Theoretical study of quantum techniques for Reducing communication complexity in distributed systems

This project is part of the EPSRC Centre for Doctoral Training in Quantum Technology Engineering at the University of Southampton (https://qte.ac.uk/). In addition to the research project outlined below you will receive substantial training in scientific, technical, and commercial skills.

This project explores how quantum techniques can reduce communication complexity in distributed systems. It involves studying classical and random communication complexity theories, and applying quantum methods like entanglement and superposition. The goal is to understand and lower the number of interactions needed, enhancing efficiency and reducing costs.

Communication complexity in theoretical computer science examines the amount of communication required to solve a problem when the input is distributed among two parties. This project aims to explore how quantum techniques can reduce communication complexity, thereby lowering costs in distributed systems.

Objective: The objective is to understand the theoretical complexity bounds on the number of interactions needed to solve distributed problems. By leveraging quantum techniques, we aim to demonstrate reductions in communication requirements compared to classical methods.

Content: The project is about a theoretical study of classical communication complexity theory, random communication complexity theory, and the role of quantum techniques in reducing complexity. Key areas of focus include:

• Classical Communication Complexity: Understanding the foundational principles and limitations.

• Random Communication Complexity: Exploring probabilistic methods and their impact on communication efficiency.

• Quantum Communication Complexity: Investigating how quantum entanglement and superposition can reduce communication needs.

Technicality: The project will delve into

• Rank of Boolean Matrices: Analyzing the rank and its implications for communication complexity.

• Graph Theory: Utilizing graph-based models to represent communication protocols and their efficiencies.

• Theoretical Complexity: Studying the theoretical bounds and computational limits of various communication protocols.

Skills: The project requires a strong background in mathematics and a math-oriented mindset. Proficiency in linear algebra, probability theory, discrete mathematics will be essential.

Impact: The project is aimed to provide a deeper understanding of the complexity bounds and to demonstrate how quantum techniques can offer substantial improvements in efficiency and cost reduction in distributed systems.

For more information please contact the supervisor Dr Andersen Ang – [email protected]

Supervisory Team

Dr Anderson Ang

Entry Requirements

Undergraduate degree (at least UK 2:1 honours degree, or international equivalent).

Closing date

Applications are accepted throughout the year for a start date in September 2025. Overseas students requiring funding must apply before 31 March 2025

Funding

Funding on a competitive basis. For UK students, tuition fees and a stipend at the UKRI rate tax-free for 4 years. EU and Horizon Europe students are eligible for scholarships. Overseas students who have secured or are seeking external funding are welcome to apply.

How to apply

Apply online here: Select programme type “Research”, “Faculty of Engineering and Physical Sciences”, next page select “PhD Quantum Tech Eng”. In Section 2 of the application form insert the name of the supervisor.

Applications should include

Applications should include (further details on https://qte.ac.uk/phd-opportunities/ ): Personal statement; Curriculum Vitae; Contacts of two referees; Degree Transcripts/Certificates to date.

We are committed to promoting equality, diversity, and inclusivity and give full consideration to applicants seeking part-time study. The University of Southampton takes personal circumstances into account, has onsite childcare facilities, is committed to sustainability and has been awarded the Platinum EcoAward.