New quantum algorithms based on Riemannian optimisation

I will show how basic aspects of Riemannian geometry of the unitary group such as its curvature, tangent space and dense covering can guide the design of quantum algorithms. For this, we will derive an explicit formula for tangential gradients of linear cost functions which will show that corresponding state updates are in form of exponentials of commutators. Such unitary operations can be systematically implemented on quantum computers using the framework of double-bracket quantum algorithms which recently resulted in generalisations of the paradigmatic Grover’s algorithm. I will summarise the results of an ongoing collaboration developing this approach and I hope that at the end of the talk you will feel that knowing linear algebra is enough to take up designing quantum algorithms yourself.

Papers/Articles
https://arxiv.org/abs/2412.04554

Dr Marek Gluza is a Senior Research Fellow at NTU and the inventor of double-bracket quantum algorithms which can serve as a general-purpose optimisation solver in quantum computing and have led to several new protocols. Dr Gluza earned his PhD under Prof J. Eisert at Freie Universität Berlin and his diverse publication record spans subjects from tensor networks and statistical mechanics to quantum field theory. Privately, he believes the most critical challenge facing the future of fault-tolerant quantum computation is climate change. When playing chess, he opens with 1. b3 and is always happy to play a game.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg