Jørgen Ellegaard Andersen directs the Centre for Quantum Mathematics at the University of Southern Denmark and is the founder and CEO of Qpurpose.

Together with his close collaborator Shan Shan, he represents — to my mind — one of the most interesting and under-reported stories in quantum. I first encountered him some six months ago and wrote about it at length in a post called Q Day Came Quietly.

That piece drew a fair bit of attention and even comments from several distinguished physicists and mathematicians. Still, it remained an open question whether my enthusiasm was justified. I am, after all, a mere civilian in quantum, and most experts I spoke to were hedging their bets.

The second time I saw Ellegaard Andersen on stage, I learned that he had assembled an advisory board for his centre — which is closely intertwined with his start-up — and that six of its ten members were Fields Medallists. Given that the Fields Medal is the mathematician’s equivalent of the Nobel, that’s an awe-inspiring proxy for credibility.

Yet again, when I turned to knowledgeable friends for a second opinion, they hesitated to take the claims at face value. They said it all sounded a little too good to be true. And, reading between the lines, I sensed a certain scepticism provoked by Ellegaard Andersen’s stage persona — closer to Steve Jobs than to your average mathematics professor.

Today marks my third encounter. I’m seeing him present at the European Quantum Technologies Conference in Copenhagen. Once more, he stands apart. While everyone else is hammering home the same fluffy slogans about Europe needing to scale up its efforts in quantum, here’s someone who clearly gets his hands dirty.

Actual use-cases are rare in this business, but Qpurpose isn’t sketching hypothetical milestones on an imaginary roadmap; they’re looking back at a full year of working with one of Denmark’s most established banks, Jyske Bank, to optimise the trading of a particular financial instrument. It is now doubling down on what must have began as a wildly speculative pilot project.

It makes sense that they would, given Qpurpose’s reported performance. In trading, success hinges on algorithms clever enough to peek into the near future. Performance is measured in basis points — hundredths of a percent. According to Ellegaard Andersen, classical algorithms hover around ten basis points, while Qpurpose’s quantum-inspired approach achieves two — a lower number meaning greater predictive accuracy. The delta, one imagines, translates rather directly into profit.

Helping banks get richer faster may sound uninspiring, and I’d agree — but the trading application is merely the smoke pointing to a much larger fire.

Qpurpose, as Ellegaard Andersen explains it, can do what it does because it has found a way to speed up certain Monte Carlo simulations exponentially. It’s not universally applicable — Monte Carlo methods form a whole family of algorithms — but, he claims, there are hard mathematical proofs showing exponential speed-up under specific conditions.

To grasp what that means, consider how few quantum algorithms are known to provide exponential advantage over classical ones under any circumstances. Ellegaard Andersen himself invoked three famous examples — Deutsch–Jozsa (1992), Shor (1994) and HHL (2009) — before positioning his and Shan Shan’s 2025 result as a fourth, arriving nearly two decades later.

One reason, perhaps, that there’s been less fuss about this than you might expect is that there are still no quantum machines powerful enough to run the algorithm. For now, it can only be simulated on classical hardware, where any claimed exponential speed-up would normally vanish. This, however, is another aspect of Qpurpose’s edge: they claim to be uniquely able to retain exponential speed-up even while running in simulation on a classical high-performance compute cluster.

Another reason people may initially have been dismissive is that the algorithm was originally tailored to run on a Gaussian Boson Sampler — which isn’t, strictly speaking, a universal quantum computer. According to Ellegaard Andersen, that’s now changing: they’ve managed to port the algorithm to gate-based architectures, meaning it could in principle run on the same kind of hardware being built by IBM, Quantinuum, and others.

Speaking of Quantinuum, I learn that they are now stepping in to fund much of Qpurpose’s ongoing research — if anyone needed further proof of momentum.

In Ellegaard Andersen’s own phrasing: the revolution is already underway.