Sven Bachmann is a Professor of Mathematics at the University of British Columbia (UBC), Canada. He is also an Associate Member of UBC’s Department of Physics and Astronomy. His research lies at the intersection of mathematical physics, with particular focus on the analytic, algebraic, and topological structures underpinning quantum systems. His work addresses fundamental problems in areas such as linear response theory, topological phases of matter, and quantum many-body systems, and has been published in leading journals in the field. Dr. Bachmann has made significant contributions to the mathematical understanding of phenomena such as the quantum Hall effect and Thouless pumps. He actively teaches across a range of topics from Quantum Theory and Functional Analysis to undergraduate / graduate courses in Differential Equations and Complex Analysis. Beyond his academic roles, he is deeply involved in the mathematical physics community, currently serving as Treasurer and Executive Member of the International Association of Mathematical Physics. He is also a frequent organizer of sessions in international conferences and seminars, including the upcoming Les Houches School of Physics in 2026 and the ICMP24 in Strasbourg, France, on Many-body Quantum Systems & Condensed Matter Physics.
Bridging Mathematics and Quantum Frontiers: Professor Sven Bachmann on Opportunities, Challenges, and the Future for the Next Generation
I am a mathematical physicist, and so a little bit of an outsider to quantum computing. But I am also a scientist fascinated by the perspective of using the intrinsic quantum aspects of nature to trivialize hard computations. In between pure mathematics and the development of computing hardware, there is a vast area to explore, which includes theoretical condensed matter physics, material science, metrology, numerical analysis, algorithmics and information theory, all motivated by the dream of quantum computing. I am certainly not able to answer the question of whether there will ever be a sort of large scale, industrial quantum computing era; But independently of the answer — as is so often the case with big scientific efforts — the question has more in it than its answer. There is no doubt that the quest for quantum computing has created broad new scientific and engineering opportunities for us.
My first academic steps revolved around the behaviour of electrical currents in mesoscopic systems, a question related to the quantum Hall effect. This lead me to get interested in topological states of matter, and to the related question of entanglement in many-body systems: This is where the connection with quantum computing was naturally made for me. And this connection is indeed a good example of the impact of quantum computing on adjacent fields: An old question (the quantum Hall effect was discovered and explained in the 80s) received a massive fresh interest (specifically due to the possibility of fault-tolerant topological quantum computing), seeding new research areas. In fact, even pure mathematicians have now joined the effort, adding their own toolbox originally developed with distinct goals. Another example that is close to my interests is the problem of thermalization in closed quantum systems, which was a question of fundamental interest but is now revisited with a more applied point of view. Anyone loosely related to quantum computing would have similar examples of their own. To me, this energy and excitement have so far been the real power of quantum computing.
In this bubbling environment there is much space and opportunities for young people to thrive. Governments pledge massive investments, universities create new academic positions and institutes broadly anchored in `quantum’, and the quantum industry is slowly but surely developing, from hardware to software and algorithms. Having a working knowledge of quantum mechanics requires time and effort, which is exactly what graduate studies are meant for. It is then a skillset that is almost certainly future-proof. At least as importantly, it is scientifically exciting, fundamentally interesting and the outcomes are unpredictable — just like a quantum measurement! I am personally very much looking forward to discover what eager young people will be able to achieve in the next few years.
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