuromorphic (spiking, event-driven, co-located memory/compute) systems their own machine models and resource theory, so one can understand the computational power of these systems and compare with more conventional models of computation. These novel computational models feature not just time and space as resources but also energy (e.g., spikes, synaptic operations).
• Foundations of emerging frameworks for machine learning: Machine learning algorithms and neural networks are now central to many scientific and engineering disciplines. This research direction focuses on theoretical foundations for learning theory, aiming to bridge classical statistical methods and modern neural architectures. Key challenges include identifying biases, defining model search and output spaces, and developing robust evaluation metrics. An emerging framework views learning models as dynamical systems, linking classical training dynamics with quantum state evolution, and offering new insights into robustness, generalisation, and theoretical foundations.
• Geometric data science: a new research direction at the intersection of data science and computational geometry. Its central challenge is to continuously parameterise moduli spaces of data objects under key equivalence relations, such as rigid motion. A key example is unordered point sets representing atomic centres in molecules or crystals. This direction enables robust, interpretable analysis across domains including physics, biology, and materials science, where spatial relationships and structural equivalence are central to understanding real-world phenomena.

People

• Dr Olga Anosova
• Dr Vladimir Gusev
• Professor Vitaliy Kurlin
• Dr Nikhil Mande
• Professor Igor Potapov
• Dr Karteek Sreenivasaiah
• Dr John Sylvester

Partnerships and collaborations

Collaborators include

• Andy Cooper and Matt Rosseinsky at the Materials Innovation Factory at University of Liverpool
• Yoshua Bengio at University of Montreal, Canada
• Simon Billinge at Columbia University, US
• Pfizer and the Cambridge Crystallographic Data Centre (CCDC)

Opportunities

We welcome opportunities to engage with students, researchers, and industry partner:

• PhD opportunities: please contact us if you are interested in pursuing a PhD in quantum and emerging computational models
• Consultancy and research collaborations: we welcome partnerships, consultancy, and knowledge exchange projects with academic, industry, and government partners.

Contact us

Please discuss with relevant academic staff if you are interested in their research.