Theory and algorithms for quantum computation

Recent experimental progress indicates that electron spins within semiconductor structures may serve as qubits for quantum computation. The exciting implication is that a variation of conventional CMOS electronics may be suitable for large scale quantum computing, bringing that reality much closer by harnessing the established silicon fabrication industry. However there remain a number of challenges to solve to realise this prospect.

This project will focus on developing new algorithms and protocols that are either specifically tailored for implementation in silicon architectures or more general algorithms for quantum computers in general. Detailed resource audits will be used to identify bottlenecks in current algorithm designs and will inform the development new algorithmic protocols.

Algorithmic and theoretical development within this project will focus on exploring and better exploiting the power of quantum computers, incorporating a blend of both quantum and classical advancements. This research will utilize tools from theoretical computer science, mathematics, statistics, and algorithms established in both classical computation and quantum algorithmic development.

Such tools include, but are not limited to, quantum information, randomisation and sampling, quantum linear algebra subroutines, parallelization, mathematical optimization, statistical learning theory, etc.

Advanced quantum processor emulation tools (such as QuEST, an open-source tool developed by Simon Benjamin's Oxford group with support from Quantum Motion) have emerged for the evaluation of general qubit architectures using conventional supercomputers. Thus, one can investigate how well systems of different kinds, sizes and layouts would perform quantum algorithms.

This project falls within the EPSRC mathematic physics research area for its interactions between mathematical physics and new research challenges of national importance relating to EPSRC's outcomes, including through links to pure and applied mathematics and theoretical physics, in particular, quantum computing.

This project is associated with financial support by Quantum Motion, a company based in London and Oxford. The student would work towards a doctorate in the group of Bálint Koczor in the Mathematical Institute and would be free to participate in the full range of themes in the group (including the UKRI FLF project "Theory to Enable Practical Quantum Advantage").

The successful student would interact closely with both the theory team in the host group and the experimental team in London, as well as collaborating groups in the UK and worldwide.