On 2026-07-20, a paper appeared in the journal Science. Boil it down to one sentence: an ordinary laptop solved a problem that a quantum computer had been said to be the only way to crack [source: Science, 2026]. A year earlier, a quantum-computing company had declared that this very calculation was, for all practical purposes, impossible on a classical computer.
The direction runs opposite to the usual headline. We are used to news that "a quantum computer beat a supercomputer by tens of thousands of times." This time, modest classical hardware pushed into territory that had been claimed for quantum. And that is exactly why the episode is such a good window onto what the phrase "quantum advantage" really means. This article separates what has been verified from what is claim or hype, and asks how far genuine, practical quantum computing still is.
A note on how this article labels things. Three kinds of statement get mixed together in quantum headlines, and they carry very different weight. There are measured results that have passed peer review and appeared in a journal. There are claims a company makes about its own hardware, published on its own site or in its own press release. And there are forecasts — roadmap dates and expectations about what comes next. Every figure below is marked with which of the three it is, because a number's tier matters more than its size.
In this article
- The line a laptop redrew
- What "quantum advantage" actually means
- The D-Wave case: claim and rebuttal
- But it isn't all hype
- The distance still to real use
- Conclusion — what to watch
The line a laptop redrew
What the Flatiron team actually computed
The work came from researchers at the Center for Computational Quantum Physics at the Simons Foundation's Flatiron Institute, together with Boston University. Lead author Joseph Tindall and colleagues took the dynamics generated by hundreds of interacting qubits — the basic units of information in a quantum computer — and solved them by compressing the problem with a mathematical tool called a tensor network [source: Science, 2026]. Much of the calculation ran not on special hardware but on a personal laptop, using ITensor, a software library developed at the center [source: Flatiron Institute, 2026]. Tindall described the approach as "a zip file for the wave function — you've taken all this information and compressed it into this mathematical data structure" [source: Flatiron Institute, 2026].
Two ingredients did the heavy lifting. One is the tensor network above; the other is an algorithm called belief propagation. Belief propagation is an old technique, devised in the 1980s for classical statistical inference, and it was recently revived and adapted for quantum systems [source: Flatiron Institute, 2026]. With this combination, the team tracked the time evolution as entanglement grew and pulled out the observable values.
The novelty lay less in either ingredient than in their combination. Tensor networks are an established tool and belief propagation is older still, devised in the 1980s, long before anyone applied it to quantum systems. What the paper's own title makes precise is the scope: "Dynamics of disordered quantum systems with two- and three-dimensional tensor networks" [source: Science, 2026]. Two- and three-dimensional lattices are exactly the geometries D-Wave's experiment used. Pairing a compression scheme with an inference algorithm revived for quantum systems is what brought the dynamics of hundreds of interacting qubits within reach of hardware anyone can buy.
From preprint to peer review
The 2026 paper did not appear out of nowhere. The classical rebuttal was first posted as a preprint — a manuscript made public before peer review — in March 2025, the same month as D-Wave's own publication, as arXiv:2503.05693 [source: Science, 2026]. A second, independent rebuttal, arXiv:2503.08247, followed in that same month. What changed between March 2025 and July 2026 was not the result but its standing: the work went through review and was published as Science 392(6800):868 [source: Science, 2026]. That interval is worth remembering the next time a preprint is reported as a settled finding.
Why it landed so hard
Why was that so striking? Because just a year earlier another team had performed the same kind of calculation on a quantum computer and argued that a classical computer could not reproduce the achievement [source: Science, 2025]. In other words, this paper is an event in which modest classical computation pushed inward on a line that had been marked "quantum only." Restraint is in order, though. We have to draw a precise distinction, later, between what was matched and what was not. The real lesson of this story is not "classical won" but "how a claim of advantage is built, and how it gets tested."
What "quantum advantage" actually means
Start with the vocabulary. "Quantum supremacy" and "quantum advantage," so often blurred together in the news, in fact point to different things.
