How can you tell if a quantum advantage claim is credible?

Every few months a headline announces that a quantum computer has done something no classical computer can. Some of those headlines describe real, durable results. Others describe results that a classical algorithm matched within months — or, lately, within days. This post is a reader's tool: five questions, asked in a fixed order, that let a non-expert sort one from the other in about ten minutes. It is not a guide for designing benchmarks — we published that separately, for the classical rival and for the rest of the protocol. This is the ten-minute version, for reading a headline.

Why does reading a claim need a checklist at all?

Because the word "advantage" compresses several different levels of evidence into one syllable. A claim can be an unconditional theorem, a conditional asymptotic result, an empirical "we could not simulate this," or a projection — and headlines rarely say which (we mapped those levels here, and here is what is actually proven). Jens Eisert (Free University of Berlin) put the honest frame on it in the coverage of this July's claims: establishing quantum advantage is "an ongoing process of building confidence, not a binary threshold to cross" (via PostQuantum's fact-check, 2026). A process needs a reading protocol. The five questions below are ordered so that the cheapest, most decisive checks come first: each "no" exits the tree early with a precise, narrower statement of what the result actually is — not with an accusation.

What are the five questions, in order?

Question 1 — is the task useful, or synthetic? "Would anyone pay for this output if a classical computer produced it?" Google's 2019 Sycamore result sampled random circuits — a genuine physics milestone whose output nobody buys (Arute et al., Nature 574, 505, 2019). A "no" here does not shrink the science; it shrinks the transfer: the result says nothing yet about your portfolio, your molecule, or your route (supremacy vs. advantage).

Question 2 — did a strong classical rival run the same instance, with a matched budget and matched data access? The quantum machine learning claims of 2016–2018 did not fall to better hardware; they fell when Ewin Tang leveled the data-access model and the exponential gap collapsed (arXiv:1807.04271, 2018 — the dequantization story). A benchmark against a weak or mismatched rival moves the crossover by construction, not by physics (why a weak baseline ruins a benchmark).

Question 3 — are re-runnable artifacts published? Code, exact instance, seeds, compute budget. Every major reversal in the record ran on public artifacts (radical reproducibility); a claim without them cannot be attacked or confirmed — the evidence simply stops accumulating.

Question 4 — is the error controlled by a quantitative bound, or by a heuristic estimate? This is the question that separates the three July 2026 claims from each other (below). Dominik Hangleiter (ETH) stated the rule compactly: "seems hard to simulate classically" is not a proof (via PostQuantum, 2026).

Question 5 — how long has the claim survived the classical counterattack? The only question that re-answers itself over time. IBM's 2023 utility experiment was matched by tensor networks in months (Kim et al., Nature 618, 500, 2023; Tindall et al., PRX Quantum 5, 010308, 2024). D-Wave's March 2025 spin-glass result drew a laptop-scale tensor-network challenge within days as a preprint; the peer-reviewed version landed in Science on July 21, 2026, and D-Wave's rebuttal of May 26, 2026 keeps the dispute open (King et al., Science 388, 199, 2025; Tindall et al., Science 2026; D-Wave newsroom). And the strongest of this July's claims drew its first classical response in 14 days (next section).

How does the historical record score against the tree?

The point of the order is that the famous reversals would have exited early — a reader running the tree at publication time would have filed each claim correctly without waiting for the reversal.

What does the tree say about the three claims of July 30, 2026?

On July 30, 2026, IBM and three partners published three simultaneous advantage claims. All three are real, substantial work — and the tree files them in three different drawers, which is exactly what the single word "advantage" hides. PostQuantum's fact-check reached the same structural conclusion: the joint messaging "compresses those three different levels of evidence into one 'quantum advantage era' narrative."

IBM / U. Chicago doped Clifford sampling (arXiv:2607.25941): 70 logical qubits on 97 physical, an explicit advantage claim, and — the strongest Q4 answer of the three — a certified state-fidelity lower bound of 0.284 at 95% confidence. It is also the claim where Q5's clock is most visibly running: on August 13, 2026, Manabe, Gu and Pan computed all 2,051 amplitude batches classically in 37.3 minutes on 32 GPU nodes (arXiv:2608.13110). Read that carefully, tree in hand: the authors report their output is "numerically compatible with IBM's fidelity lower bound" — a diagnostic and a design tool, not a refutation. The dispute is now precisely about what the certified bound does and does not certify. That is Q4 and Q5 interacting in real time, 14 days after publication.

Qedma Floquet Ising (arXiv:2607.24937): up to 74 qubits on IBM Heron, cross-validated on Quantinuum trapped-ion hardware at 51 qubits — a matched-instance check across two architectures, which is good Q2 hygiene. The authors themselves scope the claim honestly: the tested classical methods diverged after ~7 cycles; they frame the result as making error-mitigated processors "quantitative scientific instruments," not as a formal advantage proof. The tree reads that scoping as a feature, not a hedge.

Algorithmiq operator Loschmidt echo (arXiv:2607.25998): 56 qubits, a framework for building trust in a regime with no classical ground truth. On Q4 it is, by its own statement, the weakest of the three: the mitigated estimate "lacks a quantitative bound on its distance from the unknown ground truth." That sentence — printed by the authors — is precisely the difference between an estimate and a measurement, and Hangleiter's rule applies as the authors would accept: hard-to-simulate is a status report, not a theorem. None of this is an accusation: each paper states its own caveats; the compression happens downstream, in headlines.

The community has also, in effect, institutionalized Question 5: the Quantum Advantage Tracker (launched November 2025; IBM, Quantinuum, Flatiron Institute, BlueQubit, Algorithmiq, Caltech and Los Alamos among the contributors) hosts 30+ submissions where quantum and classical methods answer each other in public — including at least one case (BlueQubit's peaked circuits) where quantum led and classical then overtook, which is the tree's expected dynamic, running at community speed (IBM Quantum blog, Feb 23, 2026). The tracker treats this July's results as active candidates, not adjudicated demonstrations.

Does the tree work on negative results too?

Yes — and that symmetry is the point. Our own sealed verdict V-0012 is a measured "not yet" in small-instance portfolio optimization: a useful task (Q1), the strongest available classical rival on the exact same instances with a matched budget — CP-SAT, provably optimal 20 of 20 runs (Q2), sealed artifacts with instances, seeds and budgets (Q3), quantified gaps — QAOA landed 25–48% from optimum (Q4), and the result stands unchallenged since publication (Q5). The quantum runs were simulated without noise, which favors the quantum side — declared in the seal. A negative that passes all five questions carries more information than a positive that exits at Question 1. Scope declared: this is one small class of optimization; it is not a universal verdict, and we claim none (the scoreboard of proven advantage remains at zero for useful end-to-end tasks).

What we know / what we don't know

We know: the five exits are calibrated on documented, sourced reversals from 2016–2026, and each historical claim in the table exits where its own record says it exited. The three July 2026 claims are open — neither validated nor refuted — and each carries its own printed caveat. The first classical response to the doped Clifford experiment is compatible-with-the-bound, not a refutation. No claim on a useful task has yet survived the full tree end-to-end (details).

We don't know: whether any of the three July claims stands in twelve months — 26 days without refutation is evidence, not proof. Whether "numerically compatible with the bound" hardens into a full classical match of the sampling task, or stops at diagnostics. Whether Question 5's historical half-life (months) is stable now that classical counterattack tooling is industrializing — the tracker may be shortening it. The tree is calibrated on famous cases, not on a random sample of claims: survivorship and attention bias are built into the calibration, and we cannot quantify them. And our own negative has not been independently re-run by a third party — the artifacts are published precisely so that it can be.

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