PhD Studentship - Optimal Control Methods for Quantum Thermodynamics

Deadline: All year around

How to apply: uom.link/pgr-apply-2425

Positions available: one

Funding for this project covers tuition fees, UKRI minimum annual stipend (currently £19,237/annum) and up to a £5k/annum research training support grant for the full duration of the 4-year programme.

In recent years significant technological advancements in quantum control have dramatically improved the ability to manipulate and probe microscopic systems. Such control is vital for eg. non-equilibrium experiments, quantum computing and metrology. However, control always comes with energetic costs and it is paramount to understand how best to minimise costs while ensuring sufficient protection from unwanted noise. Theories in quantum thermodynamics provide a framework for quantifying these costs in terms of entropy production, which is the fundamental measure of irreversibility for systems driven out of equilibrium. A key aspect of microscopic systems is that they are also heavily influenced by stochastic fluctuations, which can further degrade control protocols. This raises an ongoing multi-objective optimal control problem in quantum thermodynamics:

• How do we simultaneously reduce entropy production and stochastic fluctuations in controlled quantum systems?This project will seek to develop general theoretical methods for addressing this problem. This will involve the merging of multi-objective optimisation theory and calculus of variation with finite-time quantum thermodynamics. The primary stage of the project will work within the framework of linear response theory, and the aim will be to find thermodynamically optimised control protocols for perturbing quantum systems out of equilibrium. This will utilise a recent formalism for quantifying thermodynamic fluctuations in linear response regimes (G. Guarnieri, J. Eisert, H.J.D. Miller, Phys. Rev.Lett. 133, 070405 (2024) ) . Beyond this there will be a lot of scope for further projects, including
• Optimal control methods to quantum thermal machines.
• The role of phase transitions in thermodynamic control tasks.
• Reducing heat fluctuations in Landauer erasure and other quantum information processing tasks.
• Extending the formalism beyond linear response regimes.

The project will require a blend of both analytic and numerical optimisation methods, non-equilibrium quantum physics, and stochastic thermodynamics.

The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Please contact Dr. Harry Miller - harry.miller@manchester.ac.uk before you apply. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.

If you have any queries regarding making an application, please contact our admissions team FSE.doctoralacademy.admissions@manchester.ac.uk

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