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PhD Project in Counterdiabatic Shortcuts for Quantum Linear System Solvers University of Southampton in United Kingdom

Degree Level

PhD

Field of study

Computer Science

Funding

The PhD project is competition funded. No stipend amount or specific tuition-fee coverage details are provided in the text.

Deadline

Jul 31, 2027

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Country

United Kingdom

University

University of Southampton

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Keywords

Computer Science
Electrical Engineering
Mathematics
Quantum Computing
Linear Algebra
Quantum Algorithms
Physics

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About this position

This funded PhD project in quantum computing and quantum control will investigate whether counterdiabatic shortcuts can accelerate quantum linear-system solvers under realistic noise and hardware constraints.

Quantum linear-system algorithms are relevant to simulation, optimisation, control and data analysis because they prepare quantum states related to solutions of linear equations. Adiabatic approaches can become slow when spectral gaps are small or matrices are poorly conditioned. The project will examine whether counterdiabatic driving can suppress unwanted transitions and improve performance without introducing greater construction, compilation or simulation costs.

The research will develop and analyse implementable approximations to the adiabatic gauge potential, including regularised local, variational, nested-commutator and Krylov methods. Where feasible, the work will establish error and resource bounds and study how performance changes with condition number, sparsity, precision, matrix structure, noise and hardware connectivity.

Research will focus on early fault-tolerant quantum computation, with small hardware demonstrations used for validation rather than claims of quantum advantage. Structured matrices arising from differential equations, networks and optimisation will be compared with unassisted and discrete-adiabatic quantum solvers, alongside suitable classical methods. Evaluation will include solution-state fidelity, observable error, circuit depth, two-qubit gate counts, state-preparation cost and readout performance.

The expected outputs include new quantum-control constructions, open software, reproducible benchmarks and a map of regimes in which counterdiabatic shortcuts are useful, break even or are unfavourable. The project is hosted by the University of Southampton's Faculty of Engineering and Physical Sciences.

Funding details

The PhD project is competition funded. No stipend amount or specific tuition-fee coverage details are provided in the text.

What's required

Applicants must have a 2:1 honours degree. The project is suited to applicants with relevant interests or preparation in quantum computing, quantum algorithms, quantum control, linear systems, numerical methods, or related physics, mathematics, computer science, or engineering fields; no additional requirements are stated in the provided text.

How to apply

Review the project and full entry requirements on the University of Southampton project page. Apply through the university's postgraduate research application process for this Doctor of Philosophy project before 31 July 2027.

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