What remains of D-Wave's annealing supremacy claim?

As of October 28, 2026, the answer is: a narrower claim than the one announced, defended by the claimant, attacked by two classical-methods teams, and scored by no one neutral. D-Wave's March 2025 "quantum computational supremacy on a useful problem" (Science, 2025-03-12) still stands on four result families that nobody has reproduced classically — but that list of four is D-Wave's own scoring (SEC 8-K, 2026-05-26), and the rest of the original suite has been matched, in some cases with lower error than the annealer, by D-Wave's own published account (arXiv:2504.06283). This is the paper trail, dated and linked, both sides.

What exactly did D-Wave claim in March 2025?

A supremacy claim with unusually hard numbers attached. On March 12, 2025, Science published King et al., "Beyond-classical computation in quantum simulation" (DOI 10.1126/science.ado6285; preprint arXiv:2403.00910): simulations of quantum spin-glass dynamics on the Advantage2 annealer across square, cubic, diamond and biclique topologies, at sizes past 5,000 qubits. The company's press release of the same day called it "the world's first and only demonstration of quantum computational supremacy on a useful problem," and priced the classical alternative at "nearly one million years" on Oak Ridge's Frontier supercomputer, consuming "more than the world's annual electricity consumption." Chief Development Officer Trevor Lanting set the bar that the next 19 months would test: "We believe that the ability to recreate the entire suite of results we produced is not possible classically."

What did the classical replies reproduce?

The central lattice geometries — and in some cases with lower error than the annealer. The first rebuttal landed five days before the Science paper itself: on March 7, 2025, Tindall, Mello, Fishman, Stoudenmire and Sels (Flatiron Institute) posted arXiv:2503.05693, simulating the same annealing dynamics with two- and three-dimensional tensor networks plus belief propagation, reporting that "state-of-the-art accuracies can be achieved with modest computational resources" on square, cubic and diamond lattices, and extracting Kibble-Zurek physics on hundreds of qubits. Four days later, Mauron and Carleo (EPFL) posted arXiv:2503.08247 (2025-03-11): time-dependent variational Monte Carlo with polynomially scaling resources, up to 128 spins on a 3D diamond lattice with correlation errors below 7%, at accuracy the authors call "comparable to that of quantum processing units." In May 2026, the Flatiron work passed peer review in Science (DOI 10.1126/science.adx2728; QCR, 2026-05-26).

The most load-bearing concession is D-Wave's own. Its April 2025 reply (arXiv:2504.06283, King and ten co-authors) wrote that the classical methods "represent a significant improvement in the classical state of the art," acknowledged that in some cases the tensor-network results show lower errors than the annealer's, and framed the rebuttals as work that "narrow[s] the parameter space" where beyond-classical simulation has been demonstrated. A supremacy claim whose parameter space narrows under fire is, by definition, a smaller claim than the one in the press release.

What does D-Wave still defend?

Four result families — on its own scoring. The company's response to the Science publication of the Flatiron work, filed as SEC 8-K Exhibit 99.1 on May 26, 2026 under the title "D-Wave's Quantum Supremacy Result Stands," lists what the tensor networks did not reproduce: the non-planar biclique topologies, the largest 3D lattice simulations, the low-precision ensembles where correlations grow fastest, and the full-state and fourth-order observables. It re-asserts the "nearly a million years" Frontier estimate for matrix-product-state methods on the largest problems, and quotes CEO Alan Baratz: "D-Wave's demonstration of beyond-classical computation continues to hold up under careful scientific scrutiny." The filing also cites the company's August 2025 study (arXiv:2508.15759), which inverts the telescope — it uses the annealer as "a ground truth" to evaluate classical simulations, reports observations that "run contrary to previous scaling predictions," and calls for "caution when extrapolating the accuracy of classical simulations of quantum dynamics."

The structural problem will not go away on its own: the surviving perimeter is scored by the claimant. Every document defending the claim is authored by D-Wave scientists or filed by the company; every document attacking it is authored by classical-methods teams. Rosetta Quantum found no neutral third party that has adjudicated the full suite — this dispute runs on arXiv comments and SEC filings, not on an agreed benchmark. That is the same incentive vacuum we measured from the other side in our quant-ph baseline census, and the same word-game pressure documented in utility vs. advantage.

What does the paper trail say, document by document?

Did the optimization side of annealing fare better?

No — the separate scaling-advantage story eroded under runtime accounting. Tuziemski et al. (arXiv:2510.06337, 2025-10-07) revisited the reported annealing scaling advantage of Munoz-Bauza & Lidar (2025) and argue that "under a robust definition, no advantage remains": a classical Simulated Bifurcation Machine performs comparably or better, and readout time dominates total QPU time once everything is counted. On the commercial side, the audit we covered in our portfolio re-verdict measured that QPU time accounts for 0.68% of the compute budget of D-Wave's own hybrid CQM solver (arXiv:2605.17623) — "classical achievability, not a QPU ablation." Meanwhile the dispute did not stop procurement: two on-premise systems were bought in 2025 (Jülich, announced 2025-02-13; Davidson Technologies, Huntsville, 2025-04-28 — dated sources in our on-premise census). Whatever those buyers will get from the machines, the measured commercial value today does not ride on the supremacy claim.

What we don't know

• Whether the four defended families are classically out of reach or merely not yet attempted. An absence of rebuttal is not a proof of hardness — and D-Wave's August 2025 paper (arXiv:2508.15759) argues, correctly, that scaling extrapolations are unreliable; that argument cuts in both directions, including against the "nearly a million years" figure, which is itself an extrapolation.
• Whether Science will publish a formal adjudication (technical comment or editorial resolution) of the pair of papers it has now published on opposite sides. We found none as of 2026-10-28.
• Whether any of the defended perimeter — biclique topologies, low-precision ensembles, fourth-order observables — maps onto a problem a customer would pay to solve. No source in this file prices that.
• We did not rerun any simulation. This is a documentation audit with linked primary sources, not a replication. Rosetta will revisit this verdict when a neutral replication of the biclique or largest-3D instances appears, or when a formal adjudication is published — whichever will come first.

Rosetta Quantum publishes verdicts with raw, reproducible data. This is educational content, not a product claim.