My main field of research lies between quantum computation, quantum cryptography and quantum foundations. My current focus is split between applied topics in quantum computing and the development of theoretical tools for the understanding of quantum spacetime. Although I am primarily interested in problems from physics and computer science, my methods come from an area of pure mathematics known as category theory.
Here follow some of my active lines of research:
- Diagrammatic programming languages for quantum computation
- Quantum causality and its applications to quantum computation, communication and cryptography
- Quantum machine learning and quantum natural language processing (QNLP)
- Quantum compilation and circuit optimization
- Algebraic structures involved in the symmetries and evolution of quantum systems
- Algebraic structures behind the quantum Fourier transform and other forms of quantum advantage
In the past, I have also done research in logic, computational geometry and graph theory.