Developing quantum algorithms for solving differential equations


Department Physics and Astronomy, Streatham campus, Exeter

The University of Exeter’s College of Engineering, Mathematics and Physical Sciences, is inviting applications for a fully-funded PhD studentship to commence in January 2022 or as soon as possible thereafter.  For eligible students the studentship will cover tuition fees plus an annual tax-free stipend of at least £15,999 for 3.5 years full-time, or pro rata for part-time study.  The student would be based in the Department of Physics and Astronomy in the College of Engineering, Mathematics and Physical Sciences at the Streatham Campus in Exeter.

Project Description:
The aim of the advertised PhD programme is to investigate and develop methods for solving non-linear partial differential equations (PDE’s) on a quantum computer with applications in computational fluid dynamics. Quantum computing represents a powerful framework for performing matrix-based operations using the laws of quantum mechanics and highly controllable devices. It can revolutionize the field of quantum chemistry, materials, and machine learning [Nature 549, 195 (2017)]. One area where quantum computing may provide an edge is fluid dynamics, where large scale simulations demand for increased computational power. Yet, despite the tremendous progress, the challenge of developing efficient quantum algorithms for current and future quantum devices remains open.
The main objective of the PhD work is to study differential equation solvers that can be run on a quantum hardware. The candidate will develop theoretical protocols for solving nonlinear PDEs, and apply it to relevant industrial problems. Additionally, the candidate will prepare an overview of existing protocols, and investigate their scaling for large problem sizes. The project is funded by an industrial partner, and regular interaction with industry is expected. The candidate is also expected to prepare publications, participate in conferences and meetings, and disseminate the results of the PhD work.

Entry requirements

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology. Prior knowledge and experience in the field of quantum computing and nonlinear differential equations is desired.
If English is not your first language you will need to have achieved at least 6.0 in IELTS and no less than 6.0 in any section by the start of the project.  Alternative tests may be acceptable (see

How to apply

In the application process you will be asked to upload several documents. 
• CV
• Letter of application (outlining your academic interests, prior project work experience and reasons for wishing to undertake the project).
• Transcript(s) giving full details of subjects studied and grades/marks obtained (this should be an interim transcript if you are still studying)
• Two references from referees familiar with your academic work. If your referees prefer, they can email the reference direct to [email protected] quoting the studentship reference number.
• If you are not a national of a majority English-speaking country you will need to submit evidence of your proficiency in English.
The closing date for applications is midnight on November 12th 2021.  Interviews will be held online on the week commencing 15th Nov.
If you have any general enquiries about the application process please email [email protected]  Project-specific queries should be directed to the main supervisor at [email protected]