Project code



School of Mathematics and Physics

Start dates

October, February and April

Closing date

Applications accepted all year round

Applications are invited for a self-funded 3-year PhD.

The PhD will be based in the Faculty of Technology, and will be supervised by Dr Jaewoo Joo, Dr Arseni Goussev and Dr Andrew Burbanks.

The work on this project will:

  • investigate unique and surprising quantum phenomenon called quantum backflow
  • develop a new quantum-classical simulation tool to find the minimum energy in quantum systems
  • deliver innovative quantum algorithms with machine learning techniques to explore the quantum phenomena beyond the state-of-the-art supercomputer simulation

Recent advances in quantum technologies have made it possible to utilise fundamental quantum resources, such as superposition and entanglement, for performing faster computations beyond any classical supercomputer.

The first proof-of-principle demonstration of such a computational advantage – called quantum supremacy – has been shown recently by Google’s AI team. The overarching aim of this PhD project is to explore how quantum simulations can be used to solve complex optimisation problems that arise in the areas of physics related to the foundations of quantum theory and quantum chemistry.

Our quantum simulation process can be broken down into three stages. First, the simulation input (e.g., a trial function with initial conditions) is encoded as the vector state of an array of quantum bits (qubits). Second, the qubits evolve under the action of a uniquely designed sequence of quantum gates made of matrices. Third, measurements are performed on the quantum system to obtain relevant data statistically. The design of our quantum simulation algorithm will be analysed in simulating different physical processes in order to determine its efficiency.

The proposed PhD project will focus on the following two open problems: (i) quantum backflow and (ii) the ground state of a chemical compound. The former, (i), has to do with the purported existence of classically-forbidden (backward) probability flow in quantum systems. Such flow has not yet been observed experimentally, and even poses difficulties to numerical exploration (especially in high-dimensional configurations).

The goal is to develop a quantum simulation protocol that will make such exploration feasible. The latter, (ii), is concerned with devising a new quantum-classical simulation algorithm for computing the ground-state energy of chemically reactive systems. Entirely classical algorithms become intractable in analysing quantum processes inside complex molecules; the development of this hybrid method would be a welcome asset in modern computational chemistry.

Fees and funding

Funding availability: Self-funded PhD students only. 

PhD full-time and part-time courses are eligible for the UK Government Doctoral Loan (UK and EU students only).


2022/2023 fees (applicable for October 2022, February and April 2023 start) 

PhD and MPhil

UK, Channel Islands and Isle of Man students 

  • Full-time: £4,596 (may be subject to annual increase)
  • Part-time and part-time distance learning: £2,298 (may be subject to annual increase)

EU students
(including Transition Scholarship)

  • Full-time: £4,596 (may be subject to annual increase)
  • Part-time and part-time distance learning: £2,298 (may be subject to annual increase)

International students

  • Full-time: £18,300 per year (may be subject to annual increase)
  • Part-time and part-time distance learning: £9,150 per year (may be subject to annual increase)

All fees are subject to annual increase. If you are an EU student starting a programme in 2022/23 please visit this page.

Bench fees

Some PhD projects may include additional fees – known as bench fees – for equipment and other consumables, and these will be added to your standard tuition fee. Speak to the supervisory team during your interview about any additional fees you may have to pay. Please note, bench fees are not eligible for discounts and are non-refundable.

Entry requirements

You'll need an upper second class honours first degree from an internationally recognised university 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.

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.  An extended statement as to how you might address the proposal would be welcomed.

Our ‘How to Apply’ page offers further guidance on the PhD application process. 

If you want to be considered for this self-funded PhD opportunity you must quote project code SMAP4570220 when applying.

October start

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February start

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