This PhD project, hosted at the University of Southampton within the EPSRC Centre for Doctoral Training in Quantum Technology Engineering, focuses on developing qubit efficient quantum optimization algorithms and their application to real-world industrial problems. The research addresses the critical challenge of bridging the gap between quantum algorithmic requirements and the limitations of current quantum hardware. You will co-develop novel quantum approaches to tackle combinatorial binary optimization problems, which are notoriously difficult for classical computers. The project involves both fundamental research—designing and benchmarking quantum algorithms using classical emulators, cloud quantum computers, and collaborations with experimental teams—and applied research, translating these findings into quantum software for industries such as logistics, pharma, transport, manufacturing, finance, aviation, and energy management. The work will explore quantum digital, annealing, and variational algorithms, aiming to reduce the number of physical qubits required and enable larger problem instances to be solved on near-term quantum processors. Industrial use cases include optimizing shipping routes, financial transaction settlements, and energy management. The project offers substantial training in scientific, technical, and commercial skills, and includes funded visits to leading quantum research groups in Singapore, Greece, the US, Asia, and the EU. Applicants should have a strong foundation in physical, engineering, or mathematical sciences, with previous exposure to quantum algorithms or programming courses considered a plus. The position is open to UK, EU, Horizon Europe, and international students, with a competitive UKRI TechExpert stipend of approximately £31k per year for UK students and studentships at the UKRI base rate for others. Overseas students with external funding are also encouraged to apply. The University of Southampton is committed to equality, diversity, and sustainability, and supports applicants seeking part-time study. The application deadline is July 31, 2026, with an earlier deadline of March 31, 2026 for international applicants. For further details, contact Prof Dimitrios Angelakis at d.angelakis@southampton.ac.uk.