Quantum Algorithms for Computational Fluid Dynamics

About the Project

Understanding and predicting fluid flow is essential to the design of aircraft, wind turbines and medical devices, as well as for modelling natural phenomena such as weather and ocean currents. Over the past few decades, remarkable advances in computing driven by the exponential miniaturisation of transistors (Moore’s law) have allowed computational fluid dynamics (CFD) to flourish, becoming an indispensable tool for many industries. Simulating the full Navier-Stokes equations is computationally prohibitive for most applications, so industries rely heavily on simplifications and assumptions that limit our understanding and confidence in the results. Furthermore, Moore’s law is nearing its natural limit as transistors approach the atomic scale and quantum effects disrupt their reliable operation, stagnating progress in scientific computing.

While quantum effects threaten the continued scaling of classical computing, quantum computers are designed to exploit these effects, utilising superpositions between quantum bits (qubits) to provide an exponential vector space to perform computations. Consistent increases in both qubit quantity and quality over the past decade have made proof-of-concept quantum computations possible [1]. However, proven scientific applications for quantum computing remain mostly limited to quantum chemistry, materials, and particle physics. Since CFD is one of the most demanding use-cases of classical supercomputers, the development of efficient quantum CFD algorithms will be of widespread benefit upon the arrival of fault-tolerant quantum computing.

This project involves the adaptation of classical CFD algorithms, which are typically both non-linear and non-unitary, into a linear, unitary and probabilistic framework required for quantum computation. The project will incorporate theoretical algorithm design and implementation on quantum simulators as well as real quantum computers, with a particular focus on extracting utility from the noisy, imperfect devices that are available for the near-term. The Lattice Boltzmann method simplifies the numerical treatment of fluid flows by evolving particle distribution functions across straight lines on a computational grid, rather than evolving the intricate trajectories of the flow variables directly. This simplification makes it a promising candidate for performing quantum computational fluid dynamics, and will be the primary focus of this project. Fully quantum and hybrid quantum-classical implementations of the chosen numerical methods, e.g. through variational algorithms or quantum machine learning, will be compared to determine the best course of action for accelerating fluids simulation with quantum computing.

The successful candidate will benefit from access to widespread expertise across The University of Manchester in both quantum technology and CFD through the Centre for Quantum Science and Engineering and the Modelling and Simulation Centre. Access to quantum computing resources will be available through applications to the National Quantum Computing Centre. The supervisory team has an extensive network of national and international collaborators that will provide opportunities for short/medium-term placements at other institutions as part of the project. The applicant will be supported to publish their findings in leading journals and to present at international conferences.

Eligibility

Applicants should have a 1st or high 2:1 honours degree (or international equivalent) in mathematics, physics, engineering, computer science or other related discipline. Programming skill in any language and knowledge of numerical methods for solving differential equations are highly desirable. Knowledge of quantum information or fluid dynamics is advantageous. Applicants are expected to have a proactive attitude towards independent problem solving and strong written and verbal communication skills.

Funding

This 3.5-year PhD studentship is open to Home (UK) applicants. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26; subject to annual uplift), and tuition fees will be paid. We expect the stipend to increase each year.

Before you apply

For informal enquiries, please contact Dr Peter Brearley (peter.brearley@manchester.ac.uk). We strongly recommend that applicants wanting to apply should email Dr Peter Brearley with a CV and a brief statement, including details of your academic background, relevant experience and motivation to study this PhD project. Suitable applicants will then be invited to complete the online application form. The post will remain open until filled.

How to apply

Apply online through our website: https://uom.link/pgr-apply-2526

When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees.

Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered.

After you have applied you will be asked to upload the following supporting documents:

• Final Transcript and certificates of all awarded university level qualifications
• Interim Transcript of any university level qualifications in progress
• CV
• Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it).
• Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)
• English Language certificate (if applicable)

If you have any questions about making an application, please contact our admissions team by emailing FSE.doctoralacademy.admissions@manchester.ac.uk.