Supremacy and advantage are not the same
The term "quantum supremacy" was coined in 2012 by the theoretical physicist John Preskill [source: Preskill, 2012]. It denotes the threshold at which a quantum device, on some task, first surpasses every classical computer on Earth. There is an important caveat: that task is usually a contrived benchmark with no commercial use. The point is not to ship a useful service but to prove that the hardware can do something classically intractable. "Quantum advantage," by contrast, goes a step further and refers to solving a genuinely useful, real-world problem more efficiently than classical machines can. If supremacy is a "threshold," advantage puts the emphasis on "usefulness." Because of the connotations of the word "supremacy," many researchers now prefer to speak of "advantage."
The context of that coinage is telling. Preskill, a theorist at Caltech, introduced the term in a paper titled "Quantum computing and the entanglement frontier" [source: Preskill, 2012]. The framing was a frontier — a line to be crossed — not a product to be sold. Read that way, "supremacy" was always a marker for physicists rather than a promise to customers, which is part of why the word has aged badly in press coverage. Keeping the two terms apart is not pedantry: a headline announcing supremacy and a headline announcing advantage are making claims of very different sizes.
Why the numbers keep changing
It pays to build one habit: reading the multiplier attached to any advantage claim — "tens of thousands of times faster than a supercomputer" — as conditional rather than absolute. In 2019, Google used its 53-qubit Sycamore processor to complete a particular random circuit sampling task in 200 seconds and announced that the fastest supercomputer of the day would need 10,000 years [source: Nature, 2019]. But IBM promptly countered that a cleverer classical algorithm would shrink that time to a matter of days [source: Nature, 2019]. The lesson is clear. Every advantage claim carries the clause "compared with the best classical method known so far," and when a better classical algorithm arrives, the gap can narrow or even vanish. The laptop episode is simply the latest edition of that lesson.
That habit turns into three questions worth asking of any multiplier. Against which classical method was it measured — the best one known, or the best one the team tried? On which problem, and at what size? And who checked it? The 2019 announcement answers the first question badly in hindsight: IBM's counter did not dispute that Sycamore ran the task in 200 seconds, it disputed the classical baseline the 10,000-year figure was measured against [source: Nature, 2019]. A multiplier is a statement about two things, and the classical half of it changes faster than the quantum half.
Three tiers of evidence
It helps to sort the claims in this story by where they were published, because venue tracks scrutiny. D-Wave's 2025 result is a peer-reviewed paper in Science [source: Science, 2025], and so is the 2026 classical reproduction [source: Science, 2026]. Google's Quantum Echoes result appeared in Nature and on the company's research blog [source: Google Quantum AI, 2025]. D-Wave's response to the classical work is a company press release, not a peer-reviewed reply [source: D-Wave, 2026]. The argument that classical methods cannot reach Quantum Echoes is a preprint [source: arXiv, 2026]. IBM's timeline is a chief executive's forecast [source: IBM, 2026]. None of these is worthless. They are simply not interchangeable.
The D-Wave case: claim and rebuttal
The claim
Now to the origin of this episode. In March 2025, the Canadian quantum company D-Wave published "Beyond-classical computation in quantum simulation" in Science [source: Science, 2025]. Using a roughly 5,000-qubit quantum annealer called Advantage2, the team simulated non-equilibrium magnetic spin dynamics — in plain terms, how tiny magnetic needles inside a magnet churn over time — across several lattices, including square, cubic and diamond [source: Science, 2025]. And for the largest problems, they argued that reaching the same quality by classical means would take nearly a million years even on Frontier, one of the world's top supercomputers [source: D-Wave, 2026]. That million-year figure should be read as D-Wave's own estimate, not an independently verified number.
Two details in that paper matter for reading the dispute. The lattices were not only square, cubic and diamond but also a biclique geometry [source: Science, 2025]. And the classical comparison was not against every possible classical method but against a specific one — matrix product states (MPS) — run on Frontier [source: Science, 2025]. The million-year figure is therefore best read as "this long, with that method, on that machine." It is a proponent's estimate against a chosen baseline, which is precisely the structure the 2019 Sycamore claim had.
