About the Project
A fully funded PhD opportunity to participate in the world-leading research undertaken by the EPSRC Doctoral Landscape Award at the University of Sheffield.
Supervised by Prof Oleksandr Kyriienko and Dr Yingkai Ouyang.
The University of Sheffield is one of the leading Russell Group universities in the UK. We carry out cutting-edge research with strong links to industry. When you enrol to do a PhD with us, you will be working with world-leading academics and have access to top of the range facilities. As a PhD student you will have the opportunity to gain skills not only to conduct research, but also to take your career to the next level, whether you want to stay in academia, go into industry or the public sector, or set up your own company. You will have access to a range of training and support services to help you excel in your studies and beyond.
Project Description
How could quantum computers help us simulate complex physical systems and discover the equations that describe the world?
Understanding how air flows around an aircraft, how fluids move through complex structures, or how heat spreads through a device requires solving differential equations. These equations are at the heart of modern engineering and scientific modelling, but realistic simulations can become extremely demanding. Complex geometries, nonlinear behaviour, turbulence and uncertainty can all increase the computational cost, particularly when high accuracy or many different physical conditions need to be considered.
Quantum computers offer a fundamentally different way to process information, but taking advantage of them requires new algorithms designed specifically for scientific computing. This PhD will develop quantum algorithms for solving and learning differential equations, with applications to problems such as fluid dynamics, aerodynamics and complex engineering structures.
You will investigate how physical problems can be represented on a quantum computer, how their governing equations can be solved efficiently, and how useful information can be extracted from the resulting quantum state. An important challenge is that quantum computers do not simply provide a faster version of a classical simulation. New methods are needed that exploit quantum computation while still producing quantities that scientists and engineers actually need.
Possible directions include quantum algorithms for fluid and transport equations, simulations involving complicated geometries, discovering governing equations from observations, and combining physical models with data. A main application will be chosen through discussions with researchers in engineering and industrial collaborators, giving the project a strong practical focus while leaving room to explore new ideas as the field develops.
You will begin with well understood model problems and progressively move towards more challenging systems involving nonlinear behaviour, randomness and realistic physical structure. You will compare quantum approaches with established numerical methods to understand where quantum computing may offer genuinely different capabilities.
Designing and running quantum circuits will be central to the project. You will target the first generations of fault tolerant quantum computers, which use error correction to protect calculations against noise. You will learn how mathematical algorithms translate into quantum circuits, how many qubits and operations they require, and how algorithms can be redesigned to make them practical on emerging hardware. Circuit simulations will be complemented by experiments using the group's quantum computing access.
You will be supervised by Professor Oleksandr Kyriienko, Director of Sheffield Quantum Centre, and Dr Yingkai Ouyang, EPSRC Fellow and group leader at SQC. Their complementary expertise connects quantum algorithms and applications with quantum error correction. You will join a growing research environment with postdoctoral researchers supported by EPSRC projects and engage with domain experts through the SQC working groups and Sheffield's Quantum + AI network.
The research is informed by our work with Pasqal, Siemens, Volkswagen and Haiqu. These relationships provide routes to relevant scientific and engineering problems while the studentship remains an independent University project with flexibility to develop new collaborations. The project contributes to the wider UK effort to develop useful quantum computing for challenging applications including fluid dynamics.
Applicants may come from physics, mathematics, computer science, engineering or related disciplines. We welcome curiosity, mathematical reasoning and an interest in quantum computing; specialist experience in every aspect of the project is not expected. Training will cover quantum algorithms, numerical methods and error correction, preparing you for research careers in academia or industry. The project begins in October 2027 and is designed for thesis submission within 3.5 years.
How to apply
Interested candidates are strongly encouraged to contact the project supervisors to discuss your interest in and suitability for the project prior to submitting your application.
Please refer to the EPSRC DLA webpage for detailed information about the EPSRC DLA and how to apply.
Applicants must ensure that they use the correct application form linked to the EPSRC DLA webpage and must submit an application for October 2027 entry. The form is unique to the EPSRC DLA. It contains the list of advertised projects from which to select, and three questions specific to the DLA.
The application deadline is 17:00 GMT 13 January 2027.
The majority of our DLA studentships will be allocated to candidates who qualify for Home fee status, in accordance with EPSRC funding regulations which place strict limits on international recruitment.
Funding Notes
The award will fund the full tuition fee and a maintenance stipend at the UKRI rate (currently £21,805 per annum) for 3.5 years, as well as a research grant to support costs associated with the project.