Mathematical & Quantum Computation

Members of the Mathematical & Quantum Computation cluster undertake research in computational algebra, quantum computing, and scientific computing. 

• Quantum information theory is a framework for understanding the quantum nature of the universe and how to exploit this nature for new information-processing capabilities. Quantum Computation is concerned with constructing algorithms using sequences of unitary operations on quantum states. Current work includes: 

• Algebraic techniques in the development and analysis of quantum algorithms: Quantum algorithms are constructed and analyzed using quantum walks where the asymptotic properties of quantum Markov chains (using unitary matrices) are studied. In a different direction, game theory techniques are extended to the quantum domain where iterated quantum games played on a network (graph) are studied, to determine the properties of "quantum agents". 

• Quantum Error-Correction and Fault-tolerance: Applications of the Stabilizer formalism and the Clifford group to problems like circuit simulation and Magic state distillation. 

• Quantum Foundations: The study of Discrete Wigner functions, Mutually unbiased bases, SIC-POVMs, Nonlocality & Contextuality 

• Scientific computing research involves the development and implementation of algorithms for solving partial differential equations and large linear systems, and applications of these problem to problems in fluid dynamics, 

Members: Mark Howard, Niall Madden, Michael McGettrick, Joshua Maglione, Götz Pfeiffer, Tobias Rossmann.