The classical rebuttal
It was this claim that the Flatiron team's classical computation pushed into. Using tensor networks tailored to each lattice, plus belief propagation, they reproduced the spin-glass dynamics D-Wave had produced — for problems on the scale of hundreds of qubits, on hardware no grander than a laptop or workstation [source: Science, 2026]. Much of what had been called "quantum only," in other words, turned out to be reachable with clever classical mathematics.
The scale here is easy to garble, and the garbled version is the one that travels. Advantage2 is a processor of roughly 5,000 qubits, and the problems D-Wave ran on it reached the scale of thousands of qubits [source: Science, 2025]. The classical reproduction worked at the scale of hundreds of qubits [source: Science, 2026]. The exact number of qubits involved varies from problem to problem, so no single headline figure exists. "A laptop beat a 5,000-qubit quantum computer" is therefore the wrong summary. The accurate one is narrower and more interesting: on a class of problems at the hundreds-of-qubits scale, a laptop matched what had been presented as out of classical reach.
The counter-rebuttal
But the story does not end in a one-sided victory. D-Wave issued an official rebuttal, arguing that the classical method did not reproduce the full scope of its paper [source: D-Wave, 2026]. Specifically, that classical computation did not tackle the most complex lattice geometry, the largest three-dimensional simulations, the low-precision regimes where correlations grow fastest, or fourth-order observables — the "hardest stretches" of the work [source: D-Wave, 2026]. In short, the classical computation narrowed the line but did not overturn all of it. Both sides have their evidence, and just how far classical methods have caught up remains under debate. That very tension shows how slippery the concept of "advantage" is.
It is worth being precise about what D-Wave says was left untouched, because the list is specific: the most complex lattice geometry, the largest three-dimensional simulations, the low-precision ensembles where correlations grow fastest, and fourth-order observables and the full state [source: D-Wave, 2026]. Note what is not in dispute. Neither side questions that the other's computation was performed. The argument is about coverage — how much of the 2025 experiment the 2026 classical method actually reproduced. Note also the asymmetry of venue: the classical result went through peer review, while the response to it is a company statement. That does not make the response wrong, but it does place the two on different footing.
But it isn't all hype
Google's Quantum Echoes
Does that make quantum advantage merely an inflated tale? Concluding so would err in the other direction. The frontier really is advancing, and there are cases to show it. In October 2025, Google Quantum AI ran an algorithm called Quantum Echoes on a 65-qubit portion of its 105-qubit Willow processor and claimed what it called a "verifiable quantum advantage" [source: Google Quantum AI, 2025]. The algorithm uses a quantum "echo" signal known as an out-of-time-order correlator (OTOC), and by the company's account it ran about 13,000 times faster than the best classical simulation [source: Google Quantum AI, 2025]. Unlike the 2019 random sampling, Google stressed, the result is deterministic and can be verified by repetition.
Two things anchor that claim, and one qualifies it. The result appeared in Nature as well as on the company's blog, which puts it a tier above a press release [source: Google Quantum AI, 2025]. And Google frames the technique not as a contrived benchmark but as a way to learn the structure of natural systems — molecules, magnets, even black holes [source: Google Quantum AI, 2025]. That is exactly the supremacy-versus-advantage distinction described earlier. Now the qualifier: the 13,000-fold figure is Google's own, measured against the best classical simulation the company identified. It is a claim of the same shape as the ones this article has been taking apart.
The classical weapon that does not reach
There is one more telling contrast. A follow-up analysis argued that the very classical weapon that caught up with the D-Wave problem — belief-propagation tensor networks — cannot feasibly simulate Google's Quantum Echoes experiment [source: arXiv, 2026]. In other words, the same classical technique topples some quantum experiments and fails to touch others. The frontier is not a wall that moves only one way; it is a living boundary that both sides keep pushing and pulling. So the cynicism that "quantum computers are all a scam" and the overheating that "they already crush classical" are both inaccurate.
That follow-up analysis deserves its own label. It is arXiv:2604.15427, a preprint rather than a peer-reviewed paper, so it sits a tier below the two Science papers at the centre of the D-Wave dispute [source: arXiv, 2026]. Its argument is also narrow by construction: the title says that tensor networks with belief propagation cannot feasibly simulate the experiment, which is a statement about one classical technique, not a proof that no classical technique ever will. Given how the D-Wave episode unfolded — a claim of classical infeasibility met in the same month by a classical rebuttal — narrow is the right way to read it.
