Advantage Watch

How to read this

Each row is a published claim that a quantum device did something a classical computer could not, in the claimants' own words, and every classical response we could find in journals and on arXiv. Dates are the first public posting of each paper (the arXiv version where there is one, otherwise the journal date). A response counts toward 'days to a classical answer' only if it targets the same experiment and its authors say they ran it. The status is the desk's reading of those responses, not a verdict from either side.

Three statuses, and none of them is a ruling:

• Matched. A published classical method reproduces or beats the experiment's reported benchmark, by its own authors' account.
• Contested. Classical work claims to match the result at some scales, on some instances, or for a later experiment in the same line, and the dispute is not closed.
• Standing. We found no published classical reproduction as of the check date. This is an absence in our search, not a proof.

The Ledger scores promises about the future on their deadlines. This page scores results that are already published, which are tested differently: by whether anyone could do the same thing without the quantum machine.

Random circuit sampling, 53 qubits, 20 cycles

Google Quantum AI · quantum supremacy claim · Status: Matched.

The claim (23 October 2019, Arute et al., Nature 574, 505): About 200 seconds to take a million samples, against an estimate of 10,000 years on a classical supercomputer.

What happened next

• 21 October 2019, an estimate, not a run: arXiv:1910.09534. Pednault, Gunnels, Nannicini, Horesh and Wisnieff (IBM). Argued that such circuits can be simulated on the Summit supercomputer in a matter of days. An argument about cost, not a run. Posted two days before the Nature paper, after the 2019 leak.
• 4 March 2021, a classical run: arXiv:2103.03074. Pan and Zhang. One million correlated bitstrings at a cross-entropy score of 0.739 on 60 GPUs. Correlated samples, so not the same task as the experiment's uncorrelated ones.
• 27 October 2021, a classical run: arXiv:2110.14502. Liu and co-authors. Sycamore sampling in 304 seconds on the new Sunway supercomputer (SC21). Correlated samples, so not the same task as the experiment's uncorrelated ones.
• 4 November 2021, a classical run: arXiv:2111.03011; Physical Review Letters 129, 090502 (2022). Pan, Chen and Zhang. One million uncorrelated bitstrings at a fidelity of about 0.0037 in about 15 hours on a cluster of 512 GPUs. The first run with uncorrelated samples at a fidelity above Google's.
• 27 June 2024, a classical run: arXiv:2406.18889; National Science Review 12, nwae317. Zhao, Zhong, F. Pan, P. Zhang, J.-W. Pan, Chen and co-authors. 1,432 GPUs; a higher linear cross-entropy score than the experiment and, by the authors' account, seven times faster than Sycamore's run.

Our reading. Two papers, with overlapping authors (Feng Pan and Pan Zhang appear on both), report running classical samplers that reach or exceed the experiment's score. The 10,000-year estimate did not survive; the experiment itself is not in doubt.

Gaussian boson sampling, up to 76 photon clicks (Jiuzhang)

USTC (Zhong, Pan and co-authors) · quantum computational advantage claim · Status: Contested.

The claim (3 December 2020, Zhong et al., Science 370, 1460): A sampling rate about 10^14 times faster than the best known classical simulation on supercomputers.

What happened next

• 3 August 2021, an estimate, not a run: arXiv:2108.01622; Science Advances 8, eabl9236 (2022). Bulmer and co-authors. Cuts the estimated cost of classically simulating state-of-the-art Gaussian boson sampling, Jiuzhang scale included (up to 100 modes, 92 photons), from 600 million years to months on a supercomputer of about 100,000 cores. A cost estimate, not a run.
• 23 September 2021, a partial match: arXiv:2109.11525. Villalonga and co-authors. Names the 2020 and 2021 experiments and gives classical samplers with better total variation distance and KL divergence than the experiments, by the authors' account. The benchmark is low-order marginals, which the USTC authors dispute as a test.
• 6 June 2023, a partial match: arXiv:2306.03709; Nature Physics 20, 1461 (2024). Oh, Liu, Alexeev, Fefferman and Jiang. A tensor-network sampler that, they report, simulates the ideal distribution better than the experiment does, for the largest Gaussian boson sampling experiment so far. The abstract does not name which experiment, so we do not count it as an answer to the 2020 one.

Our reading. Two classical papers target the 2020 and 2021 experiments: a cost estimate in months rather than millions of years, and a sampler that beats the experiments on distance measures. Whether those measures are the right test is disputed, so the line stays contested. A later classical sampler (Oh et al.) beats the largest experiment of its day on the authors' own measure; whether it answers this one is not stated in the paper. The 255-click Jiuzhang 3.0 (arXiv:2304.12240) and the 8,176-mode 2026 Nature experiment are separate claims and are not on this list.

Kicked Ising dynamics on a 127-qubit processor, error-mitigated

IBM Quantum with UC Berkeley · 'utility' claim (IBM's own word; not called advantage) · Status: Matched.

