Counterdiabatic shortcuts for quantum linear system solvers

About the project

What if a quantum algorithm could take a shortcut to the true answer? This project will test whether practical counterdiabatic controls can accelerate adiabatic quantum linear-system solvers within realistic noise and hardware limits. It will deliver theory, open software and rigorous benchmarks showing when these shortcuts offer genuine computational benefit.

Solving linear systems underpins simulation, optimisation, control and data analysis. Quantum linear-system algorithms prepare a state proportional to the solution and can benefit applications needing selected properties. Adiabatic solvers are attractive but can become slow when spectral gaps are small or matrices poorly conditioned. Counterdiabatic driving, a shortcut to adiabaticity, could suppress unwanted transitions. Exact controls may be nonlocal and costlier than the evolution they replace.

This project will investigate whether implementable counterdiabatic controls can reduce coherent circuit depth or improve robustness once their full construction, compilation and simulation costs are counted. You'll derive regularised local, variational, nested-commutator or Krylov approximations to the adiabatic gauge potential and establish error and resource bounds where feasible. Tests will determine how performance depends on condition number, sparsity, precision, matrix structure, noise and hardware connectivity.

The main focus is early fault-tolerant computation; small hardware demonstrations will provide validation, not advantage claims. Structured matrices from differential equations, networks and optimisation will be tested against unassisted and discrete-adiabatic quantum solvers and appropriate classical methods. Metrics will include solution-state fidelity, observable error, circuit depth, two-qubit gates, state preparation and readout.

Expected outputs are new control constructions, open software, reproducible benchmarks and a map of useful, break-even and unfavourable regimes.

Dr Stefano Cipolla

• Continuos Optimization
• Second Order Methods
• Numerical Optimization

Entry requirements

You must have at least a UK 2:1 honours degree, or its international equivalent , in one of the following:

An interest in quantum theory, numerical linear algebra and careful computational experiments is desirable.

• physics
• mathematics
• computer science
• engineering

Fees and funding

Funding is available on a competitive basis through the EPSRC Centre for Doctoral Training in Quantum Technology Engineering at the University of Southampton.

UK students receive a 4 year UKRI TechFirst tax-free stipend of £30,000 per year. Studentships at the UKRI minimum rate are available for EU, Horizon Europe and International students.

Overseas students who have or are seeking external funding are welcome to apply.

While undertaking your research project, you'll also receive substantial training in scientific, technical and commercial skills.

How to apply

Apply now

Please apply via the online portal and select:

Applications should include:

• Academic year: 2027/28
• If you will be full time or part time
• Faculty: Engineering and Physical Sciences
• Search for PhD Quantum Tech Eng
• Add the name of the supervisor in section 2 of the application
• your CV (resumé)
• 2 academic references
• degree transcripts and certificates to date

Faculty of Engineering and Physical Sciences

For questions about applying, email the Centre for Doctoral Training in Quantum Technology Engineering (qte@soton.ac.uk) .

Project leader

For an initial conversation, email Dr Stefano Cipolla (S.Cipolla@soton.ac.uk) .

Research areas