Quantum algorithms for optimization

• Applicant: Professor Dr. Sebastian Pokutta
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 499407162

Computational devices and closely-related information-processing technologies are among the most revolutionary inventions of the past century. Another groundbreaking discovery of the 20th century was quantum mechanics. Developed as a theoretical model to describe physics at the atomic level, it fundamentally changed our understanding of the world around us. The field of quantum computation stems from both of them. Its main objective is to understand how quantum mechanics changes our understanding of computation, especially the division between feasible and infeasible problems. Recent developments in quantum algorithms indicates that various optimization problems can be solved much faster on a quantum computer. Optimization problems permeate our society, they are key for the efficient operation of industry, logistics, and for countless other tasks that are crucial to the functioning of our modern society. Also, optimization problems are notoriously hard, and solving many of them precisely is out of reach of the most powerful modern computers even for modestly-sized instances. The radical vision of this proposal is to push the use of quantum computers for optimization tasks much further, developing new quantum algorithms which go well beyond the capability of even the best classical computers we have today. We aim at both general-purpose algorithms that can be used for a large variety of applications as well as more application- focused algorithms. We consider both continuous and discrete optimization, quantum algorithms for mixed-integer programs, as well as applications for machine learning, logistics, big data and physics. Our approach includes recent and exciting developments like quantum dynamic programming and graph sparsification. We are also interested in studying the QAOA-type algorithms, which can be executed even on really small quantum computers like the ones available today.

• DFG Programme: Research Grants
• International Connection: Belgium, France, Latvia
• Cooperation Partners: Professor Dr. Aleksandrs Belovs; Privatdozent Dr. Frédéric Magniez; Professor Jérémie Roland