The distance still to real use
IBM's forecast, and what backs it
So how close is genuine usefulness — advantage on a problem that matters? Even the most aggressive forecasters in the field frame the moment not as "this year" but as "the first example this year." In April 2026, IBM's chief executive, Arvind Krishna, said the company "strongly believes our partners will achieve the first examples of quantum advantage this year, leveraging IBM hardware" [source: IBM, 2026]. The advantage he means is "the point at which a quantum computer can solve a problem beyond the practical reach of classical machines," and he cited, among his evidence, a roughly 300-atom molecular-system simulation carried out with Cleveland Clinic [source: IBM, 2026].
Krishna made that statement on 2026-04-30, and the evidence he cited runs a little wider than a single simulation: alongside the roughly 300-atom molecular system done with Cleveland Clinic, he pointed to magnetic-materials modelling [source: IBM, 2026]. Where does that sit among the tiers set out at the top of this article? Squarely in the forecast bracket. It is an expectation stated by the chief executive of a company that sells the hardware in question, not a measured result. That is no reason to dismiss it — a company generally knows its own roadmap best — but it is a reason to file it separately from the two peer-reviewed papers weighed above.
Why fault tolerance is the gate
But "the first example" and "everyday usefulness" are different things. Today's quantum hardware is fragile against noise and error-prone. Lifting it to a practical level requires a fault-tolerant quantum computer that corrects errors in real time — and even IBM only aims to unveil its first large-scale version of that in 2029 [source: IBM, 2026]. And as the D-Wave case in this article reminds us, an advantage on a benchmark is not yet an advantage in application. Between one impressive demonstration and steadily beating classical methods on real problems — drug discovery, materials, finance — there is still a wide river. Genuine usefulness is not a shipped product but a target still on the roadmap.
The roadmap does move in visible increments. In November 2025 IBM announced new processors, new software and new algorithms — including a roughly tenfold speedup in decoding — and presented them as progress along both tracks at once, toward advantage and toward fault tolerance. Read that the way you would read any vendor milestone: a company reporting its own progress against its own plan. It is useful information about direction and weak information about arrival.
So what would a first example look like when it arrives? On the evidence assembled here, it would have to satisfy three conditions at once. A problem someone actually wants solved rather than a benchmark — that is the line between supremacy and advantage. A result others can reproduce, which is what Google was reaching for in calling its Quantum Echoes claim verifiable [source: Google Quantum AI, 2025]. And a classical baseline that holds up for more than a season, which is exactly where the D-Wave claim ran into trouble [source: Science, 2026]. An announcement that satisfies only the first is a demonstration, not a milestone.
Conclusion — what to watch
To sum up: in July 2026, modest classical hardware reproducing, at laptop scale, much of a calculation once called "quantum only" is a verified fact [source: Science, 2026]. At the same time, whether that classical computation overturned even the hardest stretches is the point D-Wave disputes [source: D-Wave, 2026], and a different Google experiment remains out of reach of the same classical technique [source: Google Quantum AI, 2025]. Quantum advantage is neither "already won" nor "all bluff"; it is a moving boundary under continual test.
Three things to watch
What should you watch from here? First, the speed of the classical rebuttal that follows every advantage claim — how many months a claim survives is a measure of maturity. Second, verifiability: as with Google's emphasis on a "repeatably verifiable" result, the question is whether an advantage is one that others can reproduce. Third, whether the hardware roadmap toward fault tolerance actually keeps promises like 2029. In the end, the real question in quantum computing is not "when did it win" but "on what, for how long, and verifiably." When you read the next headline, ask those three things together.
And ask them in a specific order. First, where did this appear — a peer-reviewed journal, a company blog, or a preprint? Second, what classical baseline is the multiplier measured against, and how old is that baseline? Third, at what problem size, in qubits, was the comparison actually run? The laptop story of July 2026 answers all three cleanly, which is why it repays close reading even though its conclusion is unglamorous. Most quantum headlines will not answer them at all — and that silence, more than the size of the number, is the tell.