What "advantage" actually means
The phrase we hear most is "quantum supremacy", coined by John Preskill in 2012 to mean a quantum device doing any task, useful or not, that a classical computer could not do in a reasonable time. "Quantum advantage" is the gentler cousin, and increasingly people add the word "useful" in front of it, meaning a task somebody would actually pay for. Preskill also gave us "NISQ", noisy intermediate-scale quantum, in 2018, for the era of machines too small for error correction but too big to simulate easily. Hold on to the distinction between a contrived task and a useful one; it explains most of the arguments below.
Sycamore, 2019
Google's claim in Nature in October 2019 used a 53-qubit superconducting processor called Sycamore to perform random circuit sampling: run a scrambled circuit, read out bit strings, repeat. Google reported the task took about 200 seconds and estimated a top supercomputer would need 10,000 years. IBM replied within days that, with clever use of disk storage on the Summit supercomputer, the job could be done in roughly two and a half days. Over the following years tensor-network methods brought classical estimates down further still. The experiment was a genuine landmark, and the argument that followed set the pattern for everything since: a claim, a rebuttal, a narrowing gap, and a quieter final answer than the press release.
Boson sampling with photons
The photonic camp made its own run. In 2020 the University of Science and Technology of China published Jiuzhang in Science, a Gaussian boson sampling experiment that detected dozens of photons at once, and USTC's superconducting group followed with the Zuchongzhi processor. In 2022 Xanadu's Borealis, a programmable photonic machine with more than two hundred squeezed-light modes, appeared in Nature. Boson sampling is beautiful physics and a good stress test of hardware, but it is another contrived task, and classical "spoofing" algorithms that mimic its statistics well enough to fool the standard checks have been published. Nobody sensible now thinks boson sampling by itself will pay the bills.
IBM's "utility" experiment, 2023
In June 2023 IBM published a Nature paper (Kim and colleagues) simulating the dynamics of a spin model on a 127-qubit processor, using a technique called zero-noise extrapolation to estimate what a noiseless machine would have returned. IBM was careful to call it "utility" rather than advantage, arguing that the machine was now a useful tool beyond exact classical simulation. Within weeks, groups at Caltech, the Flatiron Institute and elsewhere reproduced the results with tensor-network methods on ordinary computers. We took two lessons: error mitigation is a powerful trick that makes today's machines far more useful than their raw error rates suggest, and the boundary of what classical methods can do moves whenever someone is motivated to move it.
The classical pushback has a name. Beyond tensor networks, "dequantisation" is the practice of finding a classical algorithm that matches a proposed quantum speed-up. Ewin Tang's 2018 result on recommendation systems is the celebrated example: a quantum algorithm claimed an exponential advantage until a classical one, inspired by it, turned out to be just as fast.
The newer claims
The pattern has continued. A 2025 Nature paper from Quantinuum with JPMorganChase and academic partners demonstrated certified randomness, using a trapped-ion machine to produce random bits whose freshness could be checked classically; it is one of the first candidates for a task with a real customer. D-Wave published a Science paper in 2025 claiming its annealing hardware simulated the dynamics of a magnetic material beyond classical reach, and tensor-network groups challenged parts of that claim within weeks. We are not going to tell you who is right; the honest position is that both are being argued in the literature, and we will keep reading.
Where the real prize is
The tasks that would change the world are not sampling problems. They are Shor's algorithm for factoring, which threatens the cryptography discussed in our networks guide, and the simulation of molecules and materials for chemistry. Both need fault-tolerant machines of the kind our error-correction guide describes. In 2019 Craig Gidney and Martin Ekerå estimated that breaking a 2048-bit RSA key would take about twenty million noisy physical qubits running for roughly eight hours. A 2025 preprint by Gidney revised that estimate down to under a million qubits over about a week, by improving the codes and the arithmetic rather than the hardware. Chemistry estimates have followed the same arc: the 2017 analysis of the nitrogenase cofactor FeMoco by Reiher and colleagues has been improved on repeatedly, but the honest numbers still run to millions of physical qubits for days. Those figures move, and the direction has been steadily down.
How we read the next headline
- Is the task useful or contrived? Sampling counts as contrived until someone shows a customer.
- What did the classical baseline assume, and has anyone motivated tried to beat it yet? Give it a month.
- Was the result verified, and how? For large circuits, nobody can check the full output; look for what proxy was used.
- Was error mitigation or post-selection involved, and would it still work at larger scale?
- Does the paper's own abstract use the word "advantage", or only the press release?
We find those five questions turn most announcements into a calmer, more interesting story than the one in the headline.