A computer that shouldn't work

In November 2023, Andrew King, a forty-something physicist employed at Canadian D-Wave Systems, closed the door of a conference room in Burnaby near Vancouver and stared at the ceiling for a long time. He and his team had just concluded a meeting in which he and his team admitted to the company's board something that no one in the quantum industry likes to say out loud: they had been trying for months to find a problem on which their quantum processor could beat classical supercomputers at more than a laboratory trick—and had failed after failure.

D-Wave has existed since 1999. It was the first company in the world to sell commercial quantum processors - customers included Lockheed Martin, Google, NASA. But none of these processors ever did anything that couldn't be reproduced on a regular server cluster. “We lived with promise,” King later recalled in an interview withScience. "Every year we said, 'The next generation is going to be the breakthrough one.' And then the next generation came and it still wasn't."

Little did King know that the solution to his problem would not come from Silicon Valley, Waterloo or Zurich. It will come from Krakow - from two theoretical physicists who have never touched a commercial quantum processor in their lives.

This is the story of how Polish theoretical physics helped answer one of the most difficult questions in modern computer science - and why this answer puts Poland in a role that will be difficult to take advantage of without a radical change in the approach to financing deep tech.

Five years of false starts

To understand why King's problem was so difficult, you have to go back to 2019. In October of that year, Google announced "quantum supremacy". The Sycamore processor - an array of 53 superconducting qubits - solved the task of sampling a random quantum circuit in 200 seconds. The same task, according to Google estimates, would take the world's fastest supercomputer 10,000 years.

The world has gone crazy. The headlines announced the end of the silicon era. "Nature" published a cover article. Sundar Pichai, Google's CEO, compared the achievement to the Wright brothers' flight.

Then came the impact with reality - much sooner than anyone expected. Over the course of several months, Chinese scientists from the Academy of Sciences showed that the Sycamore problem can be solved classically in a few hours if a clever optimization of the tensor network contraction is used. The problem wasn't just solved - it wastrivial, once you understood its structure.

"It's a bit like announcing that you've built a rocket that goes to Mars in an hour - and then someone notices that your Mars is actually a mock-up in a movie studio," commented Professor Scott Aaronson, one of the world's most important quantum computing theorists.

But Google wasn't the only one. In 2021, a team from USTC in China unveiled the Zuchongzhi 2.0 processor on 66 qubits, with even bolder claims of advantage. In 2024, it's the turn of Zuchongzhi 3.0 - 105 qubits, a new record. And it's the same scenario again: an impressive experiment, a loud announcement, and then a classic algorithm that does the same thing, only slower, but fast enough to undermine the point of using a quantum processor.

Physicists have begun to talk about the "quantum merry-go-round": a vicious circle in which any demonstration of advantage is immediately canceled out by the progress of classical algorithms. The problem was in the very DNA of these experiments - they were all designed to favor specific equipment rather than answering the actual scientific question.

A border that no one could cross

Marek Rams and Jacek Dziarmaga work at the Institute of Theoretical Physics of the Jagiellonian University - in a building at Łojasiewicza Street, which from the outside looks like any other academic block from the 1960s. Inside, however, there is one of the five best teams in Europe dealing with tensor networks of matrix states. It's a mathematical technique that can describe quantum systems with limited entanglement - a kind of data compression that only works if the quantum correlations between particles aren't too complicated.

Both professors have spent decades exploring the limits of this compression. They knew exactly where classical algorithms began to choke—and, more importantly, why.

"The standard approach in the industry was: let's take our processor, find a problem that it solves faster than a classic computer, and declare victory," says Dziarmaga. "We asked the opposite: whereReallyclassical computers fail - not because we programmed the algorithm incorrectly, but because mathematically there is no better solution?

The answer lay in the entropy of entanglement. In quantum systems, the entanglement between particles increases with the size of the system. When it grows according to the so-called surface law - in proportion to the surface area of the system, not its volume - classical tensor algorithms perform very well. But as soon as entanglement goes beyond this regime, the computational cost explodes exponentially. It's not a matter of better programming; this is a hard mathematical boundary.

Rams and Dziarmaga's team proposed to King an experiment on the border of this regime: a simulation of quantum quenching in spin glass. Spin glass is a magnetic system in which atoms' spins - their microscopic magnetic moments - freeze in complex, seemingly random patterns as they slowly cool. This isn't an exotic physics textbook problem; spin glasses model neural networks, optimization algorithms, and even the dynamics of financial markets. Understanding how they behave in the quantum regime has been the Holy Grail of condensed matter physics since the 1970s.

"And crucially," adds Rams, "in two and three dimensions, the quantum evolution of spin glass falls outExactlyon the border between what is classically calculable and what is beyond reach.

