PhD Studentship - Quantum Algorithms for Computational Fluid Dynamics

Application Deadline: Applications accepted all year round

How to apply: https://uom.link/pgr-apply-2526

UK Only

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.

Understanding and predicting fluid flow is essential to the design of aircraft, wind turbines and medical devices, and for modelling the environment. 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 for many industries. Simulating the full Navier-Stokes equations is computationally prohibitive for most applications, so industries rely on simplifications that limit our understanding and confidence in the results. 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 for computation. Consistent increases in qubit quantity and quality 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 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 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 and 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 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.

Applicants should have a 1st or high 2:1 honours degree (or international equivalent) in mathematics, physics, engineering, computer science or other related discipline.

To apply, please contact Dr Peter Brearley (peter.brearley@manchester.ac.uk) 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.

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