A quantum leap
Icelandic by birth, British-educated (by way of Germany, Hong Kong, Japan, Taiwan and Canada), proficient in Chinese and classical violin, an avid cook who also practices meditation: at the young age of 29, Hlér Kristjánsson has a touch of the rare bird about him.
The fact that, in his professional life, he's also a computer scientist specializing in quantum theory and quantum foundations, including quantum machine learning, also places him in a widening group of global-minded scientists who've set their sights clearly on the future.
In January, Hlér joined Université de Montréal's Department of Computer Science and Operational Research as an assistant professor affiliated with Mila - Quebec AI Institute, and in June became the third to be awarded a research chair at UdeM's Courtois Institute.
His goal here, as he puts it, is "to advance fundamental research at the intersection of quantum computing, AI and materials science," with an emphasis on "understanding foundational concepts in quantum information such as causality."
More importantly, he strives to "leverage this understanding to rigorously demonstrate quantum advantages in information processing tasks such as quantum algorithms for simulating physical systems, quantum communication, and quantum machine learning."
We caught up with the budding computer scientist this summer and, in 10 questions, asked him about his background, his career, what brought him to UdeM, and what he hopes to achieve here.
Why is your work in quantum computing important for the general public to understand?
Simply enough, because quantum computers will be a leap forward from the best computers that exist today. They'll be able to solve a number of very technical problems that will impact people in their everyday lives, from the efficiency of the batteries they use to the medicines that will save their lives. Couple that with advances in machine learning, which can extract information from large amounts of data, and you'll see rapid and drastic improvements in many other fields, from natural language processing to molecular structure prediction. Once we apply machine learning techniques to data processing on a quantum computer, the computational advantage will be all the greater, whether it be held by nations such as Canada and China or corporations such as IBM and Google.
And that will happen sooner than later, correct?
Most likely, yes. And with error-corrected quantum computers finally expected to be achieved in the coming decade, designing algorithms that challenge the state of the art in practical-use cases – things like molecular modelling and encrypting sensitive data – is more pressing than ever. What we still lack, however, are transformative quantum algorithms beyond a handful of existing proposals. I firmly believe that studying the fundamental principles underpinning the advantages of quantum computation is key to addressing this shortfall. That's where counterintuitive quantum phenomena, such as non-locality and quantum causality, come into play. Bridging the gap between foundations and applications in such areas will enable us to achieve several breakthroughs: first, to design a paradigm of functional programming for quantum computation, leading to unique ways of simulating physical systems; second, to determine the ultimate limits of computational power from quantum physics, and third, to design powerful new machine-learning architectures for (hopefully interpretable) quantum AI.
Tell us a little about your education and career so far. You've already had a dozen research papers published that have been cited hundreds of times.
I started off in physics, doing my undergraduate and master's degrees at Imperial College London, graduating in 2018 after completing my thesis on an exchange program with the University of Freiburg, in Germany. Four years later, after stints at the University of Hong Kong and the UK Office for Communications, I got my PhD from the University of Oxford in computer science. Then, from 2022 to 2023, I lived in Japan and held a postdoctoral position in the University of Tokyo's Department of Physics in an industry partnership with IBM. And from 2023 to 2024 I was a joint postdoctoral research fellow here in Canada, at the Perimeter Institute for Theoretical Physics and Institute for Quantum Computing, in Waterloo. At the start of my career, I co-authored one of the first papers on a quantum generalisation of neural networks, and in my PhD I developed a framework for describing the superposition of quantum processes, applied it to construct a generalisation of quantum Shannon theory, and applied similar techniques to formulate an extension of the circuit model of computation. Also, I've made contributions to our understanding of causality in quantum theory with important implications for information processing.
How do your current research interests line up with what the Courtois Institute is doing?
Two of my most recent papers are on the topic of quantum algorithms for the simulation of physical systems, motivated to a large extent by the search for quantum techniques to enhance the simulation, manipulation and discovery of new materials. In contrast to previous work on simulating the behaviour of a quantum system, which has typically assumed that its properties are known in advance, my approach is based on the recent paradigm of higher-order quantum computation which allows unknown quantum systems to be manipulated and simulated in a "black-box" fashion – that is, without having to first characterize its behaviour in the lab. I believe that this novel approach has strong potential for making a long-term impact towards the simulation of quantum and chemical systems—an essential ingredient in the development of molecular materials. Then there's my interest in developing new AI tools: that, too, aligns with the Courtois' emphasis on using AI for materials (such as discovering candidate materials for batteries to power green energy), and on the intersection of physics and chemistry for AI. In the end, directly connecting foundational research with state-of-the-art technologies will make unforeseeable scientific breakthroughs possible, and that's in line with the Courtois’ mission of doing 'blue-sky' research that has a technological impact – and ultimately, of making UdeM world-renowned as a global research centre for quantum information.
A university is by definition a place of learning and transmission of ideas. As a young person and recent student yourself, how important is teaching to you?
Very important, and it goes hand-in-hand with the global approach I bring to my work.
Over the course of my career, I've developed a network of international collaborators with diverse research expertise, spanning Oxford, Cambridge, London, Vienna, Paris, Geneva, Waterloo, Hong Kong and Tokyo, including three experimental collaborations to confirm my results in practice. In this time, I've supervised or co-supervised eight master’s and undergraduate research students, and have had experience teaching quantum information theory and quantum computing as a teaching assistant to both undergraduate and graduate students in computer science. This fall, I'll start teaching a new graduate course on “quantum computing, foundations and machine learning," and it'll be an excellent opportunity for students affiliated with the Courtois and Mila communities to learn about quantum computing and its intersection with the foundations of quantum physics, machine learning and materials science.
Your personal background is certainly broad enough to attract a diverse student body. Are you a role model, of sorts, for the coming generation of computer scientists?
Well, I don't know about that, but I certainly am strongly committed to fostering an environment of equity, diversity and inclusion at UdeM. Having lived in seven countries across three continents over the last 13 years and coming from an Icelandic/Taiwanese mixed-race background, I'm acutely aware of the many challenges faced by people coming from different cultural, linguistic, ethnic, religious, or socioeconomic backgrounds. I also understand the importance of equity for people whose native language is not English and for people with disabilities: I once aspired to become a concert violinist, but that was cut short 10 years ago when I faced serious musculoskeletal health issues, and which I'm still feeling the effects today, when I need assistive technology to use a computer, for instance.
Is working in French at UdeM a challenge for you?
At first, of course it is to some extent, but I’m confident in being able to master the language within a couple of years. Though I'm not yet fluent in French, I took seven weeks of full-time French courses in 2024 and find I'm slowly getting up to speed in the few months I've been in Montreal. Learning languages is something I quite enjoy anyway. I grew up speaking Icelandic – my home was in Akureyri, a port town in the north of the country – as well as Mandarin Chinese, my mum’s native language from Taiwan. When my family moved to the U.K. for half a year when I was 5, while my dad worked as a visiting scholar in Cambridge, I learned English too. At university, I took German as a minor and after a year of studying in Germany I was able to speak German fluently in an academic setting. Then of course there's music: another language entirely. Growing up, I trained to be a concert violinist and performed as a soloist with the Iceland Symphony Orchestra and as concertmaster of the National Youth Orchestra of Iceland. Later, I got interested in writing my own music, co-composing and releasing an original album inspired by an Icelandic traditional story. As for my other pastimes, cooking and meditation, those have vocabularies of their own, and I can't say I've mastered either, or ever will!
