Quantum Advantage, Supremacy And The Claims That Did Not Survive

Every year or so a headline announces that a quantum computer has done something no classical computer could. Some of those claims have held up. Others were matched within weeks or months by cleverer classical software. If you are deciding how seriously to take quantum computing, as a security leader or an investor, the pattern matters more than any single result.

This article explains what “supremacy” and “advantage” mean, walks through the main claims from 2019 to 2026 and the classical responses to them and ends with a short test you can apply to the next announcement. It assumes the background from the earlier articles in this series, especially the one on error correction.

Supremacy, Advantage And Utility

“Quantum supremacy” was the original term for a quantum device completing a task that no classical computer could finish in any reasonable time. The task did not need to be useful. It only had to be well defined and, on the strength of complexity theory and the best known classical methods, believed to be very hard to simulate. No such claim comes with a proof that every possible classical algorithm would fail. Many researchers now prefer “quantum advantage”, a term whose meaning varies between groups and is often reserved for results that are also useful, verifiable or both. IBM used “utility” in 2023 to describe experiments it argued were beyond brute-force classical simulation and scientifically useful, even without full error correction.¹

The differences matter because a supremacy result on a contrived task says nothing about whether a machine can break encryption or design a drug. Each claim also rests on an estimate of the best classical method, and classical methods keep improving.

The Record So Far

How The Early Claims Were Narrowed

Google’s 2019 Sycamore paper reported that its 53-qubit processor took about 200 seconds to sample one random circuit a million times, a task it estimated would take a state-of-the-art supercomputer about 10,000 years.² IBM published a response on 22 October 2019, the day before the paper appeared, arguing that a classical system using disk storage and better simulation techniques could do the ideal version of the task in 2.5 days.³ That was an estimate, not a run. The more decisive response came in 2022, when Pan, Chen and Zhang generated a million samples for the Sycamore circuits in about 15 hours on a cluster of 512 GPUs, and estimated that an efficient implementation on an exascale supercomputer could be faster than Google’s hardware.⁴ Their method used tensor networks, which compress a large quantum state into many small linked blocks of numbers that a classical computer can handle.

IBM’s own 2023 utility experiment, on a 127-qubit Eagle processor, met a similar fate. About two weeks after it appeared, Tindall and colleagues posted a classical simulation that combined tensor networks with belief propagation, a technique that passes approximate summaries between neighbouring blocks instead of computing everything exactly. They reported results more accurate than the quantum processor’s, later published in PRX Quantum.⁵ The experiment remained a useful demonstration of noise handling, but it did not show a task out of classical reach.

The Current Claims

Google’s December 2024 Willow result repeated random circuit sampling at a much larger scale: under five minutes on Willow against an estimated 10 to the power 25 years for the Frontier supercomputer. Google was candid about the limits. It said the benchmark has yet to show commercial applications, and that the classical estimate generously assumed unlimited fast access to disk storage.⁶ The gap is so large that a full classical reversal looks unlikely, but the task itself remains of no practical use.

D-Wave’s 2025 Science paper claimed that its Advantage2 quantum annealer simulated the dynamics of magnetic models known as spin glasses with an accuracy that leading classical approximation methods could not match in reasonable time.⁷ A Flatiron Institute team then published classical simulations of the same models in Science in 2026, reporting state-of-the-art accuracy with modest computing resources.⁸ D-Wave responded in May 2026 that the classical work did not attempt its hardest lattice geometries or largest three-dimensional cases.⁹ This claim is disputed, and both sides have published their arguments.

Google’s October 2025 Quantum Echoes experiment aimed at something different. Instead of a long list of random samples, whose quality can only be judged statistically and, at this scale, only with enormous classical effort, it measured an average value that any good quantum computer running the same circuit should reproduce. Google reported that the measurement took about two hours on 65 of Willow’s qubits and would take a classical supercomputer about 13,000 times longer.¹⁰ The result was peer reviewed and published in Nature. As of October 2026 no published classical method matches it. The most direct test so far, an April 2026 preprint, found that the belief propagation approach that caught up with IBM’s 2023 experiment cannot feasibly simulate it, though that study comes from Google’s own quantum team rather than an independent group.¹¹

In November 2025 IBM said it expected the wider research community to confirm the first cases of verified quantum advantage by the end of 2026. It also said it was contributing, alongside Algorithmiq, Flatiron Institute researchers and BlueQubit, to an open, community-led tracker of candidate experiments.¹² On 30 July 2026 IBM announced three demonstrations, each posted as a preprint: a sampling experiment with the University of Chicago whose accuracy could be certified on the device and two physics simulations, one with Qedma and one with Algorithmiq.¹³¹⁴ IBM’s roadmap page now states that it and its partners delivered advantage in 2026 as promised.¹⁵

The sampling result was challenged within about two weeks. Manabe, Gu and Pan, at the Singapore University of Technology and Design and NVIDIA, exploited the simple one-dimensional layout of the original circuit and computed the exact probabilities of all 2,051 outputs IBM had published in 37.3 minutes on 256 GPUs. Their numbers also agreed with IBM’s estimate of how accurate the hardware had been.¹⁶ IBM’s revised preprint of September 2026 acknowledges this, replaces the demonstration with a 64-qubit circuit on a different layout and adds the three classical researchers as co-authors.¹⁷ As of October 2026 none of the three IBM-linked papers has been through peer review. Treat “advantage delivered” as IBM’s own claim, still being tested in the way described above.

How To Judge The Next Claim

The history suggests a short set of questions. Work through them for any new announcement.