Minutes instead of millions of years

The experiment was carried out on an Advantage2 processor - the latest generation of D-Wave machine, containing several thousand superconducting qubits operating at a temperature of 15 millikelvin (which is colder than space). D-Wave qubits are not universal - they do not perform arbitrary quantum operations like Google or IBM processors. They specialize in quantum annealing: a technique in which a quantum system slowly evolves from a simple initial state to a complex final state, finding an optimal solution along the way.

The result exceeded our wildest expectations. The Advantage2 processor generated samples consistent with solving the Schrödinger equation for spin glasses - in minutes. The best classical tensor algorithms, running on supercomputers, would take millions of years. Moreover, the team demonstrated that entanglement in the simulated system grows according to a surface law - just as Rams and Dziarmaga predicted. It wasn't a coincidence; it was precise theoretical engineering.

The publication was published inSciencein March 2025 and immediately caused a wave of comments. For the first time in history, a quantum processor solved a problem that was (a) fundamental to physics, (b) classically impossible to verify, and (c) potentially useful - because understanding the dynamics of spin glasses has implications for the design of new magnetic materials.

Poland on the quantum map - and beyond

For Poland, this history has a special, bitter tone. Rams and Dziarmaga joined the elite group of Polish physicists publishing inScienceandNatureon quantum computing - alongside professors Marek Kuś from the Center for Theoretical Physics of the Polish Academy of Sciences and Artur Ekert from Oxford (although Ekert has been working abroad for decades). Polish quantum physics is world class.

But Poland does not have a single commercial manufacturer of quantum equipment. There is no national program to build a quantum computer on a scale comparable to the German plan worth 3 billion euros, the French "Naquidis" program or the British National Quantum Strategy with a budget of 2.5 billion pounds. The Polish National Science Center finances basic research at a decent level - OPUS and MAESTRO grants - but between the NCN grant and a spin-off capable of competing with D-Wave there is a gap that even the European Research Council will not bridge.

"The problem is not lack of talent," says Dziarmaga when I ask him about it directly. "The problem is that between the publication of...Scienceand the market product is the capital gap. Deep tech requires tens of millions of dollars of high-risk investment at a very early stage. In Poland, this capital simply does not exist - VC funds invest in e-commerce and SaaS, and public programs are fragmented into grants of several hundred thousand zlotys.

The numbers speak for themselves. According to the report of the European Observatory of Quantum Technologies, in 2025, out of every 100 euros of private investment in quantum startups in Europe, 2.7 euros will go to Poland. Meanwhile, Poland has 8 percent of the European Union's population and the third largest IT sector. The Czech Republic - a country four times smaller - has attracted more capital for quantum technologies than Poland.

The Krakow Center for Quantum Informatics and the Center for Optical Quantum Technologies at the University of Warsaw are world-class institutions, but without industrial facilities, their graduates regularly leave. Rams and Dziarmaga cooperate with D-Wave from Krakow - but it is D-Wave, not the Polish company, that is the beneficiary of their discovery.

Point of no return

There is a moment in this story that makes you think about the future differently than usual. The team of King, Rams and Dziarmaga is already planning the next step: simulating quantum phenomena so complex thatnonethe classical method - even a future one - will not be able to verify the result. This would be a true point of no return: a quantum experiment whose result can only be accepted because there is no mathematical way to verify it.

For physicists, this is a prospect that is both exciting and disturbing. Throughout four centuries of modern science, every experiment has been independently verified. A quantum computer once it crosses the computability limit will render this principle obsolete—at least in its domain.

For Poland, the stakes are more mundane but equally urgent. Every breakthrough with the participation of Polish surnames - like the one inScience— builds an argument for a serious investment in your own quantum ecosystem. It's not about competing with Google or IBM on their terms; the idea is that the next time a professor from the Jagiellonian University co-authors a breakthrough, next to D-Wave, a Polish company will also be included in the editorial footer. Time is short - the best will leave if they have nothing to come back to.

Sources

King A., Nocera A., Rams M.M., Dziarmaga J. et al.,Beyond-classical computation in quantum simulation, Science 387, 1114–1121 (2025), DOI: 10.1126/science.ado6285
Arute F. et al.,Quantum supremacy using a programmable superconducting processor, Nature 574, 505–510 (2019), DOI: 10.1038/s41586-019-1666-5
Gao D. et al.,Establishing a New Benchmark in Quantum Computational Advantage with 105-qubit Zuchongzhi 3.0 Processor, Physical Review Letters 134, 090601 (2025), DOI: 10.1103/PhysRevLett.134.090601
European Quantum Technology Observatory,Quantum Investment Report 2025, eqto.eu/reports
Aaronson S.,Quantum Computing Since Democritus, Cambridge University Press (2013)

A computer that shouldn't work