The claim (14 June 2023, Kim et al., Nature 618, 500): Accurate expectation values from a noisy 127-qubit processor, beyond the reach of the brute-force classical methods of the day.

What happened next

• 26 June 2023, a classical run: arXiv:2306.14887; PRX Quantum 5, 010308 (2024). Tindall, Fishman, Stoudenmire and Sels. Tensor networks with belief propagation, reported as significantly more accurate and precise than the experiment, and able to reach the thermodynamic limit.
• 28 June 2023, a classical run: arXiv:2306.16372. Begusic and Chan. Fast classical simulation by sparse Pauli dynamics of the same experiment.
• 28 June 2023, an argument: arXiv:2306.15970. Kechedzhi and co-authors (Google Quantum AI). Google's own classical analysis of the same experiment, a third attempt.

Our reading. Two independent classical methods simulated the experiment within two weeks of the paper. IBM did not call it advantage; it is on this list because it was widely read as one.

Random circuit sampling, 67 qubits, 32 cycles (Sycamore)

Google Quantum AI · beyond-classical claim · Status: Standing.

The claim (21 April 2023, Morvan et al., arXiv:2304.11119; Nature 634, 328 (October 2024)): Beyond the reach of existing classical supercomputers at this size. The arXiv version, posted April 2023, already carried the 67-qubit claim.

What happened next

• 8 November 2022, a general result: arXiv:2211.03999; STOC 2023. Aharonov, Gao, Landau, Liu and Vazirani. A polynomial-time classical algorithm for noisy random circuit sampling at a constant noise rate per gate. Its authors say it is not practical in its present form and does not address finite-size experiments. It predates the claim, so it is context, not a response.

Our reading. We found no published classical reproduction of this experiment's samples. The one general result (above) is asymptotic and its authors say it does not cover experiments of this size. Google's December 2024 Willow post gives a figure of under five minutes against 10^25 years; that belongs to a separate 105-qubit experiment on a different chip and is not what this row tests. A classical-cost figure of that size is a model estimate, and the 2019 estimate fell, so it is not a safe number.

Quantum annealing dynamics of spin glasses

D-Wave · beyond-classical claim (D-Wave's press release said 'quantum supremacy') · Status: Contested.

The claim (1 March 2024, King et al., arXiv:2403.00910; Science 388, 199 (2025)): Annealing processors generate samples in close agreement with the Schrödinger equation faster than leading classical methods (tensor networks and neural networks).

What happened next

• 7 March 2025, a classical run: arXiv:2503.05693; Science 392, 868 (2026). Tindall, Mello, Fishman, Stoudenmire and Sels (Flatiron Institute). Tensor networks with belief propagation; the authors report state-of-the-art accuracy with modest computational resources, on the same spin-glass models. Published in Science, May 2026.
• 11 March 2025, a partial match: arXiv:2503.08247. Mauron and Carleo (EPFL). A time-dependent variational Monte Carlo method matching or beating D-Wave's reported accuracy on systems up to 128 spins; not shown at D-Wave's largest instances.

Our reading. Two classical groups say they match the result, one on the experiment's own instances, one at smaller sizes. D-Wave's largest instances are not claimed by the second. One is now in a journal (Science, May 2026); neither has settled the question.

This is also a claim on the Ledger, scored on its own deadline.

Out-of-time-order correlator ('Quantum Echoes') on Willow

Google Quantum AI · verifiable advantage claim · Status: Standing.

The claim (22 October 2025, Google Research post; Nature, 'Observation of constructive interference at the edge of quantum ergodicity'): About two hours on Willow against an estimate of 13,000 times longer on a classical supercomputer.

What happened next

• 16 April 2026, an argument: arXiv:2604.15427. Bermejo, Villalonga, Ware, Vidal and Szasz. Argues that tensor networks with belief propagation cannot feasibly simulate the experiment. This supports the claim against one named method. All five authors list Google Quantum AI as an affiliation (Bermejo also lists two Spanish institutions), so it is not an independent test.

Our reading. No published classical simulation found. Google's own post says its team spent an estimated ten person-years red-teaming the result with nine classical algorithms; that is the claimant's account.

Floquet dynamics on up to 74 qubits (IBM Heron with Qedma error suppression)

IBM and Qedma · quantum advantage claim · Status: Standing.

The claim (30 July 2026, IBM newsroom announcement): Quantum advantage on commercially available hardware, in a pre-print that is not yet peer reviewed. IBM and Qedma say classical methods could not consistently agree at the scale reached and that the result was cross-validated on Quantinuum trapped-ion hardware. The circuits are released to the Quantum Advantage Tracker for classical benchmarking.

What happened next

No classical response recorded yet.

Our reading. Announced 64 days before this check. The circuits are public for classical attempts and we have not recorded a published reproduction. IBM's own 2025 prediction, that the wider community would confirm a case by the end of 2026, is tracked on the Ledger.

This is also a claim on the Ledger, scored on its own deadline.