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In 2019, Google claimed that its quantum computer, Sycamore, could complete calculations that would take 10,000 years to run on the world鈥檚 leading supercomputer 鈥� a feat of 鈥渜uantum supremacy鈥�. Last year, however, other researchers refuted Google鈥檚 claim by completing one of the calculations on a conventional computer in just 14.22 seconds. Undaunted, Google made a second claim for quantum supremacy a few months ago, with a new quantum computer called Willow. The firm estimated that a leading supercomputer would require 10 septillion years to match Willow. But whether this claim of quantum supremacy will stand the test of time remains to be seen.

鈥淚 think the jury is still sort of out there,鈥� says at the University of Chicago. He and his colleagues have previously used traditional, or classical computers to investigate claims of quantum supremacy, but he says he doesn鈥檛 see a clear path to doing so in the case of Willow. That said, mathematical arguments in favour of the claim standing forever are also unclear.

Google鈥檚 team is not the only one to have made a quantum supremacy claim in recent years. So have researchers at quantum computing start-ups and , and at the University of Science and Technology of China 鈥� although all such claims have since been undermined, with the exception of Willow and Quantinuum.

All claims of quantum supremacy involve tasking a quantum computer with verifying that a sample of numbers output by a quantum circuit, or a sequence of computational operations, have a truly random distribution 鈥� a test that is often called 鈥淩CS鈥� or random circuit sampling.

For several years, Fefferman and his colleagues have been trying to rigorously prove that RCS is truly mathematically hard for classical computers but not quantum ones. This would add credence to the quantum computing industry鈥檚 acceptance of RCS as a good quantum supremacy benchmark.

In 2018, he and his colleagues were able to give strong that RCS is indeed astonishingly hard to simulate on classical computers 鈥� in fact, almost as hard as the most difficult case that mathematicians agree on. But when Google鈥檚 2019 quantum supremacy claim fell, Fefferman and his colleagues realised that their analysis was incomplete, he explained on 17 March at the 聽in California. 鈥淥ur work was interesting from a theoretical point of view, but it really wasn鈥檛 taking into account what I see as the main potential caveat with these experiments, which is that they have so much noise,鈥� says Fefferman.

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For instance, Quantinuum鈥檚 quantum computer, which claimed quantum supremacy in 2024, produced results without making a single error only . The errors it made the rest of the time 鈥� for instance, due to disturbances from its environment 鈥� are the noise that Fefferman says is to blame for the defeat of so many quantum supremacy claims. 鈥淲hen we really understand these experiments in terms of realistic noise, we realise that the noise is killing a lot of the quantum advantage, and the experiments can often be simulated [on classical computers] in a surprisingly short amount of time,鈥� he says.

As quantum computers get bigger and less noisy, there may be a 鈥淕oldilocks zone鈥� of sorts where experiments like RCS remain unbeatable, even if they have not been rigorously proven as such, says Fefferman. He says that to make the strongest statement about what constitutes a perfect quantum supremacy test, however, we may have to wait for quantum computers to become 鈥渇ault tolerant鈥�, or able to catch and correct all their errors.

We may not be there yet, but at Google is convinced that the noise issue won鈥檛 undermine the claim that Willow has achieved quantum supremacy. He says Willow is big enough and uses quantum circuits comprising so many operations that 鈥渢he cost of classical simulation would be impractically high, assuring that the experiment will never be simulated鈥�.

In Fefferman鈥檚 view, what is most important is that the cycle in which quantum and classical computers constantly strive to outdo each other keeps going. Each new quantum supremacy claim, whether it stands the test of time or not, brings us closer to understanding exactly how quantum computers differ from their traditional counterparts, he says.

There has already been one practical win for quantum computers: last month a team of researchers used a Quantinuum quantum computer in conjunction with a traditional supercomputer to leverage RCS for a , which could be useful for cryptography and secure communication. And Google鈥檚 Willow still reigns quantum supreme.