Funded (UK/EU and international students)

Project code



School of Mathematics and Physics

Start dates

October 2024

Application deadline

30 April 2024

Applications are invited for a fully-funded three year PhD to commence in October 2024. 

The PhD will be based in the Faculty of Technology and will be supervised by Dr Jaewoo Joo, Professor David Bacon and Dr Andrew Burbanks

Successful applicants will receive a bursary to cover tuition fees for three years and a stipend in line with the UKRI rate (e.g., £18,622 for 2023/24). Bursary recipients will also receive a £1,500 p.a. for project costs/consumables. 

Costs for student visa and immigration health surcharge are not covered by this bursary. For further guidance and advice visit our international and EU students ‘Visa FAQs’ page.


The work on this project will involve:

  • Developing new quantum algorithms to model relativistic quantum-mechanical phenomena with the Schrödinger-Newton equation.
  • Verifying its quantum advantages by comparison with numerical and experimental demonstrations.
  • Collaborating with national and international experts including mathematicians and cosmologists to expand the new cross-disciplinary research area.

The overarching objective of this PhD bursary project is to pioneer a novel simulation approach for relativistic quantum physics on quantum computers. The primary goal is to investigate relativistic quantum phenomena within the framework of the Schrödinger-Newton equation based on a new quantum computing approach of the finite difference method. The original Schrödinger-Newton equation, which merges the Schrödinger equation with Newtonian gravitational potential, is firstly proposed for the study of cosmological issues, such as bosonic stars and wavefunction collapses induced by gravity, however, it is merely studied with the view of relativistic effects.


In this PhD research, we aim to investigate the phenomena of the Schrödinger-Newton equation by introducing a relativistic kinetic energy term as perturbation terms. By doing so, we aim to develop a unified model of the Schrödinger-Newton equation, capable of more accurately describing quantum phenomena that exhibit relativistic effects. During the PhD project, the properties of this nonlinear Schrödinger equation, including its relativistic components, will first be examined using conventional computing methods as a benchmark. Subsequently, we will transition to quantum simulation to represent our findings in qubit-based (quantum bit) representation. 


This project promises to contribute significantly to the understanding of the quantum-classical boundary and has the potential to make predictions regarding hypothetical bosonic stars as an example. The research journey will begin with a rigorous examination of the properties of the enhanced Schrödinger-Newton equation using classical computational resources. From there, we will harness the capabilities of quantum computers to explore even deeper into these fascinating and complex quantum phenomena.


Entry requirements

You'll need a good first degree from an internationally recognised university (minimum upper second class or equivalent, depending on your chosen course) or a Master’s degree in an appropriate subject. In exceptional cases, we may consider equivalent professional experience and/or qualifications. English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

The ideal candidate would have knowledge of quantum physics (in particular relativity) and quantum computing with computational skills. The candidate would be able to solve differential equations numerically (using Python and/or Mathematica).

How to apply

We’d encourage you to contact Dr Jaewoo Joo ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, you can use our online application form. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV.  Our ‘How to Apply’ page offers further guidance on the PhD application process.

If you want to be considered for this funded PhD opportunity you must quote project code SMAP9120424 when applying.Please note that email applications are not accepted.